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version 1.2, 2004/01/29 09:38:50

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<TEI.2

><teiHeader status="new" type="text"><fileDesc

><titleStmt

<TEI.2>

><title

>A Mathematical and Philosophical Dictionary</title><author

<fileDesc><titleStmt><title>A Mathematical and Philosophical Dictionary</title><author>Charles Hutton</author></titleStmt>

>Charles Hutton</author></titleStmt>

Berlin: Max-Planck-Institut für Wissenschaftsgeschichte, 2000

</publicationStmt><sourceDesc

</publicationStmt><sourceDesc default="no"> London, 1796.

default="no"

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> <p

>London, 1796.

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doctype="tei.2"

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<language id="la">Latin

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<language id="greek">Greek

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>English

<text>

</language><language

<front>

id="la"

<pb/>

>Latin

</language><language

id="greek"

<titlePart rend="center" type="main">A

>Greek

MATHEMATICAL <hi rend="smallcaps">AND</hi> PHILOSOPHICAL

</language></langUsage></profileDesc></teiHeader><text

DICTIONARY:</titlePart>

><front

<titlePart rend="center" type="main">CONTAINING

><pb

<hi rend="italics">AN EXPLANATION OF THE TERMS, AND AN ACCOUNT OF THE SEVERAL SUBJECTS,</hi></titlePart>

/><titlePage

<titlePart rend="center" type="main">COMPRIZED UNDER THE HEADS

><docTitle

MATHEMATICS, ASTRONOMY, <hi rend="smallcaps">AND</hi> PHILOSOPHY

><titlePart

rend="center"

type="main"

MATHEMATICAL <hi

rend="smallcaps"

>AND</hi> PHILOSOPHICAL

DICTIONARY:</titlePart><titlePart

rend="center"

type="main"

>CONTAINING

<hi

rend="italics"

>AN EXPLANATION OF THE TERMS, AND AN ACCOUNT OF THE SEVERAL SUBJECTS,</hi></titlePart><titlePart

rend="center"

type="main"

>COMPRIZED UNDER THE HEADS

MATHEMATICS, ASTRONOMY, <hi

rend="smallcaps"

>AND</hi> PHILOSOPHY

BOTH NATURAL AND EXPERIMENTAL:

WITH AN

HISTORICAL ACCOUNT OF THE RISE, PROGRESS, AND PRESENT STATE OF THESE SCIENCES:

ALSO

MEMOIRS OF THE LIVES AND WRITINGS OF THE MOST EMINENT AUTHORS,

BOTH ANCIENT AND MODERN,

<hi

<hi rend="italics">WHO BY THEIR DISCOVERIES OR IMPROVEMENTS HAVE CONTRIBUTED TO THE ADVANCEMENT OF THEM.</hi>

rend="italics"

>WHO BY THEIR DISCOVERIES OR IMPROVEMENTS HAVE CONTRIBUTED TO THE ADVANCEMENT OF THEM.</hi>

IN TWO VOLUMES.

WITH MANY CUTS AND COPPER-PLATES.</titlePart></docTitle><byline

WITH MANY CUTS AND COPPER-PLATES.</titlePart>

rend="center"

</docTitle>

><hi

<byline rend="center"><hi rend="smallcaps">By</hi> <docAuthor>CHARLES HUTTON</docAuthor>, LL.D.

rend="smallcaps"

>By</hi> <docAuthor

>CHARLES HUTTON</docAuthor>, LL.D.

F. R. SS. OF LONDON AND EDINBURGH, AND OF THE PHILOSOPHICAL SOCIETIES OF HAARLEM AND AMERICA;

AND PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY, WOOLWICK.</byline><docTitle

AND PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY, WOOLWICK.</byline>

><titlePart

rend="center"

type="main"

</docTitle>

>VOL. I.</titlePart></docTitle><docImprint

<docImprint rend="center"><pubPlace rend="italics">LONDON:</pubPlace>

rend="center"

><pubPlace

rend="italics"

>LONDON:</pubPlace>

PRINTED BY J. DAVIS,

FOR J. JOHNSON, IN ST. PAUL'S CHURCH-YARD; AND G. G. AND J. ROBINSON,

IN PATERNOSTER-ROW.

<docDate

>M.DCC.XCVI.</docDate></docImprint></titlePage><div1

</titlePage>

part="n"

<div1 part="n" org="uniform" sample="complete" type="preface"><pb/><pb/><head>PREFACE.</head>AMONG the Dictionaries of Arts and Sciences which have been published, of late

org="uniform"

sample="complete"

type="preface"

><pb/><pb

/><head

>PREFACE.</head><p

>AMONG the Dictionaries of Arts and Sciences which have been published, of late

years, in various parts of Europe, it is matter of surprise that Philosophy and Mathematics

should have been so far overlooked as not to be thought worthy of a separate

Treatise, in this form. These Sciences constitute a large portion of the present stock

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to which few others are entitled; and yet we have hitherto had no distinct

Lexicon, in which their constituent parts and technical terms have been explained, with

that amplitude and precision, which the great improvements of the Moderns, as well as

the rising dignity of the Subject, seem to demand.<p

the rising dignity of the Subject, seem to demand.<hi rend="smallcaps">The</hi> only works of this kind in the English language, deserving of notice, are Harris's

><hi

rend="smallcaps"

>The</hi> only works of this kind in the English language, deserving of notice, are Harris's

Lexicon Technicum, and Stone's Mathematical Dictionary; the former of which,

though a valuable performance at the time it was written, is now become too dry and

obsolete to be referred to with pleasure or satisfaction: and the latter, consisting only

of one volume in 8vo, must be regarded merely as an unfinished sketch, or brief

compendium, extremely limited in its plan, and necessarily desieient in useful in

formation.<p

formation.<hi rend="smallcaps">It</hi> became, therefore, the only resource of the Reader, in many cases where explanation

><hi

rend="smallcaps"

>It</hi> became, therefore, the only resource of the Reader, in many cases where explanation

was wanted, to have recourse to Chambers's Dictionary, in four large Volumes folio,

or to the Encyclopædia Britannica, now in eighteen large volumes 4to, or the still more,

stupendous performance of the French Encyclopedists; and even here his expectations

might be frequently disappointed. These great and useful works, aiming at a

general comprehension of the whole circle of the Sciences, are sometimes very delicient

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considerable length in the First Volume, under the head of that Article, will afford

sufficient evidence to shew in what a superficial and partial way the inquiry has been

hitherto investigated, even by professed writers on the subject; the principal of whom

are M. Montucla, our countryman the celebrated Dr. Wallis, and the Abbé De Gua,

a late French author, who has pretended to correct the Doctor's errors and misrepresen-

tations.

<hi rend="smallcaps">REGULAR</hi> historical details are in like manner given of the origin and progress of

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such useful improvements in the sciences as may have been overlooked in this Dictionary,

or any articles that may here have been imperfectly or incorrectly treated; that

he may at some future time, by adding them to this work, render it still more complete

and deserving the public notice.<p

and deserving the public notice.<hi rend="smallcaps">As</hi> this work is an attempt to separate the words in the sciences of Astronomy, Mathematics,

><hi

rend="smallcaps"

>As</hi> this work is an attempt to separate the words in the sciences of Astronomy, Mathematics,

and Philosophy, from those of other arts or sciences, in several of which there

are already separate Dictionaries; as in Chemistry, Geography, Music, Marine and

Naval affairs, &c; words sometimes occurred which it was rather doubtful whether

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although some few words may inadvertently have been omitted; yet when the Reader

does not immediately find every word which he wishes to consult, he will not always

consider them as omissions of the Author, but for the most part as relating to some other

science foreign to this Dictionary.<p

science foreign to this Dictionary.<hi rend="smallcaps">In</hi> all cases where it could be conveniently done, the necessary figures and diagrams

><hi

rend="smallcaps"

>In</hi> all cases where it could be conveniently done, the necessary figures and diagrams

are inserted in the same page with the subjects which they are designed to

elucidate; a method which will be found much more commodious than that of

putting them in separate plates at the end of each volume, but, which has added

very considerably to the expence of the undertaking: where the subjects are of

such a nature that they could not be otherwise well represented, they are engraved on

Copperplates.<p

Copperplates.<hi rend="smallcaps">As</hi> the whole of this work was written before it was put to the press, the Reader

><hi

rend="smallcaps"

>As</hi> the whole of this work was written before it was put to the press, the Reader

will find it of an equal and uniform nature and construction throughout; in

which respect many publications of this kind are very defective, from the subjects

being diffusely treated under the first letters of the alphabet, while articles

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stances, will be found in most cases equally instructive and useful, and may be

consulted with no less advantage by the Man of Science than the Student.

</div1></front><body><pb/>

</div1>

</front>

<!-- <C>A

PHILOSOPHICAL and MATHEMATICAL

DICTIONARY.</C> -->

<div0

<div0 part="n" n="A" org="uniform" sample="complete" type="alphabetic letter"><head>A</head><cb/><div1 part="n" n="ABACIST" org="uniform" sample="complete" type="entry"><head>ABACIST</head>, an Arithmetician. In this sense we

part="n"

n="A"

org="uniform"

sample="complete"

type="alphabetic letter"

><head

>A</head><cb

/><div1

part="n"

n="ABACIST"

org="uniform"

sample="complete"

type="entry"

><head

>ABACIST</head><p

>, an Arithmetician. In this sense we

find the word used by William of Malmesbury,

in his History <hi

in his History <hi rend="italics">de Gestis Anglorum,</hi> written about the

rend="italics"

>de Gestis Anglorum,</hi> written about the

year 1150; where he shews that one Gerbert, a learned

monk of France, who was afterwards made pope of

Rome in the year 998 or 999, by the name of Silvester

the 2d, was the first who got from the Saracens the

abacus, and that he taught such rules concerning it, as

the Abacists themselves could hardly understand.</div1><div1

the Abacists themselves could hardly understand.</div1><div1 part="n" n="ABACUS" org="uniform" sample="complete" type="entry"><head>ABACUS</head>, <hi rend="italics">in Arithmetic,</hi> an ancient instrument used

part="n"

n="ABACUS"

org="uniform"

sample="complete"

type="entry"

><head

>ABACUS</head><p

>, <hi

rend="italics"

>in Arithmetic,</hi> an ancient instrument used

by most nations for casting up accounts, or performing

arithmetical calculations: it is by some derived from the

Greek <foreign

Greek <foreign lang="greek">a<*>ac</foreign>, which signifies a cupboard or beaufet, perhaps

lang="greek"

>a<*>ac</foreign>, which signifies a cupboard or beaufet, perhaps

from the similarity of the form of this instrument;

and by others it is derived from the Phœnician <hi

and by others it is derived from the Phœnician <hi rend="italics">abak,</hi>

rend="italics"

>abak,</hi>

which signifies dust or powder, because it was said that

this instrument was sometimes made of a square board

or tablet, which was powdered over with fine sand or dust,

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in the sirst part of his second distinction, thinks it

is a corruption of Arabicus, by which he meant their

Algorism, or the method of numeral computation received

from them.<p

from them.We find this instrument for computation in use, under

>We find this instrument for computation in use, under

some variations, with most nations, as the Greeks, Romans,

Germans, French, Chinese, &c.<p

Germans, French, Chinese, &c.The Grecian abacus was an oblong frame, over

>The Grecian abacus was an oblong frame, over

which were stretched several brass wires, strung with

little ivory balls, like the beads of a necklace; by the

various arrangements of which all kinds of computa-

<cb

<cb/>

tions were easily made. Mahudel, in Hist. Acad. R.

Inscr. t. 3. p. 390.<p

Inscr. t. 3. p. 390.The Roman Abacus was a little varied from the Grecian,

>The Roman Abacus was a little varied from the Grecian,

having pins sliding in grooves, instead of strings or

wires and beads. Philos. Trans. No. 180.<p

wires and beads. Philos. Trans. No. 180.The Chinese Abacus, or Shwan-pan, like the Grecian,

>The Chinese Abacus, or Shwan-pan, like the Grecian,

consists of several series of beads strung on brass

wires, stretched from the top to the bottom of the instrument,

and divided in the middle by a cross piece

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two beads, which are each counted for 5; and in the

lower space every string has five beads, of different

values, the first being counted as 1, the second as 10,

the third as 100, and so on, as with us. See S<hi

the third as 100, and so on, as with us. See S<hi rend="smallcaps">HWANPAN.</hi>The Abacus chiefly used in European countries, is

rend="smallcaps"

>HWANPAN.</hi><p

>The Abacus chiefly used in European countries, is

nearly upon the same principles, though the use of it is

here more limited, because of the arbitrary and unequal

divisions of money, weights, and measures, which, in

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like manner a counter placed in the first space, between

the first and second line, denotes 5, in the second space

50, in the third space 500, in the fourth space 5000,

<pb

n="2"

/><cb

and so on. So that there are never more than four

counters placed on any line, nor more than one placed

in any space, this being of the same value as five counters

on the next line below. So the counters on the

Abacus, in the figure here below, express the number

or sum 47382.

<figure

<figure/>Besides the above instruments of computation, there

></figure><p

>Besides the above instruments of computation, there

have been several others invented by different persons;

as <hi

as <hi rend="italics">Napier's rods</hi> or <hi rend="italics">bones,</hi> deseribed in his Rabdologia,

rend="italics"

which see under the word <hi rend="smallcaps">Napier;</hi> also the <hi rend="italics">Abacus

>Napier's rods</hi> or <hi

rend="italics"

>bones,</hi> deseribed in his Rabdologia,

which see under the word <hi

rend="smallcaps"

>Napier;</hi> also the <hi

rend="italics"

>Abacus

Rhabdologicus,</hi> a variation of Napier's, which is described

in the first vol. of <hi

in the first vol. of <hi rend="italics">Machines et Inventions approuvées

rend="italics"

>Machines et Inventions approuvées

par l'Academie Royale des Sciences.</hi> An ingenious

and general one was also invented by Mr. Gamaliel

Smethurst, and is described in the Philosophical

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Saunderson, by which he performed very intricate

calculations: an account of it is prefixed to the

first volume of his Algebra, and it is there by the editor

called <hi

called <hi rend="italics">Palpable Arithmetic:</hi> which see.<div2 part="n" n="Abacus" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Abacus</hi></head>, <hi rend="italics">Pythagorean,</hi> so denominated from its inventor,

rend="italics"

>Palpable Arithmetic:</hi> which see.<div2

part="n"

n="Abacus"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Abacus</hi></head><p

>, <hi

rend="italics"

>Pythagorean,</hi> so denominated from its inventor,

Pythagoras; a table of numbers, contrived for

readily learning the principles of arithmetic; and was

probably what we now call the multiplication-table.</div2><div2

probably what we now call the multiplication-table.</div2><div2 part="n" n="Abacus" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Abacus</hi></head>, or <hi rend="smallcaps">Abaciscus</hi>, in <hi rend="italics">Architecture,</hi> the upper

part="n"

n="Abacus"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Abacus</hi></head><p

>, or <hi

rend="smallcaps"

>Abaciscus</hi>, in <hi

rend="italics"

>Architecture,</hi> the upper

part or member of the capital of a column; serving as

a crowning both to the capital and to the whole column.

Vitruvius informs us that the <hi

Vitruvius informs us that the <hi rend="italics">Abacus</hi> was originally

rend="italics"

>Abacus</hi> was originally

intended to represent a square flat tile laid over

an urn, or a basket; and the invention is ascribed to

Calimachus, an ingenious statuary of Athens, who, it is

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executed a capital on this plan; representing the tile by

the Abacus, the leaves of the acanthus by the volutes or

scrolls, and the basket by the vase or body of the capital.

See <hi

See <hi rend="smallcaps">Acanthus.</hi><hi rend="italics">Abacus</hi> is also used by Scamozzi for a concave moulding

rend="smallcaps"

>Acanthus.</hi><p

><hi

rend="italics"

>Abacus</hi> is also used by Scamozzi for a concave moulding

in the capital of the Tuscan pedestal. And the

word is used by Palladio for other members which he

describes. Also, in the ancient architecture, the same

term is used to denote certain compartments in the incrustation

or lining of the walls of state-rooms, mosaicpavements,

and the like. There were <hi

and the like. There were <hi rend="italics">Abaci</hi> of marble,

rend="italics"

<cb/>

>Abaci</hi> of marble,

<cb

porphyry, jasper, alabaster, and even glass; variously

shaped, as square, triangular, and such-like.<p

shaped, as square, triangular, and such-like.<hi rend="smallcaps">Abacus</hi> <hi rend="italics">Logisticus</hi> is a right angled triangle, whose

><hi

rend="smallcaps"

>Abacus</hi> <hi

rend="italics"

>Logisticus</hi> is a right angled triangle, whose

sides, about the right angle, contain all the numbers

from 1 to 60; and its area the products of each two of

the opposite numbers. This is also called a <hi

the opposite numbers. This is also called a <hi rend="italics">canon of

rend="italics"

>canon of

sexagesimals,</hi> and is no other than a multiplication-table

carried to 60 both ways.<p

carried to 60 both ways.<hi rend="smallcaps">Abacus</hi> <hi rend="italics">& Palmulæ,</hi> in the Ancient Music, denote

><hi

rend="smallcaps"

>Abacus</hi> <hi

rend="italics"

>& Palmulæ,</hi> in the Ancient Music, denote

the machinery by which the strings of the polyplectra,

or instruments of many strings, were struck, with a

plectrum made of quills.<p

plectrum made of quills.<hi rend="smallcaps">Abacus</hi> <hi rend="italics">Harmonicus</hi> is used by Kircher for the structure

><hi

rend="smallcaps"

>Abacus</hi> <hi

rend="italics"

>Harmonicus</hi> is used by Kircher for the structure

and disposition of the keys of a musical instrument,

either to be touched with the hands or feet.</div2><div2

either to be touched with the hands or feet.</div2><div2 part="n" n="Abacus" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Abacus</hi>, in <hi rend="italics">Geometry</hi></head>, a table or slate upon which

part="n"

schemes or diagrams are drawn.</div2></div1><div1 part="n" n="ABAS" org="uniform" sample="complete" type="entry"><head>ABAS</head>, a weight used in Persia for weighing pearls;

n="Abacus"

and is an eighth part lighter than the European carat.</div1><div1 part="n" n="ABASSI" org="uniform" sample="complete" type="entry"><head>ABASSI</head>, a silver coin current in Perlia, deriving

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Abacus</hi>, in <hi

rend="italics"

>Geometry</hi></head><p

>, a table or slate upon which

schemes or diagrams are drawn.</div2></div1><div1

part="n"

n="ABAS"

org="uniform"

sample="complete"

type="entry"

><head

>ABAS</head><p

>, a weight used in Persia for weighing pearls;

and is an eighth part lighter than the European carat.</div1><div1

part="n"

n="ABASSI"

org="uniform"

sample="complete"

type="entry"

><head

>ABASSI</head><p

>, a silver coin current in Perlia, deriving

its name from Schaw Abbas II. King of Persia, and is

worth near eighteen pence English money.</div1><div1

worth near eighteen pence English money.</div1><div1 part="n" n="ABATIS" org="uniform" sample="complete" type="entry"><head>ABATIS</head>, or <hi rend="smallcaps">Abattis</hi>, from the French <hi rend="italics">abattre,</hi> to

part="n"

n="ABATIS"

org="uniform"

sample="complete"

type="entry"

><head

>ABATIS</head><p

>, or <hi

rend="smallcaps"

>Abattis</hi>, from the French <hi

rend="italics"

>abattre,</hi> to

throw down, or beat down, in the Military Art, denotes

a kind of retrenchment made by a quantity of whole

trees cut down, and laid lengthways beside each other,

Line 525

Line 320

occasions, especially on sudden emergencies, when trees

are near at hand; and has always been practised with

considerable success, by the ablest commanders in all

ages and nations.<p

ages and nations.ABBREVIATE; to abbreviate fractions in arithmetic

>ABBREVIATE; to abbreviate fractions in arithmetic

and algebra, is to lessen proportionally their terms,

or the numerator and denominator; which is performed

by dividing those terms by any number or quantity,

which will divide them without leaving a remainder.

And when the terms cannot be any farther so divided,

the fraction is said to be in its least terms.<p

the fraction is said to be in its least terms.So ,

>So ,

by dividing the terms continually by 2.And ,

by dividing the terms continually by 2.<p

by dividing by 2, 3, and 7.Also ,

>And ,

by dividing by 3 and by 2.And , by dividing by 4 <hi rend="sup"><hi rend="italics">ax.</hi></hi>And , by dividing by <hi rend="italics">a</hi>+<hi rend="italics">x.</hi></div1><div1 part="n" n="ABBREVIATION" org="uniform" sample="complete" type="entry"><head>ABBREVIATION</head>, of fractions, in Arithmetic

by dividing by 2, 3, and 7.<p

and Algebra, the reducing them to lower terms.</div1><div1 part="n" n="ABERRATION" org="uniform" sample="complete" type="entry"><head>ABERRATION</head>, in <hi rend="italics">Astronomy,</hi> an apparent motion

>Also ,

by dividing by 3 and by 2.<p

>And , by dividing by 4 <hi

rend="sup"

><hi

rend="italics"

>ax.</hi></hi><p

>And , by dividing by <hi

rend="italics"

>a</hi>+<hi

rend="italics"

>x.</hi></div1><div1

part="n"

n="ABBREVIATION"

org="uniform"

sample="complete"

type="entry"

><head

>ABBREVIATION</head><p

>, of fractions, in Arithmetic

and Algebra, the reducing them to lower terms.</div1><div1

part="n"

n="ABERRATION"

org="uniform"

sample="complete"

type="entry"

><head

>ABERRATION</head><p

>, in <hi

rend="italics"

>Astronomy,</hi> an apparent motion

of the celestial bodies, occasioned by the progressive

motion of light, and the earth's annual motion

in her orbit.<p

in her orbit.This effect may be explained and familiarized by the

>This effect may be explained and familiarized by the

<pb

n="3"

/><cb

motion of a line parallel to itself, much after the manner

that the composition and resolution of forces are explained.

If light have a progressive motion, let the

<figure

></figure>

proportion of its velocity to that

of the earth in her orbit, be as

the line BC to the line AC;

Line 596

Line 354

an observer along the line AC,

in the time that a particle of light

would move over the space BC,

the different places of the tube being AB, <hi

the different places of the tube being AB, <hi rend="italics">ab, cd,</hi> CD;

rend="italics"

>ab, cd,</hi> CD;

and when the eye, or end of the tube, is at A, let a

particle of light enter the other end at B; then when

the tube is at <hi

the tube is at <hi rend="italics">ab,</hi> the particle of light will be at <hi rend="italics">e,</hi> exactly

rend="italics"

in the axis of the tube; and when the tube is at <hi rend="italics">cd,</hi> the

>ab,</hi> the particle of light will be at <hi

particle of light will arrive at <hi rend="italics">f,</hi> still in the axis of the

rend="italics"

>e,</hi> exactly

in the axis of the tube; and when the tube is at <hi

rend="italics"

>cd,</hi> the

particle of light will arrive at <hi

rend="italics"

>f,</hi> still in the axis of the

tube; and lastly, when the tube arrives at CD, the particle

of light will arrive at the eye or point C, and consequently

will appear to come in the direction DC of

Line 621

Line 369

DC. So that the apparent angle made by the ray of

light with the line AE, is the angle DCE, instead of

the true angle BCE; and the difference, BCD or

ABC, is the quantity of the aberration.<p

ABC, is the quantity of the aberration.M. de Maupertuis, in his Elements of Geography,

>M. de Maupertuis, in his Elements of Geography,

gives also a familiar and ingenious idea of the aberration,

in this manner: “It is thus,” says he, “concerning

the direction in which a gun must be pointed

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Line 381

matter, the flight of the bird represents the motion of

the earth, or the line AC, in our scheme above, and

the flight of the shot represents the motion of the ray

of light, or the line BC.<p

of light, or the line BC.Mr. Clairaut too, in the Memoires of the Academy of

>Mr. Clairaut too, in the Memoires of the Academy of

Sciences for the year 1746, illustrates this effect in a

familiar way, by supposing drops of rain to fall rapidly

and quickly after each other from a cloud, under which

Line 647

Line 393

according to the velocity of the drops in respect to that

of the tube: then the angle made by the direction of

the tube and of the falling drops, is the aberration arising

from the combination of those two motions.<p

from the combination of those two motions.This discovery, which is one of the brightest that have

>This discovery, which is one of the brightest that have

been made in the present age, we owe to the accuracy

and ingenuity of the late Dr. Bradley, Astronomer

Royal; to which he was occasionally led by the result

<cb

<cb/>

of some accurate observations which he had made with

another view, namely, to determine the annual parallax

of the fixed stars, or that which arises from the motion

of the earth in its annual orbit about the sun.<p

of the earth in its annual orbit about the sun.The annual motion of the earth about the sun had

>The annual motion of the earth about the sun had

been much doubted, and warmly contested. The defenders

of that motion, among other proofs of the reality

of it, conceived the idea of adducing an incontestable

Line 674

Line 417

from their observations; and from thence they concluded

that the earth did not move round the sun, and that

there was no annual parallax in the fixed stars. M. Picard,

in the account of his <hi

in the account of his <hi rend="italics">Voyage d'Uranibourg,</hi> made

rend="italics"

>Voyage d'Uranibourg,</hi> made

in 1672, says that the pole star, at different times of

the year, has certain variations which he had observed

for about 10 years, and which amounted to about 40″

Line 686

Line 427

orbit. But it was impossible to explain it by that parallax;

because this motion was in a manner contrary to

what ought to follow only from the motion of the earth

in her orbit.<p

in her orbit.In 1674 Dr. Hook published an account of observations

>In 1674 Dr. Hook published an account of observations

which he said he had made in 1669, and by

which he had found that the star <foreign

which he had found that the star <foreign lang="greek">g</foreign> Draconis was 23

lang="greek"

>g</foreign> Draconis was 23

more northerly in July than in October: observations

which, for the present, seemed to favour the opinion of

the earth's motion, although it be now known that

there could not be any truth or accuracy in them.<p

there could not be any truth or accuracy in them.Flamsteed having observed the pole star with his

>Flamsteed having observed the pole star with his

mural quadrant, in 1689 and the following years, found

that its declination was 40″ less in July than in December;

which observations, although very just, were

Line 704

Line 441

and he recommended the making of an instrument of

15 or 20 feet radius, to be firmly fixed on a strong

foundation, for deciding a doubt which was otherwise

not soon likely to be brought to a conclusion.<p

not soon likely to be brought to a conclusion.In this state of uncertainty and doubt, then, Dr.

>In this state of uncertainty and doubt, then, Dr.

Bradley, in conjunction with Mr. Samuel Molineux,

in the year 1725, formed the project of verifying, by

a series of new observations, those which Dr. Hook

Line 721

Line 457

owing to the accuracy of the ingenious Mr. George

Graham, to whom the lovers of astronomy are also indebted

for several other exact and convenient instruments.

<pb

<pb n="4"/><cb/>The success then of the intended experiment, evidently

n="4"

/><cb

/><p

>The success then of the intended experiment, evidently

depending very much on the accuracy of the instrument,

that leading object was first to be well secured.

Mr. Molineux's apparatus then having been

completed, and fitted for observing, about the end of

November 1725, on the third day of December following,

the bright star in the head of Draco, marked <foreign

the bright star in the head of Draco, marked <foreign lang="greek">g</foreign> by

lang="greek"

>g</foreign> by

Bayer, was for the first time observed, as it passed near

the zenith, and its situation carefully taken with the instrument.

The like observations were made on the

Line 782

Line 512

back again towards the north; and about the

beginning of June, it passed at the same distance from

the zenith, as it had done in December, when it was

first observed.<p

first observed.From the quick alteration in the declination of the

>From the quick alteration in the declination of the

star about this time, increasing about one second in

three days, it was conjectured that it would now proceed

northward, as it had before gone southward, of its

Line 791

Line 520

the star continued to move northward till September

following, when it became stationary again; being then

near 20″ more northerly than in June, and upwards of

<cb

<cb/>

39″ more northerly than it had been in March. From

September the star again returned towards the south,

till, in December, it arrived at the same situation in

which it had been observed twelve months before, allowing

for the difference of declination on account of the

precession of the equinox.<p

precession of the equinox.This was a sufficient proof that the instrument had

>This was a sufficient proof that the instrument had

not been the cause of this apparent motion of the star;

and yet it seemed difficult to devise one that should be

adequate to such an unusual effect. A nutation of the

earth's axis was one of the first things that offered itself

on this occasion; but it was soon found to be insufficient;

for though it might have accounted for the

change of declination in <foreign

change of declination in <foreign lang="greek">g</foreign> Draconis, yet it would not

lang="greek"

>g</foreign> Draconis, yet it would not

at the same time accord with the phenomena observed

in the other stars, particularly in a small one almost opposite

in right ascension to <foreign

in right ascension to <foreign lang="greek">g</foreign> Draconis; and at about

lang="greek"

>g</foreign> Draconis; and at about

the same distance from the north pole of the equator:

for though this star seemed to move the same way, as a

nutation of the earth's axis would have made it; yet

changing its declination but about half as much as <foreign

changing its declination but about half as much as <foreign lang="greek">g</foreign>

lang="greek"

>g</foreign>

Draconis in the same time, as a peared on comparing

the observations of both made on the same days, at different

seasons of the year, this plainly proved that the

apparent motion of the star was not occasioned by a

real nutation; since, had that been the case, the alteration

in both stars would have been nearly equal.<p

in both stars would have been nearly equal.The great regularity of the observations left no room

>The great regularity of the observations left no room

to doubt, but that there was some uniform cause by

which this unexpected motion was produced, and which

did not depend on the uncertainty or variety of the

seasons of the year. Upon comparing the observations

with each other, it was discovered that, in both the

stars above mentioned, the apparent difference of declination

from the <hi

from the <hi rend="italics">maxima,</hi> was always nearly proportional

rend="italics"

>maxima,</hi> was always nearly proportional

to the versed sine of the sun's distance from the equinoctial

points. This was an inducement to think that

the cause, whatever it was, had some relation to the

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Line 572

of trying in what manner other stars should be affected

by the same cause, whatever it might be. For Mr. Molineux's

instrument being originally designed for observing

<foreign

<foreign lang="greek">g</foreign> Draconis, to try whether it had any sensible parallax, it

lang="greek"

>g</foreign> Draconis, to try whether it had any sensible parallax, it

was so contrived, as to be capable of but little alteration

in its direction; not above seven or eight minutes of a

degree: and there being but few stars, within half that

Line 864

Line 580

well observed, he could not, with his instrument, thoroughly

examine how this cause affected stars that were

differently situated, with respect to the equinoctial and

solsticial points of the ecliptic.<p

solsticial points of the ecliptic.These considerations determined him; and by the

>These considerations determined him; and by the

contrivance and direction of the same ingenious person,

<pb

n="5"

/><cb

Mr. Graham, his instrument was fixed up the 19th of

August 1727. As he had no convenient place where

he could make use of so long a telescope as Mr. Molineux's,

Line 894

Line 606

and situation; there being more than two hundred, inserted

in the British Catalogue, that might be observed

with it. He needed not indeed to have extended the

limb so far, but that he was willing to take in <hi

limb so far, but that he was willing to take in <hi rend="italics">Capella,</hi>

rend="italics"

>Capella,</hi>

the only star of the first magnitude that came so near his

zenith.<p

zenith.His instrument being fixed, he immediately began to

>His instrument being fixed, he immediately began to

observe such stars as he judged most proper to give him

any light into the cause of the motion already mentioned.

There was a sufficient variety of small ones,

Line 925

Line 634

northward when in the night; so that each of them

was farthest north, when it came in the evening about

six of the clock, and farthest south when it came about

six in the morning.<p

six in the morning.Though he afterwards discovered that the maxima,

>Though he afterwards discovered that the maxima,

in most of these stars, do not happen exactly when they

pass at those hours; yet, not being able at that time to

prove the contrary, and supposing that they did, he endeavoured

Line 935

Line 643

other; it being very evident that they did not all change

their declination equally. It has been before noticed,

that it appeared from Mr. Molineux's observations, that

<foreign

<foreign lang="greek">g</foreign> <hi rend="italics">Draconis</hi> changed its declination above twice as much

lang="greek"

>g</foreign> <hi

rend="italics"

>Draconis</hi> changed its declination above twice as much

as the before-mentioned small star that was nearly op-

<cb

<cb/>

posite to it; but examining the matter more nicely, he

found that the greatest change in the declination of

these stars, was as the sine of the latitude of each star

respectively. This led him to suspect that there might

be the like proportion between the <hi

be the like proportion between the <hi rend="italics">maxima</hi> of other

rend="italics"

>maxima</hi> of other

stars; but finding that the observations of some of them

would not perfectly correspond with such an hypothesis,

and not knowing whether the small difference he met

Line 961

Line 662

what errors the observations might be liable to,

or how far they might safely be depended on; but also

to judge, whether there had been any sensible change in

the parts of the instrument itself.<p

the parts of the instrument itself.When the year was completed, he began to examine

>When the year was completed, he began to examine

and compare his observations; and having pretty well

satisfied himself as to the general laws of the phenomena,

he then endeavoured to sind out the cause of

Line 983

Line 683

but that of the line passing through the object and

the eye; and that when the eye is moving in different

directions, the apparent place of the object would be

different.<p

different.He considered this matter in the following manner.

>He considered this matter in the following manner.

He imagined CA to be a ray of

<figure

></figure>

light, falling perpendicularly upon the

line BD: then, if the eye be at rest at

A, the object must appear in the direction

Line 1011

Line 709

arrives at A, would pass through the tube BC, so inclined

to the line BD, and accompanying the eye in

its motion from B to A; and that it would not come

<pb

n="6"

/><cb

to the eye, placed behind such a tube, if it had any

other inclination to the line BD. If, instead of supposing

BC so small a tube, we conceive it to be the

axis of a larger; then, for the same reason, the particle

of light at C cannot pass through that axis, unless it be

inclined to BD in the same angle DBC.<p

inclined to BD in the same angle DBC.In the like manner, if the eye move the contrary

>In the like manner, if the eye move the contrary

way, from D towards A, with the same velocity; then

the tube must be inclined in the angle BDC. Although

therefore the true or real place of an object, be perpendicular

to the line in which the eye is moving, yet the

visible place will not be so; since that must doubtless

be in the direction of the tube. But the difference between

the true and apparent place, will be, <hi

the true and apparent place, will be, <hi rend="italics">cæteris paribus,</hi>

rend="italics"

>cæteris paribus,</hi>

greater or less, according to the different proportions

between the velocity of light and that of the

eye: so that if we could suppose light to be propagated

Line 1048

Line 740

of the difference between the true and visible place of

the object, will be to the sine of the visible inclination

of the object to the line in which the eye is moving, as

the velocity of the eye, is to the velocity of light.<p

the velocity of the eye, is to the velocity of light.If light moved only 1000 times faster than the eye,

>If light moved only 1000 times faster than the eye,

and an object, supposed to be at an infinite distance,

were really placed perpendicularly over the plane in

which the eye is moving; it follows, from what has

been saíd, that the apparent place of such object will

always be inclined to that plane, in an angle of 89°

56′ 1/2; so that it will constantly appear 3′ 1/2 from its true

place, and will seem so much less inclined to the plane,

that way towards which the eye tends. That is, if

AC be to AB or AD, as 1000 to 1, the angle

ABC will be 89° 56′ 1/2, and the angle ACB 3′ 1/2, and

BCD or 2ACB will be 7′, if the direction of the motion

of the eye be contrary at one time to what it is at

another.<p

another.If the earth revolve about the sun annually, and the

>If the earth revolve about the sun annually, and the

velocity of light were to the velocity of the earth's motion

in its orbit, as 1000 is to 1; then it is easy to

conceive, that a star really placed in the pole of the

Line 1080

Line 770

and its apparent distance from the north pole of the

equator, would be 7′ less at the autumnal, than at the

vernal equinox.

<cb

<cb/>The greatest alteration of the place of a star, in the

/><p

>The greatest alteration of the place of a star, in the

pole of the ecliptic, or, which in effect amounts to the

same, the proportion between the velocity of light and

the earth's motion in its orbit, being known, it will

Line 1091

Line 779

any other star at any time; and, on the contrary, the

difference between the true and apparent place being

given, the proportion between the velocity of light, and

the earth's motion in her orbit, may be found.<p

the earth's motion in her orbit, may be found.After the history of this curious discovery, related

>After the history of this curious discovery, related

by the author nearly in the terms above, he gives the

results of a multitude of accurate observations, made on

a great number of stars, at all seasons of the year.

Line 1107

Line 794

the star's latitude; that is, radius is to the sine of the

star's latitude, as the transverse axis to the conjugate

axis: and consequently a star in the pole of the ecliptic,

its latitude being there 90°, whose sine is equal to the

radius, will appear to describe a small circle about that

pole as a centre, whose radius is equal to 20″. He

also gives the following law of the variation of the

Line 1127

Line 814

difference of declination that can be between the true

and apparent place of the star, will be to 20″, the

semitransverse axis of the ellipse, as the sine of A to the

sine of B.<p

sine of B.The author then shews, by the comparison of a number

>The author then shews, by the comparison of a number

of observations made on different stars, that they exactly

agree with the theory deduced from the progressive

motion of light, and that consequently it is highly probable

Line 1141

Line 827

observed, the parallax does not amount to 2″; nay,

that if it had amounted to 1″, he should certainly have

perceived it, in the great number of observations that

he made, especially of <foreign

he made, especially of <foreign lang="greek">g</foreign> Draconis; which agreeing

lang="greek"

>g</foreign> Draconis; which agreeing

with the hypothesis, without allowing any thing for

parallax, nearly as well when the sun was in conjunction

with, as in opposition to, this star, it seems very pro-

<pb

n="7"

/><cb

bable that the parallax of it is not so much as one

single second; and consequently that it is above 400000

times farther from us than the sun.<p

times farther from us than the sun.From the greatest variation in the place of the stars,

>From the greatest variation in the place of the stars,

namely 40″, Dr. Bradley deduces the ratio of the

velocity of light in comparison with that of the earth

in her orbit. In the preceding figure, AC is to AB,

Line 1163

Line 843

ratio of those velocities is that of radius to the tangent

of 20″, or of radius to 20″, since the tangent has no

sensible difference from so small an are: but the radius

of a circle is equal to the arc of 57° 3/10 nearly, or equal

to 206260″; therefore the velocity of light is to the

velocity of the earth, as 206260 to 20, or as 10313

to 1.<p

to 1.And hence also the time in which light passes over

>And hence also the time in which light passes over

the space from the sun to the earth, is easily deduced;

for this time will be to one year, as AB or 20″ to 360°

or the whole circle; that is, 360°: 20″ :: 365 1/4 days:

8<hi

8<hi rend="sup">m</hi> 7<hi rend="sup">s</hi>, namely, light will pass from the sun to the earth

rend="sup"

>m</hi> 7<hi

rend="sup"

>s</hi>, namely, light will pass from the sun to the earth

in the time of 8 minutes, 7 seconds; and this will be

the same, whatever the distance of the sun is.<p

the same, whatever the distance of the sun is.Dr. Bradley having annexed to his theory the rules

>Dr. Bradley having annexed to his theory the rules

or formulæ for computing the aberration of the fixed

stars in declination and right ascension; these rules have

been variously demonstrated, and reduced to other practical

forms, by Mr. Clairaut in the Memoirs of the

Line 1195

Line 869

apparent place of the star, the day of the opposition;

and the extremity of the less axe, which is farthest

from the ecliptic, marks its situation three months

after.<p

after.The greatest aberration in longitude, is equal to 20″

>The greatest aberration in longitude, is equal to 20″

divided by the cosine of its latitude. And the aberration

for any time, is equal to 20″ multiplied by the

cosine of the elongation of the star found for the same

Line 1210

Line 883

is equal to 20″ multiplied by the sine of the star's latitude,

and multiplied also by the sine of the elongation.

The aberration is subtractive before the opposition, and

additive after it.<p

additive after it.The greatest aberration in declination, is equal to 20″

>The greatest aberration in declination, is equal to 20″

multiplied by the sine of the angle of position A, and

divided by the sine of B the difference of longitude

between the sun and star when the aberration in declination

Line 1219

Line 891

at any other time, will be equal to the greatest aberration

multiplied by the sine of the difference between the

sun's place at the given time and his place when the

<cb

<cb/>

aberration is nothing. Also the sine of the latitude of

the star is to radius, as the tangent of A the angle of

position at the star, is to the tangent of B, the difference

Line 1236

Line 907

at the given time, and his place when the aberration is

nothing. Also the sine of the latitude of the star is

to radius, as the cotangent of A the angle of position,

to the tangent of C.<p

to the tangent of C.<hi rend="smallcaps">Aberration</hi> <hi rend="italics">of the Planets,</hi> is equal to the geocentric

><hi

rend="smallcaps"

>Aberration</hi> <hi

rend="italics"

>of the Planets,</hi> is equal to the geocentric

motion of the planet, the space it appears to move

as seen from the earth, during the time that light employs

in passing from the planet to the earth. Thus,

in the sun, the aberration in longitude is constantly 20″,

that being the space moved by the sun, or, which is the

same thing, by the earth, in the time of 8<hi

same thing, by the earth, in the time of 8<hi rend="sup">m</hi> 7<hi rend="sup">s</hi>, which is

rend="sup"

>m</hi> 7<hi

rend="sup"

>s</hi>, which is

the time in which light passes from the sun to the earth,

as we have seen in the foregoing article. In like manner,

knowing the distance of any planet from the earth,

by proportion it will be, as the distance of the sun is to

the distance of the planet, so is 8<hi

the distance of the planet, so is 8<hi rend="sup">m</hi> 7<hi rend="sup">s</hi> to the time of

rend="sup"

>m</hi> 7<hi

rend="sup"

>s</hi> to the time of

light passing from the planet to the earth: then computing

the planet's geocentric motion in this time,

that will be the aberration of the planet, whether it be

in longitude, latitude, right-ascension, or declination.<p

in longitude, latitude, right-ascension, or declination.It is evident that the aberration will be greatest in

>It is evident that the aberration will be greatest in

the longitude, and very small in latitude, because the

planets deviate very little from the plane of the ecliptic,

or path of the earth; so that the aberration in the latitudes

Line 1284

Line 941

These maxima of aberration for the several

planets, when their distance from the sun is least, are as

below: viz, for

<table

<table><row role="data"><cell cols="1" rows="1" role="data">Saturn</cell><cell cols="1" rows="1" role="data">27″</cell><cell cols="1" rows="1" role="data">.0</cell></row><row role="data"><cell cols="1" rows="1" role="data">Jupiter</cell><cell cols="1" rows="1" role="data">29</cell><cell cols="1" rows="1" role="data">.8</cell></row><row role="data"><cell cols="1" rows="1" role="data">Mars</cell><cell cols="1" rows="1" role="data">37</cell><cell cols="1" rows="1" role="data">.8</cell></row><row role="data"><cell cols="1" rows="1" role="data">Venus</cell><cell cols="1" rows="1" role="data">43</cell><cell cols="1" rows="1" role="data">.2</cell></row><row role="data"><cell cols="1" rows="1" role="data">Mercury</cell><cell cols="1" rows="1" role="data">59</cell><cell cols="1" rows="1" role="data">.0</cell></row><row role="data"><cell cols="1" rows="1" role="data">The Moon</cell><cell cols="1" rows="1" role="data"> 2/3</cell><cell cols="1" rows="1" role="data"/></row></table>

><row

role="data"

><cell

cols="1"

rows="1"

role="data"

>Saturn</cell><cell

cols="1"

rows="1"

role="data"

>27″</cell><cell

cols="1"

rows="1"

role="data"

>.0</cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

>Jupiter</cell><cell

cols="1"

rows="1"

role="data"

>29</cell><cell

cols="1"

rows="1"

role="data"

>.8</cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

>Mars</cell><cell

cols="1"

rows="1"

role="data"

>37</cell><cell

cols="1"

rows="1"

role="data"

>.8</cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

>Venus</cell><cell

cols="1"

rows="1"

role="data"

>43</cell><cell

cols="1"

rows="1"

role="data"

>.2</cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

>Mercury</cell><cell

cols="1"

rows="1"

role="data"

>59</cell><cell

cols="1"

rows="1"

role="data"

>.0</cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

>The Moon</cell><cell

cols="1"

rows="1"

role="data"

> 2/3</cell><cell

cols="1"

rows="1"

role="data"

></cell></row></table>

And between these numbers and nothing the aberrations

of the planets, in longitude, vary according to their

situations. But that of the sun varies not, being constantly

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Line 949

may alter his declination by a quantity, which varies

from 0 to near 8″; being greatest or 8″ about the

equinoxes, and vanishing in the solstices.

<pb

<pb n="8"/><cb/>The methods of computing these, and the formulas

n="8"

/><cb

/><p

>The methods of computing these, and the formulas

for all cases, are given by M. Clairaut in the Memoirs

of the Academy of Sciences for the year 1746, and

by M. Euler in the Berlin Memoirs, vol. 2, for 1746.<p

by M. Euler in the Berlin Memoirs, vol. 2, for 1746.<hi rend="italics">Optic</hi> <hi rend="smallcaps">Aberration</hi>, the deviation or dispersion of

><hi

rend="italics"

>Optic</hi> <hi

rend="smallcaps"

>Aberration</hi>, the deviation or dispersion of

the rays of light, when reflected by a speculum, or refracted

by a lens, by which they are prevented from

meeting or uniting in the same point, called the geometrical

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Line 965

on the axis, between the focus and the point

where the ray meets the axis. The aberrations are

very amply treated in Smith's Complete System of

Opties, in 2 volumes 4to.<p

Opties, in 2 volumes 4to.There are two species of aberration, distinguished

>There are two species of aberration, distinguished

according to their different causes: the one arises from

the figure of the speculum or lens, producing a geometrical

dispersion of the rays, when these are perfectly

Line 1431

Line 993

speculum, whose centre is C; and let AB, EF

be incident rays parallel to the axis CV. Because the

angle of incidence is equal to the angle of reflection in

<figure

></figure>

all cases, therefore if the radii CB, CF be drawn to the

points of incidence, and thence BD making the angle

CBD equal to the angle CBA, and FG making the

angle CFG equal to the angle CFE; then BD, FG

will be the reflected rays, and D, G, the points where

<cb

<cb/>

they meet the axis. Hence it appears that the point

of coincidence with the axis is equally distant from the

point of incidence and the centre: for because the angle

Line 1462

Line 1022

arrive very near the middle point or focus D, to produce

an image the most distinct, by the least aberration of

the rays. And in like manner for rays refracted through

lenses.<p

lenses.In spherical lenses, Mr. Huygens has demonstrated

>In spherical lenses, Mr. Huygens has demonstrated

that the aberration from the figure, in different lenses,

is as follows.<p

is as follows.1. In all plano-convex lenses, having their plane surface

>1. In all plano-convex lenses, having their plane surface

exposed to parallel rays, the longitudinal aberration

of the extreme ray, or that remotest from the axis, is

equal to 9/2 of the thickness of the lens.<p

equal to 9/2 of the thickness of the lens.2. In all plano-convex lenses, having their convex

>2. In all plano-convex lenses, having their convex

surface exposed to parallel rays, the longitudinal aberration

of the extreme ray, is equal to 7/6 of the thickness

of the lens. So that in this position of the same planoconvex

lens, the aberration is but about one-fourth

of that in the former; being to it only as 7 to 27.<p

of that in the former; being to it only as 7 to 27.3. In all double convex lenses of equal spheres, the

>3. In all double convex lenses of equal spheres, the

aberration of the extreme ray, is equal to 5/3 of the

thickness of the lens.<p

thickness of the lens.4. In a double convex lens, the radii of whose spheres

>4. In a double convex lens, the radii of whose spheres

are as 1 to 6, if the more convex surface be exposed to

parallel rays, the aberration from the figure is less than

in any other spherical lens; being no more than 15/14 of

its thickness.<p

its thickness.But the foregoing species of aberration, arising from

>But the foregoing species of aberration, arising from

the figure, is very small, and easily remedied, in comparison

with the other, arising from the unequal refrangibility

of the rays of light; insomuch that Sir

Line 1504

Line 1058

error arising from the spherical figure of the glass, is to

the error arising from the different refrangibility of the

rays, as 961/72000000 to 4/55, that is as 1 to 5449.

<pb

<pb n="9"/><cb/>So that it may seem strange that objects appear

n="9"

/><cb

/><p

>So that it may seem strange that objects appear

through telescopes so distinct as they do, considering

that the error arising from the different refrangibility, is

almost incomparably larger than that of the figure.

Line 1521

Line 1071

rare, so as at the circumference to become infinitely

rare; and, by reason of their rarity, they are not

strong enough to be visible, unless in the centre, and

very near it.<p

very near it.In consequence of the discovery of the unequal refrangibility

>In consequence of the discovery of the unequal refrangibility

of light, and the apprehension that equal

refractions must produce equal divergencies in every

sort of medium, it was supposed that all spherical objectglasses

Line 1534

Line 1083

their length. So that Sir Isaac Newton, and

other persons after him, despairing of success in the use

and fabric of lenses, directed their chief attention to

the construction of reflecting telescopes.<p

the construction of reflecting telescopes.However, about the year 1747, M. Euler applied

>However, about the year 1747, M. Euler applied

himself to the subject of refraction; and pursued a

hint suggested by Newton, for the design of making

object-glasses with two lenses of glass inclosing water

Line 1572

Line 1120

glass and English crown glass were found to be nearly

allied in this respect: the common English plate glass

made the rays diverge more; and the English flint

<cb

<cb/>

glass most of all. But without enquiring into the

cause of this difference, he proceeded to adapt wedges

of crown glass, and of white flint glass, ground to different

Line 1585

Line 1132

he hence concluded in general, that any two wedges

made in this proportion, and applied together so as to

refract in contrary directions, would refract the light

without any aberration of the rays.<p

without any aberration of the rays.Mr. Dollond's next object was to make similar trials

>Mr. Dollond's next object was to make similar trials

with spherical glasses of different materials, with the

view of applying his discovery to the improvement of

telescopes: and here he perceived that, to obtain a refraction

Line 1604

Line 1150

will constantly be refracted, by the difference between

two contrary refractions, in the proportion required;

and therefore the different refrangibility of the light

will be entirely removed.<p

will be entirely removed.But in the applications of this ingenious discovery

>But in the applications of this ingenious discovery

to practice, Mr. Dollond met with many and great

difficulties. At length, however, after many repeated

trials, by a resolute perseverance, he succeeded so far as

to construct refracting telescopes much superior to any

that had hitherto been made; representing objects with

great distinctness, and in their true colours.<p

great distinctness, and in their true colours.Mr. Clairaut, who had interested himself from the

>Mr. Clairaut, who had interested himself from the

beginning in this discovery, now endeavoured to ascertain

the principles of Mr. Dollond's theory, and to lay

down rules to facilitate the construction of these new

Line 1630

Line 1174

hereby supplied with the most accurate calculations,

they were very defective in practice. And the English

telescopes, made, as they imagined, without any precise

rule, were greatly superior to the best of their construction.<p

rule, were greatly superior to the best of their construction.M. Euler, whose speculations had sirst given occasion

>M. Euler, whose speculations had sirst given occasion

to this important and useful enquiry, was very reluctant

in admitting Mr. Dollond's improvements, because

they militated against a pre-conceived theory of his

own. At last however, after several altercations, being

convinced of their reality and importance by M. Clair-

<pb

n="10"

/><cb

aut, he assented; and he soon after received farther satisfaction

from the experiments of M. Zeiher, of Petersburgh.<p

from the experiments of M. Zeiher, of Petersburgh.M. Zeiher shewed by experiments that it is the lead,

>M. Zeiher shewed by experiments that it is the lead,

in the composition of glass, which gives it this remarkable

property, namely, that while the refraction of the

mean rays is nearly the same, that of the extreme rays

Line 1660

Line 1199

greatly superior to the flint glass of Mr. Dollond for

the construction of telescopes; as it occasioned three

times as great a dispersion of the rays as the common

glass, whilst the mean refraction was only as 1.61 to 1.<p

glass, whilst the mean refraction was only as 1.61 to 1.Other improvements were also made on the new or

>Other improvements were also made on the new or

achromatic telescopes by the inventor Mr. John Dollond,

and by his son Peter Dollond; which may be

seen under the proper words. For various dissertations

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Line 1211

the Berlin Ac. 1746, 1762, 1766; Swed. Mem. vol.

16; Com. Nov. Petripol. 1762; M. Euler's Dioptrics;

M. d'Alembert's Opuscules Math.; M. de Rochon

Opuscules; &c, &c.</div1><div1

Opuscules; &c, &c.</div1><div1 part="n" n="ABRIDGING" org="uniform" sample="complete" type="entry"><head>ABRIDGING</head>, <hi rend="italics">in Algebra,</hi> is the reducing a compound

part="n"

n="ABRIDGING"

org="uniform"

sample="complete"

type="entry"

><head

>ABRIDGING</head><p

>, <hi

rend="italics"

>in Algebra,</hi> is the reducing a compound

equation, or quantity, to a more simple form of

expression. This is done either to save room, or the

trouble of writing a number of symbols; or to simplisy

the expression, either to ease the memory, or to render

the formula more easy and general.<p

the formula more easy and general.So the equation , by putting

>So the equation , by putting

<hi rend="italics">p</hi> = <hi rend="italics">a, q</hi> = <hi rend="italics">ab,</hi> and <hi rend="italics">r</hi> = <hi rend="italics">abc,</hi> becomes And the equation , by putting

<hi

, and , becomes .</div1><div1 part="n" n="ABSCISS" org="uniform" sample="complete" type="entry"><head>ABSCISS</head>, <hi rend="smallcaps">Abscisse</hi>, or <hi rend="smallcaps">Abscissa</hi>, is a part or

rend="italics"

>p</hi> = <hi

rend="italics"

>a, q</hi> = <hi

rend="italics"

>ab,</hi> and <hi

rend="italics"

>r</hi> = <hi

rend="italics"

>abc,</hi> becomes <p

>And the equation , by putting

, and , becomes .</div1><div1

part="n"

n="ABSCISS"

org="uniform"

sample="complete"

type="entry"

><head

>ABSCISS</head><p

>, <hi

rend="smallcaps"

>Abscisse</hi>, or <hi

rend="smallcaps"

>Abscissa</hi>, is a part or

segment cut off a line, terminated at some certain point,

by an ordinate to a curve; as AP or BP.

<figure

<figure/>The absciss may either commence at the vertex of

></figure><p

>The absciss may either commence at the vertex of

the curve, or at any other fixed point. And it may be

taken either upon the axis or diameter of the curve,

or upon any other line drawn in a given position.

<cb

<cb/>Hence there are an infinite number of variable abscisses,

/><p

>Hence there are an infinite number of variable abscisses,

terminated at the same fixed point at one end, the

other end of them being at any point of the given line

or diameter.<p

or diameter.In the common parabola, each ordinate PQ has but

>In the common parabola, each ordinate PQ has but

<figure

></figure>

one absciss AP; in the ellipse or circle, the ordinate

has two abscisses AP, BP lying on the opposite sides

of it; and in the hyperbola the ordinate PQ has also

Line 1740

Line 1238

curve of the first kind, may have two abscisses to each

ordinate. But a line of the third order may have three

abscisses to each ordinate; a line of the fourth order

may have four; and so on.<p

may have four; and so on.The use of the abscisses is, in conjunction with the

>The use of the abscisses is, in conjunction with the

ordinates, to express the nature of the curves, either

by some proportion or equation including the abfcifs

and its ordinate, with some other fixed invariable line

Line 1751

Line 1248

is the same for every ordinate and its abscisses, whatever

point of the curve be taken. So, in the circle, the

square of any ordinate is equal to the rectangle of its

two abscisses, or AP.PB = PQ<hi

two abscisses, or AP.PB = PQ<hi rend="sup">2</hi>; in the parabola,

rend="sup"

>2</hi>; in the parabola,

the square of the ordinate is equal to the rectangle of

the absciss and a certain given line called the parameter;

in the ellipse and hyperbola, the square of the ordinate

Line 1761

Line 1256

rectangle of the two abscisses, namely, as the square of

the conjugate to the square of the transverse, or as the

parameter is to the transverse axis; and so other properties

in other curves.<p

in other curves.When the natures or properties of curves are expressed

>When the natures or properties of curves are expressed

by algebraic equations, any general absciss, as

AP, is commonly denoted by the letter <hi

AP, is commonly denoted by the letter <hi rend="italics">x,</hi> and the ordinate

rend="italics"

PQ by the letter <hi rend="italics">y;</hi> the other or constant lines

>x,</hi> and the ordinate

PQ by the letter <hi

rend="italics"

>y;</hi> the other or constant lines

being represented by other letters. Then the equations

expressing the nature of these curves are as follow;

namely, for the

circle , where <hi

circle , where <hi rend="italics">d</hi> is the diameter AB;

rend="italics"

parabola - <hi rend="italics">px</hi> = <hi rend="italics">y</hi><hi rend="sup">2</hi> , where <hi rend="italics">p</hi> is the parameter;

>d</hi> is the diameter AB;

<hi rend="brace"><note anchored="yes" place="unspecified">ellipse - <hi rend="italics">t</hi><hi rend="sup">2</hi> : <hi rend="italics">c</hi><hi rend="sup">2</hi> :: <hi rend="italics">tx</hi> - <hi rend="italics">x</hi><hi rend="sup">2</hi> : <hi rend="italics">y</hi><hi rend="sup">2</hi>,

parabola - <hi

hyperbola <hi rend="italics">t</hi><hi rend="sup">2</hi> : <hi rend="italics">c</hi><hi rend="sup">2</hi> :: <hi rend="italics">tx</hi> + <hi rend="italics">x</hi><hi rend="sup">2</hi> : <hi rend="italics">y</hi><hi rend="sup">2</hi>,</note>

rend="italics"

where <hi rend="italics">t</hi> is the transverse,

>px</hi> = <hi

& <hi rend="italics">c</hi> the conjugate axis.</hi></div1><div1 part="n" n="ABSIS" org="uniform" sample="complete" type="entry"><head>ABSIS</head>, ABSIDES. See <hi rend="smallcaps">Apsis, Apsides.</hi>

rend="italics"

<pb n="11"/><cb/>ABSOLUTE <hi rend="smallcaps">Equation</hi>, <hi rend="italics">in Aftronomy,</hi> is the

>y</hi><hi

rend="sup"

>2</hi> , where <hi

rend="italics"

>p</hi> is the parameter;

<hi

rend="brace"

><note

anchored="yes"

place="unspecified"

>ellipse - <hi

rend="italics"

>t</hi><hi

rend="sup"

>2</hi> : <hi

rend="italics"

>c</hi><hi

rend="sup"

>2</hi> :: <hi

rend="italics"

>tx</hi> - <hi

rend="italics"

>x</hi><hi

rend="sup"

>2</hi> : <hi

rend="italics"

>y</hi><hi

rend="sup"

>2</hi>,

hyperbola <hi

rend="italics"

>t</hi><hi

rend="sup"

>2</hi> : <hi

rend="italics"

>c</hi><hi

rend="sup"

>2</hi> :: <hi

rend="italics"

>tx</hi> + <hi

rend="italics"

>x</hi><hi

rend="sup"

>2</hi> : <hi

rend="italics"

>y</hi><hi

rend="sup"

>2</hi>,</note>

where <hi

rend="italics"

>t</hi> is the transverse,

& <hi

rend="italics"

>c</hi> the conjugate axis.</hi></div1><div1

part="n"

n="ABSIS"

org="uniform"

sample="complete"

type="entry"

><head

>ABSIS</head><p

>, ABSIDES. See <hi

rend="smallcaps"

>Apsis, Apsides.</hi>

<pb

n="11"

/><cb

/><p

>ABSOLUTE <hi

rend="smallcaps"

>Equation</hi>, <hi

rend="italics"

>in Aftronomy,</hi> is the

sum of the optic and excentric equations. The apparent

inequality of a planet's motion, arising from its

not being equally dislant from the earth at all times,

Line 1875

Line 1292

it will be full as evident that the sun cannot appear to

have an uniform motion in such ellipse; so that his

motion will then be subject to two equations; that is,

the optic equation, and the excentric equation. <hi

the optic equation, and the excentric equation. <hi rend="italics">See</hi>

rend="italics"

<hi rend="smallcaps">Equation</hi>, and <hi rend="smallcaps">Optic Inequality.</hi><hi rend="smallcaps">Absolute</hi> <hi rend="italics">Number,</hi> in Algebra, is that term or

>See</hi>

<hi

rend="smallcaps"

>Equation</hi>, and <hi

rend="smallcaps"

>Optic Inequality.</hi><p

><hi

rend="smallcaps"

>Absolute</hi> <hi

rend="italics"

>Number,</hi> in Algebra, is that term or

member of an equation that is completely known, and

which is equal to all the other, or unknown terms,

taken together; and is the same as what Vieta calls

the <hi

the <hi rend="italics">homogeneum comparationis.</hi> So, of the equation

rend="italics"

>homogeneum comparationis.</hi> So, of the equation

, or , the absolute

number, or known term, is 36.<p

number, or known term, is 36.<hi rend="smallcaps">Absolute</hi> <hi rend="italics">Gravity, Motion, Space, Time, &c.</hi> See

><hi

the respective substantives.ABSTRACT <hi rend="smallcaps">Mathematics</hi>, otherwise called

rend="smallcaps"

>Absolute</hi> <hi

rend="italics"

>Gravity, Motion, Space, Time, &c.</hi> See

the respective substantives.<p

>ABSTRACT <hi

rend="smallcaps"

>Mathematics</hi>, otherwise called

pure mathematics, is that which treats of the properties

of magnitude, figure, or quantity, absolutely and

generally confidered, without restriction to any species

Line 1913

Line 1309

to mixed mathematics, in which simple and abstract

properties, and the relations of quantities, primitively

considered in pure mathematics, are applied to sensible

objects; as in astronomy, hydrostatics, optics, &c.<p

objects; as in astronomy, hydrostatics, optics, &c.<hi rend="smallcaps">Abstract</hi> <hi rend="italics">Number,</hi> is a number, or collection of

><hi

rend="smallcaps"

>Abstract</hi> <hi

rend="italics"

>Number,</hi> is a number, or collection of

units, considered in itself, without being applied to

denote a collection of any particular and determinate

things. So, for example, 3 is an abstract number, so

far as it is not applied to something: but when we say

3 feet, or 3 persons, the 3 is no longer an abstract, but

a concrete number.</div1><div1

a concrete number.</div1><div1 part="n" n="ABSURD" org="uniform" sample="complete" type="entry"><head>ABSURD</head>, or <hi rend="smallcaps">Absurdum</hi>, a term commonly used

part="n"

n="ABSURD"

org="uniform"

sample="complete"

type="entry"

><head

>ABSURD</head><p

>, or <hi

rend="smallcaps"

>Absurdum</hi>, a term commonly used

in demonstrating converse propositions; a mode of demonstration,

in which the proposition intended is not

proved in a direct manner, by principles before laid

Line 1946

Line 1327

two lines coincide, those lines will coincide in all their

parts, otherwise they would inclose a space, which is

absurd or contrary to the 10th axiom. Most converse

<cb

<cb/>

propositions are proved in this way, which mode of

proof is called <hi

proof is called <hi rend="italics">reductio ad absurdum.</hi>ABUNDANT <hi rend="smallcaps">Number</hi>, in <hi rend="italics">Arithmetic,</hi> is a number

rend="italics"

>reductio ad absurdum.</hi><p

>ABUNDANT <hi

rend="smallcaps"

>Number</hi>, in <hi

rend="italics"

>Arithmetic,</hi> is a number

whose aliquot parts, added all together, make a

sum which is greater than the number itself. Thus 12

is an abundant number, because its aliquot parts,

namely 1, 2, 3, 4, 6, when added together, make 16,

which is greater than the number 12 itself.<p

which is greater than the number 12 itself.An abundant number is opposed to a deficient one,

>An abundant number is opposed to a deficient one,

which is less than the sum of its aliquot parts taken together,

as the number 14, whose aliquot parts 1, 2, 7,

make no more than 10; and to a perfect number, which

is exactly equal to the sum of all its aliquot parts, as

the number 6, which is equal to the sum of 1, 2, 3,

which are its aliquot parts.</div1><div1

which are its aliquot parts.</div1><div1 part="n" n="ACADEMICIAN" org="uniform" sample="complete" type="entry"><head>ACADEMICIAN</head>, a member of a society called

part="n"

n="ACADEMICIAN"

org="uniform"

sample="complete"

type="entry"

><head

>ACADEMICIAN</head><p

>, a member of a society called

an academy, instituted for the promotion of arts, sciences,

or natural knowledge in general.</div1><div1

or natural knowledge in general.</div1><div1 part="n" n="ACADEMICS" org="uniform" sample="complete" type="entry"><head>ACADEMICS</head>, an ancient sect of philosophers,

part="n"

n="ACADEMICS"

org="uniform"

sample="complete"

type="entry"

><head

>ACADEMICS</head><p

>, an ancient sect of philosophers,

who followed the doctrine of Socrates and Plato, as to

the uncertainty of knowledge, and the incomprehensibility

of truth.<p

of truth.<hi rend="italics">Academic,</hi> in this sense, amounts to much the same

><hi

rend="italics"

>Academic,</hi> in this sense, amounts to much the same

with Platonist; the difference between them being only

in point of time. Those who embraced the system of

Plato, among the ancients, were called <hi

Plato, among the ancients, were called <hi rend="italics">academici,</hi> academician

rend="italics"

>academici,</hi> academician

or academic; whereas those who did the same

since the restoration of learning, have assumed the denomination

of Platonists.<p

of Platonists.We usually reckon three sects of academics; though

>We usually reckon three sects of academics; though

some make five. The ancient academy was that of

which Plato was the chief.<p

which Plato was the chief.Arcessilas, one of Plato's successors, introducing

>Arcessilas, one of Plato's successors, introducing

some alterations into the philosophy of this sect, founded

what they call the second academy.<p

what they call the second academy.The establishment of the third, called also the new

>The establishment of the third, called also the new

academy, is attributed to Lacydes, or rather to Carneades.Some authors add a fourth, founded by Philo; and

academy, is attributed to Lacydes, or rather to Carneades.<p

>Some authors add a fourth, founded by Philo; and

a fifth, by Antiochus, called the Antiochan, which

tempered the ancient academy with Stoicism.<p

tempered the ancient academy with Stoicism.The ancient academy doubted of every thing; and

>The ancient academy doubted of every thing; and

carried this principle so far as to make it a doubt, whether

or no they ought to doubt. It was a kind of a

principle with them, never to be certain or satisfied of

any thing; never to affirm or to deny any thing, either

for true or false.<p

for true or false.The new academy was somewhat more reasonable;

>The new academy was somewhat more reasonable;

they acknowledged several things for truths, but without

attaching themselves to any with entire assurance.

These philosophers had found that the ordinary commerce

Line 2027

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and yet it is evident that they looked upon things

rather as probable, than as true and certain: by this

amendment thinking to secure themselves from those

absurdities into which the ancient academy had fallen.</div1><div1

absurdities into which the ancient academy had fallen.</div1><div1 part="n" n="ACADEMIST" org="uniform" sample="complete" type="entry"><head>ACADEMIST</head>, the same as Academician.</div1><div1 part="n" n="ACADEMY" org="uniform" sample="complete" type="entry"><head>ACADEMY</head>, <hi rend="smallcaps">Academia</hi>, in <hi rend="italics">Antiquity,</hi> a fine villa

part="n"

n="ACADEMIST"

org="uniform"

sample="complete"

type="entry"

><head

>ACADEMIST</head><p

>, the same as Academician.</div1><div1

part="n"

n="ACADEMY"

org="uniform"

sample="complete"

type="entry"

><head

>ACADEMY</head><p

>, <hi

rend="smallcaps"

>Academia</hi>, in <hi

rend="italics"

>Antiquity,</hi> a fine villa

or pleasure house, in one of the submbs of Athens,

about a mile from the city; where Plato, and the wise

men who followed him, held assemblies for disputes

<pb

n="12"

/><cb

and philosophical conference; which gave the name to

the sect of Academics.<p

the sect of Academics.The house took its name, <hi rend="italics">Academy,</hi> from one Academus,

>The house took its name, <hi

rend="italics"

>Academy,</hi> from one Academus,

or Ecademus, a citizen of Athens, to whom it

originally belonged: he lived in the time of Theseus;

and here he used to have gymnastic sports or exercises.<p

and here he used to have gymnastic sports or exercises.The academy was farther improved by Cimon, and

>The academy was farther improved by Cimon, and

adorned with fountains, trees, shady walks, &c, for the

convenience of the philosophers and men of learning,

who here met to confer and dispute for their mutual

improvement. It was surrounded with a wall by Hipparchus,

the son of Pisistratus; and it was also used as

the burying-place for illustrious persons, who had deserved

well of the republic.<p

well of the republic.It was here that Plato taught his philosophy; and

>It was here that Plato taught his philosophy; and

hence it was that all public places, destined for the assemblies

of the learned and ingenious, have been since

called <hi

called <hi rend="italics">Academies.</hi>Sylla facrificed the delicious walks and groves of the

rend="italics"

>Academies.</hi><p

>Sylla facrificed the delicious walks and groves of the

academy, which had been planted by Cimon, to the

ravages of war; and employed those very trees in constructing

machines to batter the walls of the city which

they had adorned.<p

they had adorned.Cicero too had a villa, or country retirement, near

>Cicero too had a villa, or country retirement, near

Puzzuoli, which he called by the same name, <hi rend="italics">Academia.</hi>

Puzzuoli, which he called by the same name, <hi

rend="italics"

>Academia.</hi>

Here he used to entertain his philosophical

friends; and here it was that he composed his Academical

Questions, and his books <hi

Questions, and his books <hi rend="italics">De Naturâ Deorum.</hi><div2 part="n" n="Academy" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Academy</hi></head>, among the moderns, denotes a regular

rend="italics"

>De Naturâ Deorum.</hi><div2

part="n"

n="Academy"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Academy</hi></head><p

>, among the moderns, denotes a regular

society or company of learned persons, instituted under

the protection of some prince, or other public authority,

for the cultivation and improvement of arts or

sciences.<p

sciences.Some authors confound Academy with University;

>Some authors confound Academy with University;

but though much the same in Latin, they are very different

things in English. An university is properly a

body composed of graduates in the feveral faculties;

Line 2117

Line 1415

in, but for those that are more knowing; for persons

of learning to confer in, and communicate their lights

and discoveries to each other, for their mutual benefit

and improvement.<p

and improvement.The first modern academy we read of, was established

>The first modern academy we read of, was established

by Charlemagne, by the advice of Alcuin, an English

monk: it was composed of the chief geniuses of the

court, the emperor himself being a member. In their

Line 2131

Line 1428

a young lord, named Augilbert, took that of Homer;

Adelard, bishop of Corbie, was called Augustin; Recluse,

bishop of Mentz, was Dametas; and the king

himself, David.<p

himself, David.Since the revival of learning in Europe, academies

>Since the revival of learning in Europe, academies

have multiplied greatly, most nations being furnished

with several, and from their communications the chief

<cb

<cb/>

improvements have been made in the arts and sciences,

and in cultivating natural knowledge. There are now

academies for almost every art, or species of knowledge;

but I shall give a short account only of those

institutions of this kind, which regard the cultivation of

subjects mathematical or philosophical, which are the

proper and peculiar objects of our undertaking.<p

proper and peculiar objects of our undertaking.Italy abounds more in academies than all the world

>Italy abounds more in academies than all the world

besides; there being enumerated by Jarckius not less

than sive hundred and fifty in all; and even to the

amount of twenty-five in Milan itself. These are however

mostly of a private and inferior nature; the consequence

of their too great number.<p

of their too great number.The first academy of a philosophical kind was established

>The first academy of a philosophical kind was established

at Naples, in the house of Baptista Porta, about

the year 1560, under the name of <hi

the year 1560, under the name of <hi rend="italics">Academy Secretorum

rend="italics"

Naturæ;</hi> being formed for the improvement of natural

>Academy Secretorum

Naturæ;</hi> being formed for the improvement of natural

and mathematical knowledge. This was succeeded by

the<p

the<hi rend="smallcaps">Academy</hi> <hi rend="italics">of Lyncei,</hi> founded at Rome by prince

><hi

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>of Lyncei,</hi> founded at Rome by prince

Frederick Cesi, towards the end of the same century.

It was rendered famous by the notable discoveries made

by several of its members; among whom was the celebrated

Galileo Galilei.<p

Galileo Galilei.Several other academies contributed also to the advancement

>Several other academies contributed also to the advancement

of the sciences; but it was by speculations

rather than by repeated experiments on the phenomena

of nature: such were the academy of Bessarian at Rome,

Line 2187

Line 1472

celebrated philosophers, were the chief members. The

compositions of all these academies, of the 16th century,

were good in their kind; but none of them comparable

to those of the Lyncei.<p

to those of the Lyncei.<hi rend="smallcaps">Academy</hi> <hi rend="italics">del Cimento,</hi> that is, of Experiments, arose

><hi

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>del Cimento,</hi> that is, of Experiments, arose

at Florence, some years after the death of Torricelli,

namely in the year 1657, under the protection of prince

Leopold of Tuscany, afterwards cardinal de Medicis,

Line 2205

Line 1485

water; then the globe being compressed by a strong

screw, the water came through the pores of the gold

rather than yield to the compression: also, Alphonsus

Borelli, well known for his ingenious treatise <hi

Borelli, well known for his ingenious treatise <hi rend="italics">De Motu

rend="italics"

>De Motu

Animalium,</hi> and other works; Candide del Buono,

brother of Paul; Alexander Marsili, Vincent Viviani,

Francis Rhedi, and the Count Laurence

Magalotti, secretary of this academy, who pub-

<pb

n="13"

/><cb

lished a volume of their curious experiments in 1667,

under the title of <hi

under the title of <hi rend="italics">Saggi di Naturali Esperienze;</hi> a

rend="italics"

>Saggi di Naturali Esperienze;</hi> a

copy of which being presented to the Royal Society,

it was translated into English by Mr. Waller, and published

at London, in 4to, 1684: A curious collection

Line 2233

Line 1506

was no mean philosopher and chemist, and that he

invented thermometers, of which the construction and

use may be seen in the collection of the academy del

Cimento.<p

Cimento.<hi rend="smallcaps">Academy</hi> <hi rend="italics">degl' Inquieti</hi> at Bologna, incorporated

><hi

afterwards into that <hi rend="italics">della traccia</hi> in the same city, followed

rend="smallcaps"

the example of that <hi rend="italics">del Cimento.</hi> The members

>Academy</hi> <hi

rend="italics"

>degl' Inquieti</hi> at Bologna, incorporated

afterwards into that <hi

rend="italics"

>della traccia</hi> in the same city, followed

the example of that <hi

rend="italics"

>del Cimento.</hi> The members

met at the house of the abbot Antonio Sampieri;

and here Geminiano Montanari, one of the chief members,

made excellent discourses on mathematical and

Line 2253

Line 1517

This academy afterwards met in an apartment

of Eustachio Manfredi; and then in that of Jacob

Sandri; but it arrived at its chief lustre while its assemblies

were held in the palace Marsilli.<p

were held in the palace Marsilli.<hi rend="smallcaps">Academy</hi> <hi rend="italics">of Rossano,</hi> in the kingdom of Naples,

><hi

called <hi rend="italics">La Societa Scientifica Rossanese degl' Incuriosi,</hi>

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>of Rossano,</hi> in the kingdom of Naples,

called <hi

rend="italics"

>La Societa Scientifica Rossanese degl' Incuriosi,</hi>

was founded about the year 1540, under the name of

<hi

<hi rend="italics">Naviganti;</hi> and was renewed under that of <hi rend="italics">Spensierati</hi>

rend="italics"

>Naviganti;</hi> and was renewed under that of <hi

rend="italics"

>Spensierati</hi>

by Camillo Tuscano, about the year 1600. It was

then an academy of belles-lettres, but was afterwards

transformed into an academy of sciences, on the solicitation

Line 2281

Line 1534

be admitted a member, it was necessary that the candidate

have degrees in some faculty. Members, in the

beginning of their books, are not allowed to take the

title of <hi

title of <hi rend="italics">academist</hi> without a written permission from the

rend="italics"

>academist</hi> without a written permission from the

president, which is not granted till the work has been

examined by the censors of the academy. This permission

is the highest honour the academy can confer;

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Line 1543

be made upon it. The president himself is not exempt

from this law: and it is not permitted that any academist

publish any thing against the writings of another,

without leave obtained from the society.<p

without leave obtained from the society.There have been several other academies of sciences

>There have been several other academies of sciences

in Italy, but which have not subsisted long, for want

of being supported by the princes. Such were at

Naples that of the <hi

Naples that of the <hi rend="italics">Investiganti,</hi> founded about the year

rend="italics"

>Investiganti,</hi> founded about the year

1679, by the marquis d'Arena, Don Andrea Concubletto;

and that which, about the year 1698, met in

the palace of Don Lewis della Cerda, the duke de

Medina, and viceroy of Naples: at Rome, that of

<hi

<hi rend="italics">Fisico-Matematici,</hi> which in 1686 met in the house of

rend="italics"

<cb/>

>Fisico-Matematici,</hi> which in 1686 met in the house of

Signior Ciampini: at Verona, that of <hi rend="italics">Aletosili,</hi> founded

<cb

Signior Ciampini: at Verona, that of <hi

rend="italics"

>Aletosili,</hi> founded

the same year by Signior Joseph Gazola, and which

met in the house of the count Serenghi della Cucca:

at Brescia, that of <hi

at Brescia, that of <hi rend="italics">Filesotici,</hi> founded the same year

rend="italics"

>Filesotici,</hi> founded the same year

for the cultivation of philosophy and mathematics, and

terminated the year following: that of F. Francisco

Lana, a jesuit of great skill in these sciences: and lastly

that of Fisico-Critici at Sienna, founded in 1691, by

Signior Peter Maria Gabrielli.<p

Signior Peter Maria Gabrielli.Some other academies, still subsisting in Italy, repair

>Some other academies, still subsisting in Italy, repair

with advantage the loss of the former. One of the

principal is the academy of Filarmonici at Verona, supported

by the marquis Scipio Maffei, one of the most

learned men in Italy; the members of which academy,

though they cultivate the belles lettres, do not

neglect the sciences. The academy of <hi

neglect the sciences. The academy of <hi rend="italics">Ricovrati</hi> at

rend="italics"

>Ricovrati</hi> at

Padua still subsists with reputation; in which; from

time to time, learned discourses are held on philosophical

subjects. The like may be said of the academy of the

<hi

<hi rend="italics">Muti di Reggio,</hi> at Modena. At Bologna is an academy

rend="italics"

>Muti di Reggio,</hi> at Modena. At Bologna is an academy

of sciences, in a flourishing condition, known by the

name of <hi

name of <hi rend="italics">The Institute of Bologna;</hi> which was founded

rend="italics"

>The Institute of Bologna;</hi> which was founded

in 1712 by count Marsigli, for cultivating physics,

mathematics, medicine, chemistry, and natural history.

The history of it is written by M. de Limiers, from

Line 2356

Line 1590

number of these academies may also be ranked the assembly

of the learned, who of late years met at Venice

in the house of Signior Cristino Martinelli, a noble

Venetian, and a great patron of learning.<p

Venetian, and a great patron of learning.<hi rend="smallcaps">Academia</hi> <hi rend="italics">Cosmografica,</hi> or that of the Argonauts,

><hi

rend="smallcaps"

>Academia</hi> <hi

rend="italics"

>Cosmografica,</hi> or that of the Argonauts,

was instituted at Venice, at the instance of F. Coronelli,

for the improvement of geography; the design

being to procure exact maps, geographical, topographical,

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Line 1612

themselves who are willing to engage in this design. The

Argonauts number near 200 members in the different

countries of Europe; and their device is the terraqueous

globe, with the motto <hi

globe, with the motto <hi rend="italics">Plus ultra.</hi> All the globes, maps,

rend="italics"

>Plus ultra.</hi> All the globes, maps,

and geographical writings of F. Coronelli have been

published at the expence of this academy.

<pb

<pb n="14"/><cb/><hi rend="smallcaps">The Academy</hi> <hi rend="italics">of Apatists,</hi> or Impartial Academy,

n="14"

/><cb

/><p

><hi

rend="smallcaps"

>The Academy</hi> <hi

rend="italics"

>of Apatists,</hi> or Impartial Academy,

deserves to be mentioned on account of the extent of its

plan, including universally all arts and sciences. It

holds from time to time public meetings at Florence,

where any person, whether academist or not, may read

his works, in whatever form, language, or subject; the

academy receiving all with the greatest impartiality.<p

academy receiving all with the greatest impartiality.In France there are many academies for the improvement

>In France there are many academies for the improvement

of arts and sciences. F. Mersenne, it is

said, gave the first idea of a philosophical academy in

France, about the beginning of the seventeenth century,

Line 2423

Line 1641

the word. The English example, in its turn,

animated the French. In 1666 Louis XIV, assisted by

the counsels of M. Colbert, founded an academy of

fciences at Paris, called the<p

fciences at Paris, called the<hi rend="smallcaps">Academie</hi> <hi rend="italics">Royale des Sciences, or Royal Academy of

><hi

rend="smallcaps"

>Academie</hi> <hi

rend="italics"

>Royale des Sciences, or Royal Academy of

Sciences,</hi> for the improvement of philosophy, mathematics,

chemistry, medicine, belles-lettres, &c. Among

the principal members, at the commencement in 1666,

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Line 1661

and on the first Thursday of every month all the classes

met together, and by their secretaries made a mutual

report of what had been transacted by each class during

the preceding month.<p

the preceding month.In 1699, on the application of the president, the

>In 1699, on the application of the president, the

abbé Bignon, the academy received, under royal authority

and protection, a new form and constitution; by

the articles of which, the academy was to consist of four

sorts of members, namely honorary, pensionary, associates,

Line 2460

Line 1672

honorary class, and the secretary and treasurer to be

perpetual, and of the pensionary class. The meetings

to be twice a week, on the Wednesday and Saturday;

besides two public meetings in the year.<p

besides two public meetings in the year.Of the pensionaries, or those who receive salaries,

>Of the pensionaries, or those who receive salaries,

three to be geometricians, three astronomers, three mechanists,

three anatomists, three botanists, and three

<cb

<cb/>

chemists, the other two being the secretary and treasurer.

Of the twenty associates, of which twelve to be

French, and eight might be foreigners, two were to

Line 2477

Line 1687

nor religious to be admitted, except into the

honorary class: nor any person to be admitted a pensioner

who was not known by some considerable work,

or some remarkable discovery.<p

or some remarkable discovery.In 1716 the Duke of Orleans, then regent of France,

>In 1716 the Duke of Orleans, then regent of France,

by the king's authority made some alteration in their

constitution. The class of eleves was suppressed; and

instead of them were instituted twelve adjuncts, two to

Line 2493

Line 1702

And no person to be allowed to make use of

his quality of academician, in the title of any of his

books that he published, unless such book were first approved

by the academy.<p

by the academy.The academy has for a device or motto, <hi rend="italics">Invenit &

>The academy has for a device or motto, <hi

rend="italics"

>Invenit &

perficit.</hi> And the meetings, which were formerly held

in the king's library, have since the year 1699 been

held in a fine hall of the old Louvre.<p

held in a fine hall of the old Louvre.Finally, in the year 1785 the king confirmed, by

>Finally, in the year 1785 the king confirmed, by

letters patent, dated April 23, the establishment of the

academy of sciences, making the sollowing alterations,

and adding classes of agriculture, natural history, mineralogy,

Line 2508

Line 1713

adjuncts, and limiting to six the members of each class,

namely three pensioners and three associates; by which

the former receive an increase of salary, and the latter

approach nearer to becoming pensioners.<p

approach nearer to becoming pensioners.By the articles of this instrument it is ordained, that

>By the articles of this instrument it is ordained, that

the academy shall consist of eight classes, namely, that

of geometry, 2d astronomy, 3d mechanics, 4th general

physics, 5th anatomy, 6th chemistry and metallurgy,

Line 2520

Line 1724

perpetual secretary and treasurer, of twelve free-associates

and of eight associate strangers or foreigners, the

same as before, except that the adjunct-geographer for

the future be called the associate-geographer.<p

the future be called the associate-geographer.The classes at first to be filled by the following

>The classes at first to be filled by the following

persons, namely, that of geometry by Messieurs de

Borda, Jeaurat, Vandermonde, as pensioners; and

Messieurs Cousin, Meusnier, and Charles, as associates:

Line 2532

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Rochon, and de la Place, as pensioners; and Messieurs

Coulomb, le Gendre, and Perrier, as associates: that

of general physics by Messieurs Leroy, Brisson, and

<pb

n="15"

/><cb

Bailly, as pensioners; and Messieurs Monge, Mechain,

and Quatremere, as associates: that of anatomy by

Messieurs Daubluton, Tenon, and Portal, as pensioners;

Line 2552

Line 1752

Darcet, l'abbe Haui, and l'abbe Tessier, as associates.

All names respectable in the common-wealth of letters;

and from whom the world might expect still farther

improvements in the several branches of science.<p

improvements in the several branches of science.The late M. Rouille de Meslay, counsellor of the

>The late M. Rouille de Meslay, counsellor of the

parliament of Paris, founded two prizes, the one of

2500 livres, the other of 2000 livres, which the academy

distributed alternately every year: the subjects of

the former prize respecting physical astronomy, and of

the latter, navigation and commerce.<p

the latter, navigation and commerce.The world is highly indebted to this academy for the

>The world is highly indebted to this academy for the

many valuable works they have executed, or published,

both individually and as a body collectively, especially

by their memoirs, making upwards of a hundred

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Line 1772

in the history, the minutes or extracts from the

registers, containing some preliminary account of the

subjects of the memoires; but still however retaining

the eloges of distinguished men, lately deceased.<p

the eloges of distinguished men, lately deceased.M. l'abbe Rozier also has published in four 4to

>M. l'abbe Rozier also has published in four 4to

volumes, an excellent index of the contents of all the

volumes, and the writings of all the members, from the

beginning of their publications to the year 1770; with

convenient blank spaces for continuing the articles in

writing.<p

writing.Their history also, to the year 1697, was written by

>Their history also, to the year 1697, was written by

M. Du Hamel; and after that time continued from

year to year by M. Fontenelle, under the following titles,

Du Hamel Historiæ Regiæ Academiæ Scientiarum,

Paris, 4to. Histoire de l'Academie Royale des Sciences,

avec les Memoires de Mathematique & de Physique,

tirez des Registres de l'Academie, Paris, 4to.

Line 2594

Line 1790

the period from whence M. de Fontenelle commences,

has been formed; with a series of the works published

under the name of this academy, during the first

interval.<p

interval.Since the foregoing account was written, it is said the

>Since the foregoing account was written, it is said the

Academy has been suppressed and abolished, by the present

convention of France.<p

convention of France.Besides the academies in the capital, there are a

>Besides the academies in the capital, there are a

great many in other parts of France. The

<hi

<hi rend="smallcaps">Academie</hi> <hi rend="italics">Royale,</hi> at Caen, was established by letters

rend="smallcaps"

<cb/>

>Academie</hi> <hi

rend="italics"

>Royale,</hi> at Caen, was established by letters

<cb

patent in the year 1705; but it had its rise fifty years

earlier in private conferences, held first in the house of

M. de Brieux. M. de Segrais retiring to this city, to

Line 2619

Line 1808

number of whom was fixed to thirty, chosen for this

time by M. Foucault. But besides the thirty original

members, leave<*>was given to add six supernumerary members,

from the ecclesiastical communities in that city.<p

from the ecclesiastical communities in that city.At Toulouse is the <hi rend="italics">Academie des jeux floraux,</hi> composed

>At Toulouse is the <hi

rend="italics"

>Academie des jeux floraux,</hi> composed

of forty persons, the oldest of the kingdom: besides

an academy of sciences and belles-lettres, founded

in 1750.<p

in 1750.At Montpelier is the royal society of sciences, which

>At Montpelier is the royal society of sciences, which

since 1708 makes but one body with the royal academy

of sciences at Paris.<p

of sciences at Paris.There are also other academies at Bourdeaux, founded

>There are also other academies at Bourdeaux, founded

in 1703, at Soissons in 1674, at Marseilles in 1726,

at Lyons in 1700, at Pau in Bearn in 1721, at Montauban

in 1744, at Angers in 1685, at Amiens in 1750,

at Villefranche in 1679, at Dijon in 1740, at Nimes in

1682, at Besançon in 1752, at Chalons in 1775, at

Rochelle in 1734, at Beziers in 1723, at Rouen in

1744, at Metz in 1760, at Arras in 1773, &c.

The number of these academies is continually augmenting;

and even in such towns as have no academies,

the literati form themselves into literary societies, having

nearly the same objects and pursuits.<p

nearly the same objects and pursuits.In Germany and other parts of Europe, there are

>In Germany and other parts of Europe, there are

various academies of sciences, &c. The<hi rend="smallcaps">Academie</hi> <hi rend="italics">Royale des Sciences & des Belles Lettres</hi> of

various academies of sciences, &c. The<p

><hi

rend="smallcaps"

>Academie</hi> <hi

rend="italics"

>Royale des Sciences & des Belles Lettres</hi> of

Prussia, was founded at Berlin, in the year 1700, by

Frederic I. king of Prussia, of which the famous

M. Leibnitz was the first president, and its great promoter.

Line 2667

Line 1845

of any of the classes have free access into the assemblies

of the rest. Several volumes of their transactions have

been published in Latin, from time to time, under the

title of Miscellanea Berolinensia.<p

title of Miscellanea Berolinensia.In 1743 the late famous Frederic II. king of Prussia,

>In 1743 the late famous Frederic II. king of Prussia,

made great alterations and improvements in the academy.

Instead of a great lord or minister of state,

who had usually presided over the academy, he wisely

Line 2678

Line 1855

namely M. Maupertuis, a distinguished character

in the literary world, and whose conduct in improving

the academy was a proof of the sound judgment of the

<pb

n="16"

/><cb

king, who at the same time made new regulations for

the academy, and took the title of its Protector.

From that time the transactions of the academy have

been published, under the title of Histoire de l'Academie

Royale des Sciences et Belles Lettres à Berlin, much

in the manner of those of the French academy of sciences,

and in the French language; and the volumes

are now commonly published annually. Besides the ordinary

Line 2699

Line 1873

circumstance, that it embraces also metaphysics,

logic, and morality; having one class particularly appropriated

to these objects, called the class of Speculative

Philosophy.<p

Philosophy.<hi rend="italics">Imperial</hi> <hi rend="smallcaps">Academy</hi> <hi rend="italics">of Petersburgh.</hi> This academy

><hi

rend="italics"

>Imperial</hi> <hi

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>of Petersburgh.</hi> This academy

was projected by the Czar Peter I, commonly called

Peter the Great, who in so many other instances also

was instrumental in raising Russia from the state of barbarity

Line 2723

Line 1890

academy, by his consort the czarina Catherine, who

succeeded him. And soon after the academy composed

the first volume of their works, published in 1728,

under the title of Commentarii Academiæ Scientiarum

Imperialis Petropolitanæ; which they continued almost

annually till 1746, the whole amounting to 14 volumes,

which were published in Latin, and the subjects divided

and classed under the following heads, namely mathematics,

physics, history, and astronomy. Their device

a tree bearing fruit not ripe, with the modest motto

<hi

<hi rend="italics">paullatim.</hi>Most part of the strangers who composed this academy

rend="italics"

>paullatim.</hi><p

>Most part of the strangers who composed this academy

being dead, or having retired, it was rather in a

languishing state at the beginning of the reign of the

empress Elizabeth, when the count Rasomowski was

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Line 1917

was published for the years 1747 and 1748, and

they have been fince continued from year to year, now

to the amount of near thirty volumes, under the title of

Novi Commentarii Academiæ Scientiarum Imperialis

<cb

<cb/>

Petropolitanæ. They are printed in the Latin language,

and contain many excellent compositions in all

the sciences, especially the mathematical papers of the

late excellent M. L. Euler, which always made a considerable

Line 2768

Line 1931

or memoir, after the manner of the volumes of the

French academy; but wanting however the eloges of

deceased eminent men. Their device is a heap of ripe

fruits piled on a table, with the motto <hi

fruits piled on a table, with the motto <hi rend="italics">En addit fructus

rend="italics"

ætate recentes.</hi><hi rend="italics">Imperial and Royal</hi> <hi rend="smallcaps">Academy</hi> <hi rend="italics">of Sciences and Belles

>En addit fructus

ætate recentes.</hi><p

><hi

rend="italics"

>Imperial and Royal</hi> <hi

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>of Sciences and Belles

Lettres, at Brussels.</hi> This academy was founded in the

year 1773; and several volumes of their memoirs have

been published.<p

been published.<hi rend="italics">Royal</hi> <hi rend="smallcaps">Academy</hi> <hi rend="italics">of Sciences,</hi> at Stockholm, was instituted

><hi

rend="italics"

>Royal</hi> <hi

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>of Sciences,</hi> at Stockholm, was instituted

in 1739, and since that time it has published

about sixty volumes of transactions, quarterly, in 8vo,

in the Swedish language.<p

in the Swedish language.For an account of the Royal Society of London,

>For an account of the Royal Society of London,

and several other similar institutions, see the words

Journal, Society, &c.<p

Journal, Society, &c.<hi rend="italics">American</hi> <hi rend="smallcaps">Academy</hi> <hi rend="italics">of Arts and Sciences,</hi> was established

><hi

rend="italics"

>American</hi> <hi

rend="smallcaps"

>Academy</hi> <hi

rend="italics"

>of Arts and Sciences,</hi> was established

in 1780 by the council and house of representatives

in the province of Massachuset's Bay, for

promoting the knowledge of the antiquities of America,

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Line 1955

which may tend to advance the interest, honour, dignity,

and happiness, of a free, independent, and virtuous

people. The members of this academy are never

to be less than forty, nor more than two hundred.<p

to be less than forty, nor more than two hundred.<hi rend="smallcaps">Academy</hi> is also used among us for a kind of collegiate

><hi

rend="smallcaps"

>Academy</hi> is also used among us for a kind of collegiate

school, or seminary; where youth are instructed

in the liberal arts and sciences in a private way: now

indeed it is used for all kinds of schools.<p

indeed it is used for all kinds of schools.Frederic 1, king of Prussia, established an academy

>Frederic 1, king of Prussia, established an academy

at Berlin in 1703, for educating the young nobility of

the court, suitable to their extraction. The expence

of the students was very moderate, the king having

undertaken to pay the extraordinaries. This illustrious

school, which was then called the academy of

princes, has now lost much of its first splendour.<p

princes, has now lost much of its first splendour.The Romans had a kind of military academies established

>The Romans had a kind of military academies established

in all the cities of Italy, under the name of

<hi

<hi rend="italics">Campi Martis.</hi> Here the youth were admitted to be

rend="italics"

>Campi Martis.</hi> Here the youth were admitted to be

trained sor war at the public expence. And the

Greeks, besides academies of this kind, had military

professors, called <hi

professors, called <hi rend="italics">Tactici,</hi> who taught all the higher

rend="italics"

offices of war, &c.We have two royal academies of this kind in England,

>Tactici,</hi> who taught all the higher

offices of war, &c.<p

>We have two royal academies of this kind in England,

the expences of which are defrayed by the government;

the one at Woolwich, for the artillery and

military engineers; and the other at Portsmouth, for

the navy. The former was established by his late

<pb

n="17"

/><cb

majesty king George II, by warrants dated April the 30th

and November the 18th, 1741, for instructing persons

belonging to the military part of the ordnance, in the

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Line 2009

for the purposes of the institution; and that the

salaries of the professors and masters should be so inadequate

to their labours, and the benefit of their

services.<p

services.The Royal Naval Academy at Portsmouth was

>The Royal Naval Academy at Portsmouth was

founded by George I, in 1722, for instructing young

gentlemen in the sciences useful for navigation, to

breed officers for the royal navy. The establishment

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Line 2017

give salaries to two masters, by one of whom the students

are boarded and lodged, the expence of which

is defrayed by their own friends, nothing being supplied

by the government but their education.</div2></div1><div1

by the government but their education.</div2></div1><div1 part="n" n="ACANTHUS" org="uniform" sample="complete" type="entry"><head>ACANTHUS</head>, <hi rend="italics">in Architecture,</hi> the leaves of a plant

part="n"

n="ACANTHUS"

org="uniform"

sample="complete"

type="entry"

><head

>ACANTHUS</head><p

>, <hi

rend="italics"

>in Architecture,</hi> the leaves of a plant

which forms the ornament of the capital of the Corinthian

order. Vitruvius ascribes the use of it to the

following accident. A young girl dying, her nurse

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in a manner embraced the basket; which Callimachus,

a noted Greek sculptor, casting his eyes upon, from

thence took the hint of this elegant ornament. See

<hi

<hi rend="smallcaps">Abacus.</hi>ACCELERATED <hi rend="italics">Motion,</hi> is that which receives

rend="smallcaps"

>Abacus.</hi><p

>ACCELERATED <hi

rend="italics"

>Motion,</hi> is that which receives

fresh accessions of velocity; and the acceleration may be

either equably or unequably: if the accessions of velocity

be always equal in equal times, the motion is

said to be equably or uniformly accelerated; but if the

<cb

<cb/>

accessions, in equal times, either increase or decrease,

then the motion is unequably or variably accelerated.<p

then the motion is unequably or variably accelerated.Acceleration is directly opposite to retardation,

>Acceleration is directly opposite to retardation,

which denotes a diminution of velocity.<hi rend="smallcaps">Acceleration</hi> comes chiefly under consideration

which denotes a diminution of velocity.<p

><hi

rend="smallcaps"

>Acceleration</hi> comes chiefly under consideration

in physics, in the descent of heavy bodies, tending or

falling towards the centre of the earth, by the force of

gravity.<p

gravity.That bodies are accelerated in their natural descent,

>That bodies are accelerated in their natural descent,

is evident both to the sight, and from observing that

the greater height they fall from, the greater force they

strike with, and the deeper impressions they make in

soft substances.<p

soft substances.The acceleration of falling bodies has been ascribed

>The acceleration of falling bodies has been ascribed

to various causes, by different philosophers. Some

have attributed it to the pressure of the air downwards:

the more a body descends, the longer and

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whole mass; and that consequently the nearer a body

approaches to it, the more must it receive of the

pressure of a multitude of lines tending to unite in

the central point.<p

the central point.Mr. Hobbes endeavours to account for this acceleration

>Mr. Hobbes endeavours to account for this acceleration

from a new impression of the cause which makes

bodies fall; in which he is so far right. But then he

as far mistakes, as to the cause of the fall, which he

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circular and progressive, the air must at once both

ascend and circulate; whence it follows, that a body

falling in this medium, and receiving a new pressure

every instant, must have its motion accelerated.<p

every instant, must have its motion accelerated.But to both these systems it may be answered, that

>But to both these systems it may be answered, that

the air is quite out of the question; for it is very evident

that bodies fall, and in falling have their motion

accelerated, in vacuo, as in open air, and even more

than in the air, in as much as this opposes and somewhat

retards their fall.<p

retards their fall.The Gassendists assign another reason for the acceleration:

>The Gassendists assign another reason for the acceleration:

they pretend that there are continually issuing

out of the earth certain attractive corpuscles, directed

in an infinite number of rays; those, say they,

afcend and then descend, in such sort that the nearer a

body approaches to the earth's centre, the more of

these attractive rays press upon it, in consequence of

which its motion becomes more accelerated.<p

which its motion becomes more accelerated.The peripatetics endeavour to explain the matter

>The peripatetics endeavour to explain the matter

thus: the motion of heavy bodies downward, arises,

say they, out of an intrinsic principle that causes a

tendency in them to the centre, as the place appropriated

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arrive, they will be at perfect rest; and therefore, continue

they, the nearer bodies approach to it, the more

the velocity of their motion is increased: a notion too

idle to merit confutation.<p

idle to merit confutation.The Cartesians account for acceleration, by reiterated

>The Cartesians account for acceleration, by reiterated

impulses of their <hi rend="italics">materia subtilis,</hi> acting continually

impulses of their <hi

rend="italics"

>materia subtilis,</hi> acting continually

<pb

n="18"

/><cb

on falling bodies, and propelling them downwards: a

conceit equally unintelligible and absurd with the

former.<p

former.But, leaving all such visionary causes of acceleration,

>But, leaving all such visionary causes of acceleration,

and only admitting the existence of such a force as gravity,

so evidently inherent in all bodies, without regard

to what may be the cause of it, the whole mystery of

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on heavy bodies; and it will be easy to conceive

that the principle of gravitation, which determines

bodies to descend, must by a necessary consequence

accelerate them in falling.<p

accelerate them in falling.A body then having once begun to descend, through

>A body then having once begun to descend, through

the impulse of gravity; the state of descending is now,

by Newton's first law of nature, become as it were natural

to it; insomuch that, were it left to itself, it

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than what either could produce separately.

And as long as the velocity is thus continued, the same

cause still subsisting to increase it more, the descent

must of necessity be continually accelerated.<p

must of necessity be continually accelerated.Supposing then that gravity, from whatever principle

>Supposing then that gravity, from whatever principle

it arises, acts uniformly upon all bodies at the

same distance from the centre of the earth: dividing

the time which the heavy body takes up in falling to

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body will continue perpetually to advance uniformly

toward the earth's centre, with an indefinitely small

velocity, equal to that which resulted from the first

impulse.<p

impulse.But then if we suppose that the action of gravity

>But then if we suppose that the action of gravity

still continues the same after the first impulse; in the

second instant, the body will receive a new impulse toward

the earth, equal to that which it received in the

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on continually: for the impulse made in any preceding

instant, is no ways altered by that which is made in the

following one; but they are, on the contrary, always

accumulated on each other.<p

accumulated on each other.So that the instants of time being supposed indefinitely

>So that the instants of time being supposed indefinitely

small, and all equal, the velocity acquired by

the falling body, will be, in every instant, proportional

to the times from the beginning of the descent; and

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time in which it is produced. So that if a body, by

this constant force, acquire a velocity of 16 1/12 feet suppose

in one second of time; it will acquire a velocity

<cb

<cb/>

of 32 1/6 feet in two seconds, 48 1/4 feet in 3 seconds,

64 1/3 in 4 seconds, and so on. Nor ought it to seem

strange that all bodies, small or large, acquire, by the

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and in the same manner, as if its particles were not

united, but as if each fell by itself, separated all from one

another. And thus all being let go at once, they would

fall together, just as if they were united into one mass.<p

fall together, just as if they were united into one mass.The foregoing law of the descent of falling bodies,

>The foregoing law of the descent of falling bodies,

namely that the velocities are always proportional to

the times of descent, as well as the following laws concerning

the spaces passed over, &c, were first discovered

and taught by the great Galileo, and that nearly in the

following manner.<p

following manner.Because the constant velocity with which any body

>Because the constant velocity with which any body

moves, or the space it passes over in a given time, as

suppose one second, being multiplied by the time, or

number of seconds it is in motion, expresses the space

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denotes the length, and the velocity the breadth. Suppose

then A to be the heavy body which descends, and

AB to denote the whole time of any descent; which

<figure

></figure>

let be divided into a certain number of equal parts,

denoting intervals or portions of the given time, as

AC, CD, DE, &c. Imagine the body to descend,

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AF, the breadth of the rectangle CF; then the space

run through during the time denoted by AC, with the

velocity denoted by AF, will be expressed by the rectangular

space CF.<p

space CF.Now the action of gravity having produced, in the

>Now the action of gravity having produced, in the

first moment, the velocity AF, in the body, before at

rest; in the first two moments it will produce the velocity

CG, the double of the former; in the third moment,

to the velocity CG will be added one degree

<pb

n="19"

/><cb

more, by which means will be produced the velocity

DH, triple of the first; and so of the rest; so that

during the whole time AB, the body will have acquired

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we may say, all at once, at the end of certain portions

of finite time; for instance at C, at D, &c; so that the

degree of motion remains the same to the instant that a

new acceleration takes place.<p

new acceleration takes place.By conceiving the divisions of time to be shorter,

>By conceiving the divisions of time to be shorter,

for example but half as long as the former, the indentures

of the figure will be proportionably more

contracted, and it will approach nearer to a triangle;

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time, which is really the case, the rectangles so successively

produced, will form a true triangle, as ABC;

the whole time AB consisting of minute portions A 1,

<figure

></figure>

12, 23, &c; and the area of the triangle ABC, of

all the minute surfaces, or minute trapeziums, which

answer to the divisions of the times; the area of the

whole triangle ABC, denoting the space run through

during the whole time AB; and the area of any

smaller triangle A 7 <hi

smaller triangle A 7 <hi rend="italics">g,</hi> denoting the space run through

rend="italics"

>g,</hi> denoting the space run through

during the corresponding time A 7. Bnt the triangles

A 1 <hi

A 1 <hi rend="italics">a,</hi> A 7 <hi rend="italics">g,</hi> &c, being similar, have their areas to

rend="italics"

>a,</hi> A 7 <hi

rend="italics"

>g,</hi> &c, being similar, have their areas to

each other as the squares of their like sides A 1, A 7,

&c; and consequently the spaces gone through, in

any times counted from the beginning, are to each

other as the squares of the times.<p

other as the squares of the times.Hence, in any right-angled triangle, as ABC, the

>Hence, in any right-angled triangle, as ABC, the

one side AB represents the time, the other side BC

the velocity acquired in that time, and the area of the

triangle the space described by the falling body.<p

triangle the space described by the falling body.From the preceding demonstration is also drawn

>From the preceding demonstration is also drawn

this other general theorem in motions that are uniformly

accelerated; namely, that a body descending

with a uniformly accelerated motion, describes in the

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whole space which the falling body has run through in

the time AB, is represented by the triangle ABC,

the last velocity being BC; and the space which the

<cb

<cb/>

body would run through uniformly in the same time

AB, constantly with the said greatest velocity BC, is

represented by the rectangle ABCD: but it is well

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through by the accelerated motion, is just half of that

which the body would describe in the same time, moving

uniformly with the velocity acquired at the end of

its accelerated fall.<p

its accelerated fall.Hence then, from the foregoing considerations are

>Hence then, from the foregoing considerations are

deduced the following general laws of uniformly accelerated

motions, namely,<p

motions, namely,1st. That the velocities acquired, are constantly proportional

>1st. That the velocities acquired, are constantly proportional

to the times; in a double time a double velocity,

&c.<p

&c.2d. That the spaces described in the whole times,

>2d. That the spaces described in the whole times,

each counted from the commencement of the motion,

are proportional to the squares of the times, or to the

squares of the velocities; that is, in twice the time,

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on. And as the spaces fallen through are as the

squares of the times, or of the velocities; therefore the

times, or the velocities, are proportional to the square

roots of the spaces.<p

roots of the spaces.3d. The spaces described by falling bodies, in a

>3d. The spaces described by falling bodies, in a

series of equal instants or intervals of time, will be as

the odd numbers 1, 3, 5, 7, 9, &c,

<hi

rend="brace"

><note

anchored="yes"

place="unspecified"

>1, 4, 9, 16, 25, &c,</note>

which are the differences of

the squares or whole spaces</hi>

that is, the body which has run through 16 1/12 feet in the

firft second, will in the next second run through 48 1/3

feet, in the third second 80 3/12, and so on.<p

feet, in the third second 80 3/12, and so on.4th. If the body fall through any space in any time,

>4th. If the body fall through any space in any time,

it acquires a velocity equal to double that space; that

is, in an equal time, with the last velocity acquired, if

uniformly continued, it would pass over just double the

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over 32 1/6 feet in this one second: and if in any time

the body fall through 100 feet; then in another equal

time, if it move uniformly with the velocity last acquired,

it will pass over 200 feet. And so on.<p

it will pass over 200 feet. And so on.But, as the method of demonstration used by Galileo,

>But, as the method of demonstration used by Galileo,

by means of infinitely small parts forming a regular

triangle, is not approved of by many persons, the same

laws may be otherwise demonstrated thus: let the

whole time of a body's free descent be divided into

any number of parts, calling each of these parts 1; and

let <hi

let <hi rend="italics">a</hi> denote the velocity acquired at the end of the first

rend="italics"

>a</hi> denote the velocity acquired at the end of the first

part of time; then will 2<hi rend="italics">a,</hi> 3<hi rend="italics">a,</hi> 4<hi rend="italics">a,</hi> &c, represent

<pb

n="20"

/><cb

part of time; then will 2<hi

rend="italics"

>a,</hi> 3<hi

rend="italics"

>a,</hi> 4<hi

rend="italics"

>a,</hi> &c, represent

the velocities at the end of the 2d, 3d, 4th, &c, part of

time, because the velocities are as the times; and for

the same reason 1/2<hi

the same reason 1/2<hi rend="italics">a,</hi> 3/2<hi rend="italics">a,</hi> 5/2<hi rend="italics">a,</hi> &c, will be the

rend="italics"

>a,</hi> 3/2<hi

rend="italics"

>a,</hi> 5/2<hi

rend="italics"

>a,</hi> &c, will be the

velocities at

the middle point of the first, second, third, &c, part of

time. But now as the velocities increase uniformly,

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middle velocity, or the velocity in the middle of that

part of time; and therefore multiplying those mean

velocities each by their common time 1, we have the

same fractions 1/2<hi

same fractions 1/2<hi rend="italics">a,</hi> 3/2<hi rend="italics">a,</hi> 5/2<hi rend="italics">a,</hi> &c, for the spaces

rend="italics"

>a,</hi> 3/2<hi

rend="italics"

>a,</hi> 5/2<hi

rend="italics"

>a,</hi> &c, for the spaces

passed

over in the successive parts of the time; that is, the

space 1/2<hi

space 1/2<hi rend="italics">a</hi> in the first time, 3/2<hi rend="italics">a</hi> in the second, 5/2<hi rend="italics">a</hi>

rend="italics"

>a</hi> in the first time, 3/2<hi

rend="italics"

>a</hi> in the second, 5/2<hi

rend="italics"

>a</hi>

in the

third, and so on: then add these spaces successively to

one another, and we obtain 1/2<hi

one another, and we obtain 1/2<hi rend="italics">a,</hi> 4/2<hi rend="italics">a,</hi> 9/2<hi rend="italics">a,</hi>

rend="italics"

16/2<hi rend="italics">a,</hi> &c, for

>a,</hi> 4/2<hi

rend="italics"

>a,</hi> 9/2<hi

rend="italics"

>a,</hi>

16/2<hi

rend="italics"

>a,</hi> &c, for

the whole spaces described from the beginning of the

motion to the end of the first, second, third, &c, portion

of time; namely 1/2<hi

of time; namely 1/2<hi rend="italics">a</hi> space in one time, 4/2<hi rend="italics">a</hi> in 2

rend="italics"

times, 9/2<hi rend="italics">a</hi> in 3 times, and so on: and it is evident that

>a</hi> space in one time, 4/2<hi

rend="italics"

>a</hi> in 2

times, 9/2<hi

rend="italics"

>a</hi> in 3 times, and so on: and it is evident that

these spaces are as the numbers 1, 4, 9, 16, &c, which

are as the squares of the times.<p

are as the squares of the times.And from this mode of demonstration, all the properties

>And from this mode of demonstration, all the properties

above mentioned evidently flow: such as that

the whole spaces 1/2<hi

the whole spaces 1/2<hi rend="italics">a,</hi> 4/2<hi rend="italics">a,</hi> 9/2<hi rend="italics">a,</hi> &c,

rend="italics"

>a,</hi> 4/2<hi

rend="italics"

>a,</hi> 9/2<hi

rend="italics"

>a,</hi> &c,

are as the squares of the times 1, 2, 3, &c,

that the separate spaces 1/2<hi

that the separate spaces 1/2<hi rend="italics">a,</hi> 3/2<hi rend="italics">a,</hi> 5/2<hi rend="italics">a,</hi> &c,

rend="italics"

>a,</hi> 3/2<hi

rend="italics"

>a,</hi> 5/2<hi

rend="italics"

>a,</hi> &c,

<hi

rend="brace"

><note

anchored="yes"

place="unspecified"

>1, 3, 5, &c,</note>

described in the successive times,

are as the odd numbers</hi>

and that the velocity <hi

and that the velocity <hi rend="italics">a</hi> acquired in any time 1, is

rend="italics"

double the space 1/2<hi rend="italics">a</hi> described in the same time.As the laws of acceleration are very important, I

>a</hi> acquired in any time 1, is

double the space 1/2<hi

rend="italics"

>a</hi> described in the same time.<p

>As the laws of acceleration are very important, I

shall here insert the two following propositions, sent

me by my learned friend Mr. Abram Robertson, of

Christ Church College Oxford, in which those laws are

demonstrated in a manner somewhat different.

<hi

<hi rend="center">“<hi rend="smallcaps">Ppoposition</hi> 1.</hi>If from the point P in the straight line AB, the

rend="center"

>“<hi

rend="smallcaps"

>Ppoposition</hi> 1.</hi><p

>If from the point P in the straight line AB, the

points M, N begin to move at the same time, namely,

M towards A with a motion, uniformly retarded, and

N from rest towards B with a motion uniformly accelerated;

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the velocity of N increases in the same time; then the

space MN is generated by an uniform motion, equal

to the velocity with which M begins to move.

<figure

<figure/>For, by hypothesis, whatever is lost in the velocity

></figure><p

>For, by hypothesis, whatever is lost in the velocity

of M by retardation, is added to the velocity of N by

acceleration: the joint velocities, therefore, of M and N

must always be equal. But it is by the joint velocities

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MN is generated by an uniform motion,

which is evidently equal to the velocity with which

M begins to move.

<hi

<hi rend="center">“<hi rend="smallcaps">Proposition</hi> II.</hi>If a point begins to move in the direction of a

rend="center"

>“<hi

rend="smallcaps"

>Proposition</hi> II.</hi><p

>If a point begins to move in the direction of a

straight line, and continues to move in the same di-

<cb

<cb/>

rection with a velocity uniformly aocelerated; the

space passed over in any given time, will be equal to

half the space passed over in the same time with the

velocity with which the acceleration ends.<p

velocity with which the acceleration ends.Let the point D begin to move from A towards B,

>Let the point D begin to move from A towards B,

along the straight line AB, with a motion unisormly

accelerated; the space AD passed over, is equal to

half the space which the point would pass over, in the

same time with the acquired velocity at D.

<figure

<figure/>Let the points M, N begin to move in the straight

></figure><p

>Let the points M, N begin to move in the straight

line GH, at the same time, with equal velocities uniformly

accelerated; M beginning to move from G,

and N from P; and at the same time that M comes to

the point P, let N come to H. Then as M and N

<figure

></figure>

move with equal velocities, uniformly accelerated, it is

evident that the spaces, which they pass over in the

same time, are equal to one another; consequently the

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over with the velocity of N at H, in the same time

that PH is passed over by N beginning to move from

P with a velocity uniformly accelerated to H. But

PH is half of GH. “Hence the prop. is manifest.”<p

PH is half of GH. “Hence the prop. is manifest.”And hence the other laws of the spaces, before<*>

>And hence the other laws of the spaces, before<*>

mentioned, easily follow.Since the spaces descended are as the squares of the

mentioned, easily follow.<p

>Since the spaces descended are as the squares of the

times, and the abscisses of a parabola are as the squares

of the ordinates, therefore the relation of the times and

spaces descended may be very well represented by the

ordinates and abscisses of that figure. Thus if AB be

the axis of the parabola A<hi

the axis of the parabola A<hi rend="italics">bdfh,</hi> and AC a tangent

rend="italics"

>bdfh,</hi> and AC a tangent

<pb

n="21"

/><cb

<figure

></figure>

at the vertex perpendicular to

the axis, divided into any number

of equal parts A<hi

of equal parts A<hi rend="italics">a, ac, ce,</hi>

rend="italics"

>a, ac, ce,</hi>

&c, for the times; and if there

be drawn <hi

be drawn <hi rend="italics">ab, cd, ef,</hi> &c, parallel

rend="italics"

to the axis: hence if <hi rend="italics">ab</hi>

>ab, cd, ef,</hi> &c, parallel

to the axis: hence if <hi

rend="italics"

>ab</hi>

be the space descended in the

time A<hi

time A<hi rend="italics">a,</hi> then <hi rend="italics">cd</hi> will be the

rend="italics"

>a,</hi> then <hi

rend="italics"

>cd</hi> will be the

space descended in the time

A<hi

A<hi rend="italics">c,</hi> and <hi rend="italics">ef</hi> the space defcended

rend="italics"

in the time A<hi rend="italics">e,</hi> and so on continually.From the properties above-demonstrated, are derived

>c,</hi> and <hi

rend="italics"

>ef</hi> the space defcended

in the time A<hi

rend="italics"

>e,</hi> and so on continually.<p

>From the properties above-demonstrated, are derived

the following practical formulas or theorems for use.

Namely, if <hi

Namely, if <hi rend="italics">g</hi> denote the space passed over in the first

rend="italics"

>g</hi> denote the space passed over in the first

second of time, by a body urged by any constant force,

denoted by 1, and <hi

denoted by 1, and <hi rend="italics">t</hi> denote the time or number of seconds

rend="italics"

in which the body passes over any other space <hi rend="italics">s,</hi>

>t</hi> denote the time or number of seconds

and <hi rend="italics">v</hi> the velocity acquired at the end of that time;

in which the body passes over any other space <hi

then from the foregoing laws we have <hi rend="italics">v</hi> = 2<hi rend="italics">gt,</hi> and

rend="italics"

<hi rend="italics">s</hi> = <hi rend="italics">gt</hi><hi rend="sup">2</hi>; and from these two equations result the

>s,</hi>

following general formulas:And here, when the constant force 1, is the natural

and <hi

force of gravity, then the distance <hi rend="italics">g</hi> descended in the

rend="italics"

>v</hi> the velocity acquired at the end of that time;

then from the foregoing laws we have <hi

rend="italics"

>v</hi> = 2<hi

rend="italics"

>gt,</hi> and

<hi

rend="italics"

>s</hi> = <hi

rend="italics"

>gt</hi><hi

rend="sup"

>2</hi>; and from these two equations result the

following general formulas:<p

>And here, when the constant force 1, is the natural

force of gravity, then the distance <hi

rend="italics"

>g</hi> descended in the

first second, in the latitude of London, is 16 1/12 feet:

but if it be any other constant force, the value of <hi

but if it be any other constant force, the value of <hi rend="italics">g</hi>

rend="italics"

>g</hi>

will be different, in proportion as the force is more or

less.<p

less.The motion of an ascending body, or of one that

>The motion of an ascending body, or of one that

is impelled upwards, is diminished or retarded by the

same principle of gravity, acting in a contrary direction,

after the same manner that a falling body is accelerated.<p

after the same manner that a falling body is accelerated.A body projected upwards, ascends until it has lost

>A body projected upwards, ascends until it has lost

all its motion; which it does in the same space of time,

that the body would have taken up in acquiring, by

falling, a velocity equal to that with which the falling

body began to be projected upwards. And consequently

the heights to which bodies ascend, when projected

upwards with different velocities, are to each

other as the squares of those velocities.<p

other as the squares of those velocities.<hi rend="smallcaps">Accelerated</hi> <hi rend="italics">Motion of Bodies on Inclined Planes.</hi>

><hi

rend="smallcaps"

>Accelerated</hi> <hi

rend="italics"

>Motion of Bodies on Inclined Planes.</hi>

The same general laws obtain here, as in bodies falling

freely, or perpendicularly; namely, that the velocities

are as the times, and the spaces descended down the

planes as the squares of the times, or of the velocities.

But those velocities are less, according to the sine of

the plane's inclination; and the spaces less, according

to the square of the sine. See <hi

to the square of the sine. See <hi rend="smallcaps">Inclined</hi> <hi rend="italics">Plane.</hi><hi rend="smallcaps">Accelerated</hi> <hi rend="italics">Motion of Pendulums.</hi> See P<hi rend="smallcaps">ENDULUM.</hi><hi rend="smallcaps">Accelerated</hi> <hi rend="italics">Motion of Projectiles.</hi> See P<hi rend="smallcaps">ROJECTILE.</hi><hi rend="smallcaps">Accelerated</hi> <hi rend="italics">Motion of Compressed Bodies,</hi> in ex-

rend="smallcaps"

<cb/>

>Inclined</hi> <hi

panding or restoring themselves. See <hi rend="smallcaps">Dilatation,

rend="italics"

Compression</hi>, and <hi rend="smallcaps">Elasticity.</hi><hi rend="smallcaps">Accelerating Force</hi>, in Physics, is the force

>Plane.</hi><p

><hi

rend="smallcaps"

>Accelerated</hi> <hi

rend="italics"

>Motion of Pendulums.</hi> See P<hi

rend="smallcaps"

>ENDULUM.</hi><p

><hi

rend="smallcaps"

>Accelerated</hi> <hi

rend="italics"

>Motion of Projectiles.</hi> See P<hi

rend="smallcaps"

>ROJECTILE.</hi><p

><hi

rend="smallcaps"

>Accelerated</hi> <hi

rend="italics"

>Motion of Compressed Bodies,</hi> in ex-

<cb

panding or restoring themselves. See <hi

rend="smallcaps"

>Dilatation,

Compression</hi>, and <hi

rend="smallcaps"

>Elasticity.</hi><p

><hi

rend="smallcaps"

>Accelerating Force</hi>, in Physics, is the force

that accelerates the motion or velocity of bodies;

and it is equal to, or expressed by, the quotientarising

from the motive or absolute force, divided by the

Line 3619

Line 2508

the body drawn along the plane doubled; then the accelerating

force will be only one-third of what it was

at first, and the space descended in one second, and velocity

acquired, each one-third of the sirst: and so on.<p

acquired, each one-third of the sirst: and so on.But accelerating forces are sometimes variable, as

>But accelerating forces are sometimes variable, as

well as sometimes constant; and the variation may be

either increasing or decreasing.<p

either increasing or decreasing.The nature of constant and variable accelerating

>The nature of constant and variable accelerating

forces, may be illuftrated in the following manner.

Let two weights W, <hi

Let two weights W, <hi rend="italics">w,</hi> be connected by a thread

rend="italics"

>w,</hi> be connected by a thread

<figure

></figure>

passing over a pully at A, B, or C; and let the weight

W descend perpendicularly down, while it draws the

smaller weight <hi

smaller weight <hi rend="italics">w</hi> up the line AD, or BE, or CF, the

rend="italics"

>w</hi> up the line AD, or BE, or CF, the

<pb

n="22"

/><cb

first being a straight inclined plane, and the other two

curves, the one convex and the other concave to the

perpendicular. Then the small weight <hi

perpendicular. Then the small weight <hi rend="italics">w</hi> will always make

rend="italics"

>w</hi> will always make

some certain resistance to the free descent of the large

weight W, and that resistance will be constantly the

same in every part of the plane AD, the difficulty to

Line 3654

Line 2531

be always equal in equal times; that is, in this case W

descends by a uniformly accelerating force. But in

the two curves BE, CF, the resistance or opposition

of the small weight <hi

of the small weight <hi rend="italics">w</hi> will be constantly altering as it

rend="italics"

>w</hi> will be constantly altering as it

is drawn up the curves, because every part of them has

a different inclination to the horizon, or to the perpendicular:

in the former curve, the direction becomes

more and more upright, or nearer perpendicular, as the

small weight <hi

small weight <hi rend="italics">w</hi> ascends, and the opposition it makes to

rend="italics"

>w</hi> ascends, and the opposition it makes to

the descent of W, becomes more and more; and consequently

the accessions to the velocity of W will be

always less and less in equal times; that is, W descends

by a decreasing accelerating force: but in the latter

curve CF, as <hi

curve CF, as <hi rend="italics">w</hi> ascends, the direction of the curve becomes

rend="italics"

>w</hi> ascends, the direction of the curve becomes

less and less upright, and the opposition it makes

to the descent of W, becomes always less and less; and

consequently the accessions to the velocity of W will

Line 3681

Line 2552

the times of motion, in the plane AD; the velocity

increases in a less ratio than the time it ascended up

BE, and in a greater ratio than the time increases in

the other curve CF.<p

the other curve CF.Now the relations between the times and velocities

>Now the relations between the times and velocities

in all these cases, may be very well represented by the

relations between the abscisses and ordinates of certain

lines. Thus let AB and AC be two straight lines,

<figure

></figure>

making any angle BAC; and AD, AE two curves,

the former concave, and the latter convex towards AB:

divide AB into any parts A<hi

divide AB into any parts A<hi rend="italics">a,</hi> A<hi rend="italics">b,</hi> &c, representing

rend="italics"

>a,</hi> A<hi

rend="italics"

>b,</hi> &c, representing

the times of motion; and draw the perpendiculars

<hi

<hi rend="italics">acde, bfgh,</hi> &c, representing the velocities. Then

rend="italics"

in the right line AC, the ordinates <hi rend="italics">ad, bg,</hi> being as

>acde, bfgh,</hi> &c, representing the velocities. Then

the abscisses A<hi rend="italics">a,</hi> A<hi rend="italics">b,</hi> this represents the case of uniformly

in the right line AC, the ordinates <hi

rend="italics"

>ad, bg,</hi> being as

the abscisses A<hi

rend="italics"

>a,</hi> A<hi

rend="italics"

>b,</hi> this represents the case of uniformly

accelerated motion, in which the velocities are

always as the times: but in the curve AD, the ordinates

<hi

<hi rend="italics">ac, bf</hi> increase in a less ratio than the abscisses

rend="italics"

A<hi rend="italics">a,</hi> A<hi rend="italics">b;</hi> and therefore this represents the case of

>ac, bf</hi> increase in a less ratio than the abscisses

A<hi

rend="italics"

>a,</hi> A<hi

rend="italics"

>b;</hi> and therefore this represents the case of

decreasing acceleration, in which the velocities increase

<cb

<cb/>

in a less ratio than the times: and in the other curve

AE, the ordinates <hi

AE, the ordinates <hi rend="italics">ae, bh</hi> increase in a greater ratio

rend="italics"

>ae, bh</hi> increase in a greater ratio

than the abscisses; and therefore this represents the

case of increasing acceleration, in which the velocities

increase in a greater ratio than the times.<p

increase in a greater ratio than the times.The several algebraic formulas or theorems, respecting

>The several algebraic formulas or theorems, respecting

the time, velocity, space, for constant accelerating

forces, are delivered above, at the article <hi

forces, are delivered above, at the article <hi rend="italics">Accelerated Motion,</hi>

rend="italics"

>Accelerated Motion,</hi>

where the value of each circumstance is expressed in

finite determinate quantities. But in the cases of variably

accelerated motions, the formulas will require the

Line 3739

Line 2584

general relations themselves, but the fluxions of them;

and consequently, taking the fluents of those expressions,

in particular cases, the relations of time,

space, velocity, &c, are obtained.<p

space, velocity, &c, are obtained.Now if <hi rend="italics">t</hi> denote the time in motion,

>Now if <hi

<hi rend="italics">v</hi> the velocity generated by any force,

rend="italics"

<hi rend="italics">s</hi> the space passed over,

>t</hi> denote the time in motion,

and 2<hi rend="italics">g</hi> the variable force at any part of the motion,

<hi

rend="italics"

>v</hi> the velocity generated by any force,

<hi

rend="italics"

>s</hi> the space passed over,

and 2<hi

rend="italics"

>g</hi> the variable force at any part of the motion,

or the velocity the force would generate in one second

of time, if it should continue invariable, like the force

of gravity, during that one second; and therefore the

value of this velocity 2<hi

value of this velocity 2<hi rend="italics">g,</hi> will be in proportion to 32 1/6

rend="italics"

>g,</hi> will be in proportion to 32 1/6

feet, as that variable force, is to 1 the force of gravity.

Then because the force may be supposed constant during

the indefinitely small time <hi

the indefinitely small time <hi rend="italics">t,</hi> and that in uniform

rend="italics"

>t,</hi> and that in uniform

motions the spaces and velocities are proportional to the

times, we from thence obtain these two general fundamental

porportions,<p

porportions,From which are derived the four formulas below, in

>From which are derived the four formulas below, in

which the value of each quantity is expressed in terms

of the rest.<p

of the rest.And these theorems equally hold good for the destruction

>And these theorems equally hold good for the destruction

of motion and velocity, by means of retarding

forces, as for the generation of the same by means

of accelerating forces.<div2

of accelerating forces.<div2 part="n" n="Acceleration" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Acceleration</hi>, in <hi rend="italics">Mechanics</hi></head>, the increase of velocity

part="n"

in a moving body.<hi rend="smallcaps">Acceleration.</hi> <hi rend="italics">Astron.</hi> The Diurnal Acceleration

n="Acceleration"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Acceleration</hi>, in <hi

rend="italics"

>Mechanics</hi></head><p

>, the increase of velocity

in a moving body.<p

><hi

rend="smallcaps"

>Acceleration.</hi> <hi

rend="italics"

>Astron.</hi> The Diurnal Acceleration

of the fixed stars, is the time which the stars, in one diurnal

revolution, anticipate the mean diurnal revolution

of the sun; which is 3<hi

of the sun; which is 3<hi rend="sup">m</hi> 55<hi rend="sup">s</hi> 9/10 of mean time, or nearly

rend="sup"

3<hi rend="sup">m</hi> 56<hi rend="sup">s</hi>: that is, a star rises, or sets, or passes the meridian,

>m</hi> 55<hi

about 3<hi rend="sup">m</hi> 56<hi rend="sup">s</hi> sooner each day. This acceleration

rend="sup"

>s</hi> 9/10 of mean time, or nearly

3<hi

rend="sup"

>m</hi> 56<hi

rend="sup"

>s</hi>: that is, a star rises, or sets, or passes the meridian,

about 3<hi

rend="sup"

>m</hi> 56<hi

rend="sup"

>s</hi> sooner each day. This acceleration

of the stars, which is only apparent in them, arises

from the real retardation of the sun, owing to his appa-

<pb

n="23"

/><cb

rent motion in his orbit towards the east, which is about

59′ 8″ 2/10 of a degree every day. So that the star which

passed the meridian yesterday at the same moment with

the sun, is to-day about 59′ 8″ past the meridian to the

west, when the sun arrives at it; which will take him

up about 3<hi

up about 3<hi rend="sup">m</hi> 56<hi rend="sup">s</hi> of time to pass over; and therefore

rend="sup"

the star passes by 3<hi rend="sup">m</hi> 56<hi rend="sup">s</hi> sooner than the sun each day,

>m</hi> 56<hi

rend="sup"

>s</hi> of time to pass over; and therefore

the star passes by 3<hi

rend="sup"

>m</hi> 56<hi

rend="sup"

>s</hi> sooner than the sun each day,

or anticipates his motion at that rate. The true quantity

of this anticipation, or acceleration, is found by

this proportion, 360° 59′ 8″ 1/5 :: 24 hours:

3<hi

3<hi rend="sup">m</hi> 55<hi rend="sup">s</hi> 9/10, the fourth term of which is the acceleration.The diurnal acceleration serves to regulate the lengths

rend="sup"

>m</hi> 55<hi

rend="sup"

>s</hi> 9/10, the fourth term of which is the acceleration.<p

>The diurnal acceleration serves to regulate the lengths

or vibration of pendulums. If I observe a fixed star

set or pass behind a hill, steeple, or such like, when the

pendulum marks for instance 8<hi

pendulum marks for instance 8<hi rend="sup">h</hi> 10<hi rend="sup">m</hi>; and the next day,

rend="sup"

>h</hi> 10<hi

rend="sup"

>m</hi>; and the next day,

the eye being in the same place as before, the passage

be at 8<hi

be at 8<hi rend="sup">h</hi> 6<hi rend="sup">m</hi> 4<hi rend="sup">s</hi>; I thence conclude that the pendulum

rend="sup"

is well regulated, or truly measures mean time.<hi rend="smallcaps">Acceleration</hi> <hi rend="italics">of a Planet.</hi> A planet is said to be

>h</hi> 6<hi

rend="sup"

>m</hi> 4<hi

rend="sup"

>s</hi>; I thence conclude that the pendulum

is well regulated, or truly measures mean time.<p

><hi

rend="smallcaps"

>Acceleration</hi> <hi

rend="italics"

>of a Planet.</hi> A planet is said to be

accelerated in its motion, when its real diurnal motion

exceeds its mean diurnal motion. And, on the other

hand, the planet is said to be retarded in its motion,

Line 3866

Line 2636

inequality arises from the change in the distance of the

planet from the sun, which is continually varying; the

planet moving always quicker in its orbit when nearer

the sun, and slower when farther off.<p

the sun, and slower when farther off.<hi rend="smallcaps">Acceleration</hi> <hi rend="italics">of the Moon,</hi> is a term used to express

><hi

rend="smallcaps"

>Acceleration</hi> <hi

rend="italics"

>of the Moon,</hi> is a term used to express

the increase of the moon's mean motion from the

sun, compared with the diurnal motion of the earth;

by which it appears that, from some uncertain cause, it

Line 3897

Line 2662

ancient eclipses, and more forward than her true place

in later eclipses; and thence he justly inferred that her

motion in ancient times was slower, and in later times

quicker, than the tables give it.<p

quicker, than the tables give it.Not content however with barely ascertaining the

>Not content however with barely ascertaining the

fact, he proceeded to determine, as well as the observations

would allow, the quantity of the acceleration;

and by means of the most authentic eclipse, of which

Line 3908

Line 2672

quarters sooner than the beginning by the tables; and

that therefore the moon's true place preceded her place

by computation by about 50′ of a degree at that time.

<cb

<cb/>

Then admitting the acceleration to be uniform, and

the aggregate of it as the square of the time, it will

be at the rate of about 10″ in 100 years.<p

be at the rate of about 10″ in 100 years.Dr. Long, vol. ii. p. 436 of his Astronomy, enumerates

>Dr. Long, vol. ii. p. 436 of his Astronomy, enumerates

the following causes from some one or more

of which the acceleration may arise. Either 1st, the

annual and diurnal motion of the earth continuing the

Line 3941

Line 2703

continually streaming from it, the motion of the earth

about the sun may become slower: if the earth increases

in bulk, the motion of the moon about the

earth may thereby be quickened.<p

earth may thereby be quickened.ACCELERATIVE <hi rend="smallcaps">Force</hi>, <hi rend="italics">&c,</hi> the same as A<hi rend="smallcaps">CCELERATING.</hi></div2></div1><div1 part="n" n="ACCESSIBLE" org="uniform" sample="complete" type="entry"><head>ACCESSIBLE</head>, something that may be approached,

>ACCELERATIVE <hi

rend="smallcaps"

>Force</hi>, <hi

rend="italics"

>&c,</hi> the same as A<hi

rend="smallcaps"

>CCELERATING.</hi></div2></div1><div1

part="n"

n="ACCESSIBLE"

org="uniform"

sample="complete"

type="entry"

><head

>ACCESSIBLE</head><p

>, something that may be approached,

or to which we can come. In Surveying, it is such

a place as will admit of having a distance or length of

ground measured from it; or such a height or depth as

can be measured by actually applying a proper instrument

to it. For the means of doing which, see A<hi

to it. For the means of doing which, see A<hi rend="smallcaps">LTIMETRY,

rend="smallcaps"

Longimetry</hi>, or <hi rend="smallcaps">Heights-and-Distances.</hi></div1><div1 part="n" n="ACCIDENS" org="uniform" sample="complete" type="entry"><head>ACCIDENS</head>, <hi rend="smallcaps">Accident</hi>, <hi rend="italics">Philos.</hi><hi rend="italics">Per</hi> <hi rend="smallcaps">Accidens</hi> is a term often used among philosophers,

>LTIMETRY,

Longimetry</hi>, or <hi

rend="smallcaps"

>Heights-and-Distances.</hi></div1><div1

part="n"

n="ACCIDENS"

org="uniform"

sample="complete"

type="entry"

><head

>ACCIDENS</head><p

>, <hi

rend="smallcaps"

>Accident</hi>, <hi

rend="italics"

>Philos.</hi><p

><hi

rend="italics"

>Per</hi> <hi

rend="smallcaps"

>Accidens</hi> is a term often used among philosophers,

to denote what does not follow from the nature

of a thing, but from some accidental quality of it: in

this sense it stands opposed to <hi

this sense it stands opposed to <hi rend="italics">per se,</hi> which denotes

rend="italics"

>per se,</hi> which denotes

the nature and essence of a thing. Thus, fire is said to

burn <hi

burn <hi rend="italics">per se,</hi> or considered as sire, and not <hi rend="italics">per accidens;</hi>

rend="italics"

but a piece of iron, though red-hot, only burns <hi rend="italics">per

>per se,</hi> or considered as sire, and not <hi

rend="italics"

>per accidens;</hi>

but a piece of iron, though red-hot, only burns <hi

rend="italics"

>per

accidens,</hi> by a quality accidental to it, and not considered

as iron.<div2

as iron.<div2 part="n" n="Accidents" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Accidents</hi>, in <hi rend="italics">Astrology</hi></head>, denote the most extraordinary

part="n"

n="Accidents"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Accidents</hi>, in <hi

rend="italics"

>Astrology</hi></head><p

>, denote the most extraordinary

occurrences in the course of a person's life, either

good or bad: such as a remarkable instance of good

fortune, a signal deliverance, a great sickness, &c.</div2></div1><div1

fortune, a signal deliverance, a great sickness, &c.</div2></div1><div1 part="n" n="ACCIDENTAL" org="uniform" sample="complete" type="entry"><head>ACCIDENTAL</head>, something that partakes of the

part="n"

n="ACCIDENTAL"

org="uniform"

sample="complete"

type="entry"

><head

>ACCIDENTAL</head><p

>, something that partakes of the

nature of an accident; or that is indifferent, or not essential

to its subject.—Thus whiteness is accidental to

marble, and sensible heat to iron.<p

marble, and sensible heat to iron.<hi rend="smallcaps">Accidental</hi> <hi rend="italics">Colours,</hi> so called by M. Buffon, are

><hi

rend="smallcaps"

>Accidental</hi> <hi

rend="italics"

>Colours,</hi> so called by M. Buffon, are

those which depend on the affections of the eye, in

contradistinction to such as belong to light itself.<p

contradistinction to such as belong to light itself.The impressions made upon the eye, by looking stedfastly

>The impressions made upon the eye, by looking stedfastly

on objects of a particular colour, are various

<pb

n="24"

/><cb

according to the single colour, or assemblage of

colours, in the object; and they continue for some

time after the eye is withdrawn, and give a false colouring

Line 4049

Line 2738

a machine for measuring the duration of those

impressions on the eye; and from the result of several

trials he inserred, that the effect of the action of light

on the eye continued about eight thirds of a minute.<p

on the eye continued about eight thirds of a minute.The subject has also been considered by M. de la

>The subject has also been considered by M. de la

Hire, and M. Aepinus, &c. See Mem. Acad. Paris

1743, and 1765; Nov. Com. Petrop. vol. 10; also Dr.

Priestley's Hist. of Discoveries relating to Vision,

pa. 631.<p

pa. 631.<hi rend="smallcaps">Accidental</hi> <hi rend="italics">Point,</hi> in Perspective, is the point in

><hi

rend="smallcaps"

>Accidental</hi> <hi

rend="italics"

>Point,</hi> in Perspective, is the point in

which a right line drawn from the eye, parallel to another

right line, cuts the picture or perspective plane.

<figure

<figure/>Let AB be the line given to be put into perspective,

></figure><p

>Let AB be the line given to be put into perspective,

CFD the picture or perspective plane, and E the eye:

draw EF parallel to AB; so shall F be the accidental

point of the line AB, and indeed of all lines parallel

to it, since only one parallel to them, namely EF, can

be drawn from the same point E: and in the accidental

point concur or meet the representations of all the parallels

to AB, when produced.<p

to AB, when produced.It is called the accidental point, to distinguish it

>It is called the accidental point, to distinguish it

from the principal point, or point of view, where a line

drawn from the eye perpendicular to the perspective

plane, meets this plane, and which is the accidental

point to all lines that are perpendicular to the same plane.<p

point to all lines that are perpendicular to the same plane.<hi rend="smallcaps">Accidental</hi> <hi rend="italics">Dignities,</hi> and <hi rend="italics">Debilities,</hi> in <hi rend="italics">Astrology,</hi>

><hi

rend="smallcaps"

>Accidental</hi> <hi

rend="italics"

>Dignities,</hi> and <hi

rend="italics"

>Debilities,</hi> in <hi

rend="italics"

>Astrology,</hi>

are certain casual dispositions, and affections, of the

planets, by which they are supposed to be either

strengthened, or weakened, by being in such a house

of the figure.</div1><div1

of the figure.</div1><div1 part="n" n="ACCLIVITY" org="uniform" sample="complete" type="entry"><head>ACCLIVITY</head>, the slope or steepness of a line or

part="n"

n="ACCLIVITY"

org="uniform"

sample="complete"

type="entry"

><head

>ACCLIVITY</head><p

>, the slope or steepness of a line or

plane inclined to the horizon, taken upwards; in contradistinction

to <hi

to <hi rend="italics">declivity,</hi> which is taken downwards.

rend="italics"

So the ascent of a hill, is an <hi rend="italics">acclivity:</hi> the descent of the

>declivity,</hi> which is taken downwards.

same, a <hi rend="italics">declivity.</hi>Some writers on fortification use acclivity for <hi rend="italics">talus:</hi>

So the ascent of a hill, is an <hi

rend="italics"

>acclivity:</hi> the descent of the

same, a <hi

rend="italics"

>declivity.</hi><p

>Some writers on fortification use acclivity for <hi

rend="italics"

>talus:</hi>

though more commonly the word talus is used to denote

the slope, whether in ascending or descending.</div1><div1

the slope, whether in ascending or descending.</div1><div1 part="n" n="ACCOMPANYMENT" org="uniform" sample="complete" type="entry"><head>ACCOMPANYMENT</head>, in <hi rend="italics">Music,</hi> denotes either

part="n"

n="ACCOMPANYMENT"

org="uniform"

sample="complete"

type="entry"

><head

>ACCOMPANYMENT</head><p

>, in <hi

rend="italics"

>Music,</hi> denotes either

the different parts of a piece of music for the different

instruments, or the instruments themselves which accompany

a voice, to sustain it, as well as to make the

music more full.<p

music more full.The Accompanyment is used in recitative, as well as

>The Accompanyment is used in recitative, as well as

in song; on the stage, as well as in the choir, &c.

<cb

<cb/>The ancients had likewise their accompanyments

/><p

>The ancients had likewise their accompanyments

on the theatre; and they had even different kinds of

instruments to accompany the chorus, from those which

accompanied the actors in the recitation.<p

accompanied the actors in the recitation.The accompanyment among the moderns, is often a

>The accompanyment among the moderns, is often a

different part, or melody, from the song it accompanies.

But it is disputed whether it was so among the ancients.<p

But it is disputed whether it was so among the ancients.Organists sometimes apply the word to several pipes

>Organists sometimes apply the word to several pipes

which they occasionally touch to accompany the treble;

as the drone, the flute, &c.<p

as the drone, the flute, &c.ACCOMPT. See <hi rend="smallcaps">Account.</hi></div1><div1 part="n" n="ACCORD" org="uniform" sample="complete" type="entry"><head>ACCORD</head>, according to the modern French music,

>ACCOMPT. See <hi

rend="smallcaps"

>Account.</hi></div1><div1

part="n"

n="ACCORD"

org="uniform"

sample="complete"

type="entry"

><head

>ACCORD</head><p

>, according to the modern French music,

is the union of two or more sounds heard at the same

time, and forming together a regular harmony.<p

time, and forming together a regular harmony.They divide Accords into <hi rend="italics">persect</hi> and <hi rend="italics">imperfect;</hi> and

>They divide Accords into <hi

again into <hi rend="italics">consonances</hi> and <hi rend="italics">dissonances.</hi>Accord is more commonly called <hi rend="smallcaps">Concord</hi>, which

rend="italics"

see.<hi rend="smallcaps">Accord</hi> is also spoken of the state of an instrument,

>persect</hi> and <hi

rend="italics"

>imperfect;</hi> and

again into <hi

rend="italics"

>consonances</hi> and <hi

rend="italics"

>dissonances.</hi><p

>Accord is more commonly called <hi

rend="smallcaps"

>Concord</hi>, which

see.<p

><hi

rend="smallcaps"

>Accord</hi> is also spoken of the state of an instrument,

when its fixed sounds have among themselves all the

justness that they ought to have.</div1><div1

justness that they ought to have.</div1><div1 part="n" n="ACCOUNT" org="uniform" sample="complete" type="entry"><head>ACCOUNT</head>, or <hi rend="smallcaps">Accompt</hi>, in <hi rend="italics">Arithmetic,</hi> &c, a

part="n"

n="ACCOUNT"

org="uniform"

sample="complete"

type="entry"

><head

>ACCOUNT</head><p

>, or <hi

rend="smallcaps"

>Accompt</hi>, in <hi

rend="italics"

>Arithmetic,</hi> &c, a

calculation or computation of the number or order of

certain things; as the computation of time, &c.<p

certain things; as the computation of time, &c.There are various ways of accounting; as, by enumeration,

>There are various ways of accounting; as, by enumeration,

or telling one by one; or by the rules of

arithmetic, addition, subtraction, &c.<div2

arithmetic, addition, subtraction, &c.<div2 part="n" n="Account" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Account</hi>, in <hi rend="italics">Chronology</hi></head>, is nearly synonymous with

part="n"

n="Account"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Account</hi>, in <hi

rend="italics"

>Chronology</hi></head><p

>, is nearly synonymous with

style. Thus, we say the English, the foreign, the Julian,

the Gregorian, the Old, or the New account, or

style.<p

style.We account time by years, months, &c; the

>We account time by years, months, &c; the

Greeks accounted it by olympiads; the Romans, by

indictions, lustres, &c.</div2><div2

indictions, lustres, &c.</div2><div2 part="n" n="Acherner" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Acherner</hi></head>, or <hi rend="smallcaps">Acharner</hi>, in <hi rend="italics">Astronomy,</hi> a star of

part="n"

n="Acherner"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Acherner</hi></head><p

>, or <hi

rend="smallcaps"

>Acharner</hi>, in <hi

rend="italics"

>Astronomy,</hi> a star of

the first magnitude in the southern extremity of the

constellation Eridanus, marked <foreign

constellation Eridanus, marked <foreign lang="greek">a</foreign> by Bayer. Its longitude

lang="greek"

for 1761, <figure/> 11° 55′ 1″; and latitude south

>a</foreign> by Bayer. Its longitude

59° 22′ 4″.</div2></div1><div1 part="n" n="ACHILLES" org="uniform" sample="complete" type="entry"><head>ACHILLES</head>, a name given by the schools to the

for 1761, <figure

></figure> 11° 55′ 1″; and latitude south

59° 22′ 4″.</div2></div1><div1

part="n"

n="ACHILLES"

org="uniform"

sample="complete"

type="entry"

><head

>ACHILLES</head><p

>, a name given by the schools to the

principal argument alleged by each sect of philosophers

in behalf of their system. In this sense we say this is

his Achilles; that is, his master-proof: alluding to

the strength and importance of the hero Achilles among

the Greeks.<p

the Greeks.Zeno's argument against motion is peculiarly termed

>Zeno's argument against motion is peculiarly termed

Achilles. That philosopher made a comparison between

the swiftness of Achilles, and the slowness of a tortoise,

pretending that a very swift animal could never overtake

Line 4260

Line 2821

to an infinite series of 100th parts: from which he

concluded that the swifter could never overtake the

slower in any finite time, but that they must go on ap-

<pb

n="25"

/><cb

proaching to infinity. But this sophism lay in their

considering as an infinite time, the sum of the infinite

series of small times in which Achilles could run over

Line 4271

Line 2829

1/1000000 &c, not knowing that the sum of this infinite

series is equal to the quantity 1 1/99 of a mile, and that

therefore Achilles will overtake the tortoise when the

latter has crawled over 1/99th of a mile.</div1><div1

latter has crawled over 1/99th of a mile.</div1><div1 part="n" n="ACHROMATIC" org="uniform" sample="complete" type="entry"><head>ACHROMATIC</head>, in <hi rend="italics">Optics,</hi> without colour; a

part="n"

n="ACHROMATIC"

org="uniform"

sample="complete"

type="entry"

><head

>ACHROMATIC</head><p

>, in <hi

rend="italics"

>Optics,</hi> without colour; a

term which, it seems, was first used by M. de la Lande,

in his astronomy, to denote telescopes of a new invention,

contrived to remedy aberrations and colours. See

<hi

<hi rend="italics">Aberration</hi> and <hi rend="italics">Telescope.</hi><hi rend="smallcaps">Achromatic Telescope</hi>, a singular species of refracting

rend="italics"

>Aberration</hi> and <hi

rend="italics"

>Telescope.</hi><p

><hi

rend="smallcaps"

>Achromatic Telescope</hi>, a singular species of refracting

telescope, said to be invented by the late Mr.

John Dollond, optician to the king, and since improved

by his son Mr. Peter Dollond, and others.<p

by his son Mr. Peter Dollond, and others.Every ray of light passing obliquely from a rarer

>Every ray of light passing obliquely from a rarer

into a denser medium, changes its direction towards the

perpendicular; and every ray passing obliquely from a

denser into a rarer medium, changes its direction from the

Line 4313

Line 2853

of the component rays, in such sort, that the more the

original or component ray is refracted, the more will

the compound rays diverge when the light is refracted

by one given medium only.<p

by one given medium only.From hence it has been concluded, that any two different

>From hence it has been concluded, that any two different

mediums that can be made to produce equal refractions,

will necessarily produce equal divergencies:

whence it should also follow, that equal and contrary

Line 4322

Line 2861

the divergency of the colours caused by one refraction,

should be corrected by the other; and that to produce

refraction that would not be affected by the different

refrangibility of light, is impossible.<p

refrangibility of light, is impossible.But Mr. Dollond has proved, by many experiments,

>But Mr. Dollond has proved, by many experiments,

that these conclusions are not well founded; from which

experiments it appeared, that a ray of light, after equal

and contrary refractions, was still spread into component

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Line 2876

by one refraction shall be exactly counteracted by the

divergency caused by the other; and so an object may

be seen through mediums which, together, cause the

rays to converge, without appearing of different colours.<p

rays to converge, without appearing of different colours.This is the foundation of Mr. Dollond's improvement

>This is the foundation of Mr. Dollond's improvement

of refracting telescopes. By subsequent experiments he

found, that different sorts of glass differed greatly in their

refractive qualities, with respect to the divergency of colours.

He found that crown glass causes the least diver-

<cb

<cb/>

gency, and white flint the most, when they are wrought

into forms that produce equal refractions. He ground a

piece of white flint glass into a wedge, whose angle was

about 25 degrees; and a piece of crown glass to another,

whose angle was about 29 degrees; and these he found

refracted nearly alike, but that their divergency of

colours was very different.<p

colours was very different.He then ground several other pieces of crown glass

>He then ground several other pieces of crown glass

to wedges of different angles, till he got one that was

equal, in the divergency it produced, to that of a wedge

of flint glass of 25 degrees; so that when they were

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Line 2901

this proportion, would, when applied together so as to

refract in contrary directions, refract the light without

any effect ariling from the different refrangibility of the

component rays.<p

component rays.Therefore, to make two spherical glasses that refract

>Therefore, to make two spherical glasses that refract

the light in contrary directions, one must be concave,

and the other convex; and as the rays, after passing

through both, must meet in a focus, the excess of the

refraction must be in the convex one: and as the convex

is to refract most, it appears from the experiment

that it must be made of crown glass; and as the concave

is to refract least, it must be made of white flint.<p

is to refract least, it must be made of white flint.And farther, as the refractions of spherical glasses

>And farther, as the refractions of spherical glasses

are in an inverse ratio of their focal distances, it follows

that the focal distances of the two glasses should be in

the ratio of the refractions of the wedges; for, being

Line 4384

Line 2917

will constantly be refracted by the difference between

two contrary refractions, in the proportion required;

and therefore the effect of the different refrangibility

of light will be prevented.<p

of light will be prevented.The removal of this impediment, however, produced

>The removal of this impediment, however, produced

another: for the two glasses, which were thus combined,

being segments of very deep spheres, the aberrations

from the spherical surfaces became so considerable,

Line 4398

Line 2930

of any two glasses equal; and that, as in this case the

refractions of the two glasses were contrary to each

other, and their aberrations being equal, these would

destroy each other.<p

destroy each other.Thus he obtained a persect theory of making object

>Thus he obtained a persect theory of making object

glasses, to the apertures of which he could hardly perceive

any limits: for if the practice could come up to

the theory, they must admit of apertures of great extent,

and consequently bear great magnifying powers.<p

and consequently bear great magnifying powers.The difficulties of the practice are, however, still

>The difficulties of the practice are, however, still

very considerable. For first, the focal distances, as

well as the particular surfaces, must be proportioned

with the utmost accuracy to the densities and refracting

powers of the glasses, which vary even in the same sort

of glass, when made at different times. Secondly,

there are four surfaces to be wrought persectly spherical.

<pb

n="26"

/><cb

However, Mr. Dollond could construct refracting telescopes

upon these principles, with fuch apertures and

magnifying powers, under limited lengths, as greatly

Line 4422

Line 2949

images of objects bright, distinct, and uninfected with

colours about the edges, through the whole extent of a

very large field or compass of view; of which he has

given abundant and undeniable testimony. See T<hi

given abundant and undeniable testimony. See T<hi rend="smallcaps">ELESCOPE.</hi>There has lately appeared in the Gentleman's Magazine

rend="smallcaps"

>ELESCOPE.</hi><p

>There has lately appeared in the Gentleman's Magazine

(1790, pa. 890) a paper on the refracting telescope,

by an author who signs <hi

by an author who signs <hi rend="italics">Veritus,</hi> in which the

rend="italics"

>Veritus,</hi> in which the

invention is ascribed to another person, not heretofore

mentioned; in these words: “As the invention has

been claimed by M. Euler, M. Klingenstierna, and

Line 4453

Line 2975

them this name), that bore an aperture of more than

2 1/2 inches, though the focal length did not exceed 20

inches; one of which is now in the possession of the

Rev. Mr. Smith, of Charlotte Street, Rathbone Place.<p

Rev. Mr. Smith, of Charlotte Street, Rathbone Place.This glass has been examined by several gentlemen

>This glass has been examined by several gentlemen

of eminence and scientific abilities, and found to possess

the properties of the present achromatic glasses.<p

the properties of the present achromatic glasses.Mr. Hall used to employ the working opticians to

>Mr. Hall used to employ the working opticians to

grind his lenses; at the same time he finished them

with the radii of the surfaces, not only to correct the

different refrangibility of rays, but also the aberration

arising from the spherical figure of the lenses. Old Mr.

Bass, who at that time lived in Bridewell precinct, was

one of these working opticians, from whom Mr. Hall's

invention seems to have been obtained.<p

invention seems to have been obtained.In the trial at Westminster hall about the patent for

>In the trial at Westminster hall about the patent for

making achromatio telescopes, Mr. Hall was allowed

to be the inventor; but Lord Mansfield observed, that

“It was not the person that locked up his invention in

Line 4476

Line 2995

of property, and did not look to any pecuniary advantage

from his discovery; and, consequently, it is very

probable that he might not have an intention to make

it generally known at that time.<p

it generally known at that time.That Mr. Ayscough, optician on Ludgate Hill,

>That Mr. Ayscough, optician on Ludgate Hill,

was in possession of one of Mr. Hall's achromatic telescopes

in 1754, is a fact which at this time will not be

disputed.”</div1><div1

disputed.”</div1><div1 part="n" n="ACHRONICAL" org="uniform" sample="complete" type="entry"><head>ACHRONICAL</head>, or <hi rend="italics">Achronycal.</hi> See <hi rend="smallcaps">Acronychal.</hi>

part="n"

<cb/>ACOUSTICS. This term, in physico-mathematical

n="ACHRONICAL"

org="uniform"

sample="complete"

type="entry"

><head

>ACHRONICAL</head><p

>, or <hi

rend="italics"

>Achronycal.</hi> See <hi

rend="smallcaps"

>Acronychal.</hi>

<cb

/><p

>ACOUSTICS. This term, in physico-mathematical

meaning, signifies the doctrine of hearing, and the art

of assisting that sense by means of speaking trumpets,

hearing trumpets, whispering galleries, and such like.

See <hi

See <hi rend="smallcaps">Stentrophonic Tube.</hi>Sturmius, in his Elements of Universal Mechanics,

rend="smallcaps"

>Stentrophonic Tube.</hi><p

>Sturmius, in his Elements of Universal Mechanics,

treating of Acoustics, after examining into the nature

of sounds, describes the several parts of the external

and internal ear, and their several uses and connexions

Line 4510

Line 3011

of hearing: and lastly, he treats of the means of

adding an intensity of force to the voice and other

sounds; and explains the nature of echoes, otacoustic

tubes, and speaking trumpets. See <hi

tubes, and speaking trumpets. See <hi rend="smallcaps">Sound, Ear, Voice</hi>,

rend="smallcaps"

and <hi rend="smallcaps">Echo.</hi>Dr. Hook, in the preface to his Micrography, asserts

>Sound, Ear, Voice</hi>,

and <hi

rend="smallcaps"

>Echo.</hi><p

>Dr. Hook, in the preface to his Micrography, asserts

that the lowest whisper, by certain means, may be

heard at the distance of a furlong; and that he knew a

way by which it is easy to hear any one speak through

a wall of three feet thick; also that by means of an extended

wire, sound may be conveyed to a very great

distance, almost in an instant.</div1><div1

distance, almost in an instant.</div1><div1 part="n" n="ACRE" org="uniform" sample="complete" type="entry"><head>ACRE</head>, from the Saxon <hi rend="italics">æcre,</hi> or German <hi rend="italics">acker,</hi> a <hi rend="italics">field,</hi>

part="n"

of the Latin <hi rend="italics">ager.</hi> It is a measure of land, containing,

n="ACRE"

org="uniform"

sample="complete"

type="entry"

><head

>ACRE</head><p

>, from the Saxon <hi

rend="italics"

>æcre,</hi> or German <hi

rend="italics"

>acker,</hi> a <hi

rend="italics"

>field,</hi>

of the Latin <hi

rend="italics"

>ager.</hi> It is a measure of land, containing,

by the ordinance for measuring land, made in the 33d

and 34th of Edward I, 160 perches or square poles of

land; that is, 16 in length and 10 in breadth, or in that

Line 4552

Line 3032

10 chains in length and one in breadth, or in that proportion.

Farther, as a mile contains 1760 yards, or

80 chains in length, therefore the square mile contains

640 acres.<p

640 acres.The acre, in surveying, is divided into 4 roods, and

>The acre, in surveying, is divided into 4 roods, and

the rood is 40 perches.The French acre, <hi rend="italics">arpent,</hi> is equal to 1 1/4 English acre;The Strasburg contains about 1/2 an English acre;The Welch acre contains about 2 English acres;The Irish acre contains 1 ac. 2 r. 19 27/121 p. English.Sir William Petty, in his Political Arithmetic,

the rood is 40 perches.<p

>The French acre, <hi

rend="italics"

>arpent,</hi> is equal to 1 1/4 English acre;<p

>The Strasburg contains about 1/2 an English acre;<p

>The Welch acre contains about 2 English acres;<p

>The Irish acre contains 1 ac. 2 r. 19 27/121 p. English.<p

>Sir William Petty, in his Political Arithmetic,

reckons that England contains 39 million acres:

but Dr. Greve shews, in the Philos. Trans. N° 330,

that England contains not less than 46 million acres.

Whence he infers that England is above 46 times as

large as the province of Holland, which it is said contains

but about one million of acres.<p

but about one million of acres.By a statute of the 31st of Elizabeth, it is ordained,

>By a statute of the 31st of Elizabeth, it is ordained,

that if any man erect a cottage, he shall annex four

acres of land to it.</div1><div1

acres of land to it.</div1><div1 part="n" n="ACRONYCHAL" org="uniform" sample="complete" type="entry"><head>ACRONYCHAL</head>, or <hi rend="smallcaps">Acronycal</hi>, in <hi rend="italics">Astronomy,</hi>

part="n"

n="ACRONYCHAL"

org="uniform"

sample="complete"

type="entry"

><head

>ACRONYCHAL</head><p

>, or <hi

rend="smallcaps"

>Acronycal</hi>, in <hi

rend="italics"

>Astronomy,</hi>

is said of a star or planet, when it is opposite to the

sun. It is from the Greek <foreign

sun. It is from the Greek <foreign lang="greek">axronuxos</foreign>, the point or extremity

lang="greek"

>axronuxos</foreign>, the point or extremity

of night, because the star rose at sun-set, or the

beginning of night, and set at sun-rise, or the end of

night; and so it shone all the night.<p

night; and so it shone all the night.The acronychal is one of the three Greek poetic

>The acronychal is one of the three Greek poetic

risings and settings of the stars; and stands distinguished

from Cosmical and Heliacal. And by means of

which, for want of accurate instruments, and other observations,

they might regulate the length of their year.

<pb

<pb n="27"/><cb/></div1><div1 part="n" n="ACROTERIA" org="uniform" sample="complete" type="entry"><head>ACROTERIA</head>, or <hi rend="smallcaps">Acroters</hi>, in <hi rend="italics">Architecture,</hi> small

n="27"

/><cb

/></div1><div1

part="n"

n="ACROTERIA"

org="uniform"

sample="complete"

type="entry"

><head

>ACROTERIA</head><p

>, or <hi

rend="smallcaps"

>Acroters</hi>, in <hi

rend="italics"

>Architecture,</hi> small

pedestals, usually without bases, placed on pediments,

and serving to support statues.<p

and serving to support statues.Those at the extremities ought to be half the height

>Those at the extremities ought to be half the height

of the tympanum; and that in the middle, according

to Vitruvius, one eighth part more.<p

to Vitruvius, one eighth part more.<hi rend="smallcaps">Acroteria</hi> also are sometimes used to signify

><hi

rend="smallcaps"

>Acroteria</hi> also are sometimes used to signify

figures, whether of stone or metal, placed as ornaments

or crownings, on the tops of temples, or other

buildings.<p

buildings.It is also sometimes used to denote those sharp pinacles

>It is also sometimes used to denote those sharp pinacles

or spiry battlements, that stand in ranges about

flat buildings, with rails and balustres.</div1><div1

flat buildings, with rails and balustres.</div1><div1 part="n" n="ACTION" org="uniform" sample="complete" type="entry"><head>ACTION</head>, in <hi rend="italics">Mechanics</hi> or <hi rend="italics">Physics,</hi> a term used to

part="n"

n="ACTION"

org="uniform"

sample="complete"

type="entry"

><head

>ACTION</head><p

>, in <hi

rend="italics"

>Mechanics</hi> or <hi

rend="italics"

>Physics,</hi> a term used to

denote, sometimes the effort which some body or power

exerts against another body or power, and sometimes

it denotes the effects resulting from such esfort.<p

it denotes the effects resulting from such esfort.The Cartesians resolve all physical action into metaphysical.

>The Cartesians resolve all physical action into metaphysical.

Bodies, according to them, do not act on one

another; the action comes all immediately from the

Deity; the motions of bodies, which seem to be the

cause, being only the occasions of it.<p

cause, being only the occasions of it.It is one of the laws of nature, that action and reaction

>It is one of the laws of nature, that action and reaction

are always equal, and contrary to each other

in their directions.<p

in their directions.Action is either instantaneous or continued; that is,

>Action is either instantaneous or continued; that is,

either by collition or perc<*>ssion, or by pressure. These

two sorts of action are heterogeneous quantities, and

are not comparable, the smallest action by percussion

Line 4662

Line 3083

measured the one by the other, but each must have a

measure of its own kind, like as solids must be measured

by solids, and surfaces by surfaces: time being

concerned in the one, but not in the other.<p

concerned in the one, but not in the other.If a body be urged at the same time by equal and

>If a body be urged at the same time by equal and

contrary actions, it will remain at rest. But if one of

these actions be greater than its opposite, motion will

ensue towards the part least urged.<p

ensue towards the part least urged.The actions of bodies upon each other, in a space

>The actions of bodies upon each other, in a space

that is carried uniformly forward, are the same as if

the space were at rest; and any powers or forces that

act upon all bodies, so as to produce equal velocities in

Line 4680

Line 3099

bodies and agents at its surface, except in so far as it

is not uniform and rectilineal. In general, the actions

of bodies upon each other, depend not on their absolute,

but relative motion.<p

but relative motion.<hi rend="italics">Quantity of</hi> <hi rend="smallcaps">Action</hi>, in Mechanics, a name given

><hi

rend="italics"

>Quantity of</hi> <hi

rend="smallcaps"

>Action</hi>, in Mechanics, a name given

by M. de Maupertuis, in the Memoirs of the Academy

of Sciences of Paris for 1744, and in those of Berlin

for 1746, to the continual product of the mass of a

body, by the space which it runs through, and by its

celerity. He lays it down as a general law, that in the

<cb

<cb/>

changes made in the state of a body, the quantity of

action necessary to produce such change is the least possible.

This principle he applies to the investigation of

Line 4706

Line 3119

bodies, upon one and the same law, which before had

always been referred to separate laws; and to reduce

the laws of motion, and those of equilibrium, to one

and the same principle.<p

and the same principle.But this quantity of motion, of Maupertuis, which

>But this quantity of motion, of Maupertuis, which

is defined to be the product of the mass, the space

passed over, and the celerity, comes to the same thing

as the mass multiplied by the square of the velocity,

Line 4715

Line 3127

the velocity is measured; and so the quantity of force

will be proportional to the mass multiplied by the

square of the velocity; since the space is measured by

the velocity continued for a certain time.<p

the velocity continued for a certain time.In the same year that Maupertuis communicated the

>In the same year that Maupertuis communicated the

idea of his principle, professor Euler, in the supplement

to his book, intitled <hi

to his book, intitled <hi rend="italics">Methodus inveniendi lineas curvas

rend="italics"

>Methodus inveniendi lineas curvas

maximi vel minimi proprietate gaudentes,</hi> demonstrates,

that in the trajectories which bodies describe by central

forces, the velocity multiplied by what the foreign mathematicians

call the element of the curve, always

makes a minimum; which Maupertuis considered as

an application of his principle to the motion of the

planets.<p

planets.It appears from Maupertuis's Memoir of 1744, that

>It appears from Maupertuis's Memoir of 1744, that

it was his reflections on the laws of refractions, that led

him to the theorem above mentioned. The principle

which Fermat, and after him Leibnitz, made use of,

Line 4745

Line 3153

its incidence shall be to the sine of its refraction, as

its velocity in the first medium is to its velocity in

the second: whence they deduced the well known law

of the constant ratio of those sines.<p

of the constant ratio of those sines.This explanation, though very ingenious, is liable

>This explanation, though very ingenious, is liable

to this pressing difficulty, namely, that the particle

must approach towards the perpendicular, in that medium

where its velocity is the least, and which consequently

resists it the most: which seems contrary to

all the mechanical explanations of the refraction of

bodies, that have hitherto been advanced, and of the

refraction of light in particular.<p

refraction of light in particular.Sir Isaac Newton's way of accounting for it, is the

>Sir Isaac Newton's way of accounting for it, is the

most satisfactory of any that has hitherto been offered,

and gives a clear reason for the constant ratio of the

sines, by ascribing the refraction to the attractive force

of the mediums; from which it follows, that the densest

<pb

n="28"

/><cb

mediums, whose attraction is the strongest, should

cause the ray to approach the perpendicular; a fact

confirmed by experiment. But the attraction of the

medium could not caúse the ray to approach towards

the perpendicular, without increasing its velocity; as

may easily be demonstrated. Thus then, according to

Newton, the refraction must be towards the perpendicular,

when the velocity is increased: contrary to

the law of Fermat and Leibnitz.<p

the law of Fermat and Leibnitz.Maupertuis has attempted to reconcile Newton's

>Maupertuis has attempted to reconcile Newton's

explanation with metaphysical principles. Instead of

supposing, as the aforesaid gentlemen do, that a particle

of light proceeds from one point to another in

Line 4785

Line 3187

only the sines are in a constant ratio, but also that they

are in the inverse ratio of the velocities, according to

Newton's explanation, and not in the direct ratio, as

had been pretended by Fermat and Leibnitz.<p

had been pretended by Fermat and Leibnitz.It is remarkable that, of the many philosophers who

>It is remarkable that, of the many philosophers who

have written on refraction, none should have fallen

upon so simple a manner of reconciling metaphysics

with mechanics; since no more is necessary to that,

Line 4796

Line 3197

velocity, should be a minimum; so that calling the

space run through in the first medium S, with the

velocity V, and the space run through in the second

medium <hi

medium <hi rend="italics">s,</hi> with the velocity <hi rend="italics">v,</hi> we shall have minimum; that is to say, . Now it is easy to perceive, that the sines of incidence

rend="italics"

and refraction are to each other, as S<hi rend="sup">.</hi> to-<hi rend="italics">s<hi rend="sup">.</hi></hi>;

>s,</hi> with the velocity <hi

rend="italics"

>v,</hi> we shall have minimum; that is to say, . Now it is easy to perceive, that the sines of incidence

and refraction are to each other, as S<hi

rend="sup"

>.</hi> to-<hi

rend="italics"

>s<hi

rend="sup"

>.</hi></hi>;

whence it follows, that those sines are in the direct

ratio of the velocities V, <hi

ratio of the velocities V, <hi rend="italics">v</hi>; which is exactly what

rend="italics"

>v</hi>; which is exactly what

Fermat makes it to be. But in order to have those

sines to be in the inverse ratio of the velocities, it is

only supposing ; which gives a minimum: which is Maupertuis's

principle.<p

principle.In the Memoirs of the Academy of Berlin, above

>In the Memoirs of the Academy of Berlin, above

cited, may be seen all the other applications which

Maupertuis has made of this principle. And whatever

may be determined as to his metaphysical basis of it, as

also to the idea he has annexed to the quantity of action,

it will still hold good, that the product of the

space by the velocity is a minimum in some of the

most general laws of nature.</div1><div1

most general laws of nature.</div1><div1 part="n" n="ACTIVE" org="uniform" sample="complete" type="entry"><head>ACTIVE</head>, the quality of an agent, or of communicating

part="n"

n="ACTIVE"

org="uniform"

sample="complete"

type="entry"

><head

>ACTIVE</head><p

>, the quality of an agent, or of communicating

motion or action to some body. In this sense

the word stands opposed to passive: thus we say an

active cause, active principle, &c.<p

active cause, active principle, &c.Sir Isaac Newton shews that the quantity of motion

>Sir Isaac Newton shews that the quantity of motion

in the world must be always deereasing, in consequence

of the vis inertiæ, &c. So that there is a necessity for

<cb

<cb/>

certain active principles to recruit it: such he takes the

cause of gravity to be, and the cause of fermentation;

adding, that we see but little motion in the universe,

except what is owing to these active principles.</div1><div1

except what is owing to these active principles.</div1><div1 part="n" n="ACTIVITY" org="uniform" sample="complete" type="entry"><head>ACTIVITY</head>, the virtue or faculty of acting. As

part="n"

n="ACTIVITY"

org="uniform"

sample="complete"

type="entry"

><head

>ACTIVITY</head><p

>, the virtue or faculty of acting. As

the activity of an acid, a poison, &c: the activity of

fire exceeds all imagination.<p

fire exceeds all imagination.According to Sir Isaac Newton, bodies derive their

>According to Sir Isaac Newton, bodies derive their

activity from the principle of attraction.<hi rend="italics">Sphere of</hi> <hi rend="smallcaps">Activity</hi>, is the space which surrounds

activity from the principle of attraction.<p

><hi

rend="italics"

>Sphere of</hi> <hi

rend="smallcaps"

>Activity</hi>, is the space which surrounds

a body, as far as its efficacy or virtue extends to produce

any sensible effect. Thus we say, the sphere of

activity of a loadstone, of an electric body, &c.</div1><div1

activity of a loadstone, of an electric body, &c.</div1><div1 part="n" n="ACUBENE" org="uniform" sample="complete" type="entry"><head>ACUBENE</head>, in <hi rend="italics">Astronomy,</hi> the Arabic name of a

part="n"

n="ACUBENE"

org="uniform"

sample="complete"

type="entry"

><head

>ACUBENE</head><p

>, in <hi

rend="italics"

>Astronomy,</hi> the Arabic name of a

star of the fourth magnitude, in the southern claw of

Cancer, marked <foreign

Cancer, marked <foreign lang="greek">a</foreign> by Bayer. Its longitude for 1761,

lang="greek"

<figure/> 10° 18′ 9″, south latitude 5° 5′ 56″.</div1><div1 part="n" n="ACUTE" org="uniform" sample="complete" type="entry"><head>ACUTE</head>, or sharp; a term opposed to obtuse.

>a</foreign> by Bayer. Its longitude for 1761,

Thus, <hi rend="smallcaps">Acute</hi> <hi rend="italics">Angle,</hi> in <hi rend="italics">Geometry,</hi> is that which is less

<figure

than a right angle; and is measured by less than 90°,

></figure> 10° 18′ 9″, south latitude 5° 5′ 56″.</div1><div1

part="n"

n="ACUTE"

org="uniform"

sample="complete"

type="entry"

><head

>ACUTE</head><p

>, or sharp; a term opposed to obtuse.

Thus, <hi

rend="smallcaps"

>Acute</hi> <hi

rend="italics"

>Angle,</hi> in <hi

rend="italics"

>Geometry,</hi> is that which is less

than a right angle; and is measured by less than 90°,

or by less than a quadrant of a circle. As the angle

ABC.

<figure

<figure/><hi rend="smallcaps">Acute</hi> <hi rend="italics">angled Triangle,</hi> is that whose three angles

></figure><p

><hi

rend="smallcaps"

>Acute</hi> <hi

rend="italics"

>angled Triangle,</hi> is that whose three angles

are all acute; and is otherwise called an oxygenous

triangle. As the triangle DEF.<p

triangle. As the triangle DEF.<hi rend="smallcaps">Acute</hi>-<hi rend="italics">angled Cone,</hi> is that whose opposite sides

><hi

rend="smallcaps"

>Acute</hi>-<hi

rend="italics"

>angled Cone,</hi> is that whose opposite sides

make an acute angle at the vertex, or whose axis, in a

right cone, makes less than half a right angle with the

side As the cone GHI.<p

side As the cone GHI.Pappus, in his Mathematical Collections, says, this

>Pappus, in his Mathematical Collections, says, this

name was given to such a cone by Euclid and the ancients,

before the time of Apollonius. And they

called an<p

called an<hi rend="smallcaps">Acute</hi>-<hi rend="italics">angled Section of a Cone,</hi> an Ellipsis, which

><hi

rend="smallcaps"

>Acute</hi>-<hi

rend="italics"

>angled Section of a Cone,</hi> an Ellipsis, which

was made by a plane cutting both sides of an acuteangled

cone: not knowing that such a section could

be generated from any cone whatever, till it was shewn

by Apollonius.<div2

by Apollonius.<div2 part="n" n="Acute" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Acute</hi>, in <hi rend="italics">Music</hi></head>, is understood of a tone, or sound,

part="n"

n="Acute"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Acute</hi>, in <hi

rend="italics"

>Music</hi></head><p

>, is understood of a tone, or sound,

which is high, sharp, or shrill, in respect of some other:

in which sense the word stands opposed to grave. And

both these sounds are independent of loudness or force:

Line 4947

Line 3255

loud; and loud without being high or acute. For

both the affections of acute and grave, depend intirely

on the quickness or slowness of the vibrations by which

they are produced.<p

they are produced.Sounds considered as grave and acute, that is, in the

>Sounds considered as grave and acute, that is, in the

relation of gravity and acuteness, constitute what is

called tune, the soundation of all harmony.</div2></div1><div1

called tune, the soundation of all harmony.</div2></div1><div1 part="n" n="ADAGIO" org="uniform" sample="complete" type="entry"><head>ADAGIO</head>, in <hi rend="italics">Music,</hi> one of the terms used by the

part="n"

Italians to express a degree or distinction of time.Adagio denotes the slowest time except grave.Sometimes the word is repeated, as <hi rend="italics">adagio, adagio,</hi>

n="ADAGIO"

org="uniform"

sample="complete"

type="entry"

><head

>ADAGIO</head><p

>, in <hi

rend="italics"

>Music,</hi> one of the terms used by the

Italians to express a degree or distinction of time.<p

>Adagio denotes the slowest time except grave.<p

>Sometimes the word is repeated, as <hi

rend="italics"

>adagio, adagio,</hi>

to denote a still slower time than the former.

<pb

<pb n="29"/><cb/>Adagio also signifies a slow movement, when used

n="29"

substantively.</div1><div1 part="n" n="ADAMAS" org="uniform" sample="complete" type="entry"><head>ADAMAS</head>, in <hi rend="italics">Astrology,</hi> a name given to the moon.</div1><div1 part="n" n="ADAR" org="uniform" sample="complete" type="entry"><head>ADAR</head>, in the Hebrew <hi rend="italics">Chronology,</hi> is the 6th month

/><cb

/><p

>Adagio also signifies a slow movement, when used

substantively.</div1><div1

part="n"

n="ADAMAS"

org="uniform"

sample="complete"

type="entry"

><head

>ADAMAS</head><p

>, in <hi

rend="italics"

>Astrology,</hi> a name given to the moon.</div1><div1

part="n"

n="ADAR"

org="uniform"

sample="complete"

type="entry"

><head

>ADAR</head><p

>, in the Hebrew <hi

rend="italics"

>Chronology,</hi> is the 6th month

of their civil year, but the 12th of their ecclesiastical

year. It contains only 29 days; and it answers to our

February; but sometimes entering into the month of

March, according to the course of the moon.</div1><div1

March, according to the course of the moon.</div1><div1 part="n" n="ADDITION" org="uniform" sample="complete" type="entry"><head>ADDITION</head>, the uniting or joining of two or more

part="n"

n="ADDITION"

org="uniform"

sample="complete"

type="entry"

><head

>ADDITION</head><p

>, the uniting or joining of two or more

things together; or the finding of one quantity equal

to two or more others taken together.<div2

to two or more others taken together.<div2 part="n" n="Addition" org="uniform" sample="complete" type="subentry"><head><hi rend="smallcaps">Addition</hi>, in <hi rend="italics">Arithmetic</hi></head>, is the first of the four fundamental

part="n"

n="Addition"

org="uniform"

sample="complete"

type="subentry"

><head

><hi

rend="smallcaps"

>Addition</hi>, in <hi

rend="italics"

>Arithmetic</hi></head><p

>, is the first of the four fundamental

rules or operations of that science; and it

consists in finding a number equal to several others

taken together, or in finding the most simple expression

of a number according to the established notation. The

quantity so found equal to several others taken together,

is named their sum.<p

is named their sum.The sign or character of addition is +, and is called

>The sign or character of addition is +, and is called

<hi rend="italics">plus.</hi> This character is set between the quantities to

<hi

rend="italics"

>plus.</hi> This character is set between the quantities to

be added, to denote their sum: thus, , that

is, 3 plus 6 are equal to 9; and ,

that is, 2 plus 4 plus 6 are equal to 12.<p

that is, 2 plus 4 plus 6 are equal to 12.Simple numbers are either added as above;

>Simple numbers are either added as above;

or else by placing them under one another, as

in the margin, and adding them together, one

after another, beginning at the bottom: thus 2

and 4 make 6, and 6 make 12.

<table

<table><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">6</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">4</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">2</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">12</cell></row></table>Compound numbers, or numbers consisting of more

><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>6</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>4</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>2</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>12</cell></row></table><p

>Compound numbers, or numbers consisting of more

figures than one, are added, by first ranging the numbers

in columns under each other, placing always the

numbers of the same denomination under each other,

Line 5078

Line 3293

tens, and in that case setting down only the overplus,

and carrying one for each ten to the next column.

Thus, to add 451 and 326,

<table

<table><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">451</cell><cell cols="1" rows="1" rend="rowspan=2" role="data"><hi rend="size(6)">}</hi></cell><cell cols="1" rows="1" rend="rowspan=2 align=center" role="data">that is</cell><cell cols="1" rows="1" rend="rowspan=2" role="data"><hi rend="size(6)">{</hi></cell><cell cols="1" rows="1" rend="align=right" role="data">400 + 50 + 1</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">326</cell><cell cols="1" rows="1" rend="align=right" role="data">300 + 20 + 6</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">Sum 777</cell><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=center" role="data">=</cell><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">700 + 70 + 7</cell></row></table>Also to add the numbers ; set them down as

><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>451</cell><cell

cols="1"

rows="1"

rend="rowspan=2"

role="data"

><hi

rend="size(6)"

>}</hi></cell><cell

cols="1"

rows="1"

rend="rowspan=2 align=center"

role="data"

>that is</cell><cell

cols="1"

rows="1"

rend="rowspan=2"

role="data"

><hi

rend="size(6)"

>{</hi></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>400 + 50 + 1</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>326</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>300 + 20 + 6</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>Sum 777</cell><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>=</cell><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>700 + 70 + 7</cell></row></table><p

>Also to add the numbers ; set them down as

in the margin, and beginning at the lowest

number on the right hand, say 8 and 7

make 15, and 2 make 17, and 9 make

Line 5165

Line 3310

of the columns set under one another, as

in the margin, and then these added up in the same

manner.

<cb

<cb/>When a great number of separate sums or numbers

/><p

>When a great number of separate sums or numbers

are to be added, as in long accounts, it is easier to

break or separate them into two or more parcels, which

are added up severally, and then their sums added together

for the total sum. And thus also the truth of

the addition may be proved, by dividing the numbers

into parcels different ways, as the totals must be the

same in both cases when the operation is right.<p

same in both cases when the operation is right.Another method of proving addition was given by

>Another method of proving addition was given by

Dr. Wallis, in his Arithmetic, published 1657, by casting

out the nines, which method of proof extends also

to the other rules of arithmetic. The method is this:

Line 5187

Line 3329

as also by the former excesses of 9, so shall the last excesses

be equal when the work is right. So the former

example will be proved as below:

<table

<table><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">329</cell><cell cols="1" rows="1" rend="rowspan=6" role="data">Excess of 9's</cell><cell cols="1" rows="1" role="data">5</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">1562</cell><cell cols="1" rows="1" role="data">5</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">20347</cell><cell cols="1" rows="1" role="data">7</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">712048</cell><cell cols="1" rows="1" role="data">4</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">734286</cell><cell cols="1" rows="1" role="data">3</cell></row></table>When the numbers are of different denominations;

><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>329</cell><cell

cols="1"

rows="1"

rend="rowspan=6"

role="data"

>Excess of 9's</cell><cell

cols="1"

rows="1"

role="data"

>5</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>1562</cell><cell

cols="1"

rows="1"

role="data"

>5</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>20347</cell><cell

cols="1"

rows="1"

role="data"

>7</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>712048</cell><cell

cols="1"

rows="1"

role="data"

>4</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>734286</cell><cell

cols="1"

rows="1"

role="data"

>3</cell></row></table><p

>When the numbers are of different denominations;

as pounds, shillings, and pence; or yards, seet, and

inches; place the numbers of the same kind under one

another, as pence under pence, shillings under shillings,

&c; then add each column separately, and carry the

overplus as before, from one column to another. As

in the following examples:

<table

<table><row role="data"><cell cols="1" rows="1" rend="align=center" role="data">l.</cell><cell cols="1" rows="1" rend="align=center" role="data">s.</cell><cell cols="1" rows="1" rend="align=center" role="data">d.</cell><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=center" role="data">Yards.</cell><cell cols="1" rows="1" rend="align=center" role="data">Feet.</cell><cell cols="1" rows="1" rend="align=center" role="data">Inches.</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">271</cell><cell cols="1" rows="1" rend="align=right" role="data">12</cell><cell cols="1" rows="1" rend="align=right" role="data">3</cell><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">271</cell><cell cols="1" rows="1" rend="align=right" role="data">10</cell><cell cols="1" rows="1" rend="align=center" role="data">3</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">94</cell><cell cols="1" rows="1" rend="align=right" role="data">14</cell><cell cols="1" rows="1" rend="align=right" role="data">7</cell><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">36</cell><cell cols="1" rows="1" rend="align=right" role="data">2</cell><cell cols="1" rows="1" rend="align=center" role="data">7</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">42</cell><cell cols="1" rows="1" rend="align=right" role="data">5</cell><cell cols="1" rows="1" rend="align=right" role="data">10</cell><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">14</cell><cell cols="1" rows="1" rend="align=right" role="data">2</cell><cell cols="1" rows="1" rend="align=center" role="data">5</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">408</cell><cell cols="1" rows="1" rend="align=right" role="data">12</cell><cell cols="1" rows="1" rend="align=right" role="data">8</cell><cell cols="1" rows="1" rend="align=center" role="data">sums</cell><cell cols="1" rows="1" rend="align=right" role="data">323</cell><cell cols="1" rows="1" rend="align=right" role="data">0</cell><cell cols="1" rows="1" rend="align=center" role="data">3</cell></row></table><hi rend="smallcaps">Addition</hi> <hi rend="italics">of Decimals,</hi> is performed in the same

><row

role="data"

><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>l.</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>s.</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>d.</cell><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>Yards.</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>Feet.</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>Inches.</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>271</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>12</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>3</cell><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>271</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>10</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>3</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>94</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>14</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>7</cell><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>36</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>2</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>7</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>42</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>5</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>10</cell><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>14</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>2</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>5</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>408</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>12</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>8</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>sums</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>323</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>0</cell><cell

cols="1"

rows="1"

rend="align=center"

role="data"

>3</cell></row></table><p

><hi

rend="smallcaps"

>Addition</hi> <hi

rend="italics"

>of Decimals,</hi> is performed in the same

manner as that of whole numbers, placing the numbers

of the same denomination under each other, in which

case the decimal separating points will range straight

in one column; as in this example, to add together

these numbers .

<table

<table><row role="data"><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">371.0496</cell></row><row role="data"><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">25.213 </cell></row><row role="data"><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">1.704 </cell></row><row role="data"><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">924.61  </cell></row><row role="data"><cell cols="1" rows="1" role="data"/><cell cols="1" rows="1" rend="align=right" role="data">.0962</cell></row><row role="data"><cell cols="1" rows="1" rend="align=right" role="data">The sum</cell><cell cols="1" rows="1" rend="align=right" role="data">1322.6728</cell></row></table><hi rend="smallcaps">Addition</hi> <hi rend="italics">of Vulgar Fractions,</hi> is performed by

><row

role="data"

><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>371.0496</cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>25.213 </cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>1.704 </cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>924.61  </cell></row><row

role="data"

><cell

cols="1"

rows="1"

role="data"

></cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>.0962</cell></row><row

role="data"

><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>The sum</cell><cell

cols="1"

rows="1"

rend="align=right"

role="data"

>1322.6728</cell></row></table><p

><hi

rend="smallcaps"

>Addition</hi> <hi

rend="italics"

>of Vulgar Fractions,</hi> is performed by

bringing all the proposed fractions to a common denominator,

if they have different ones, which is an indispensable

preparation; then adding all the numerators

<pb

n="30"

/><cb

together, and placing their sum over the common denominator

for the sum total required.<p

for the sum total required.So .ADDITION <hi rend="italics">in Algebra,</hi> or the addition of indeterminate

>So .<p

>ADDITION <hi

rend="italics"

>in Algebra,</hi> or the addition of indeterminate

quantities, denoted by letters of the alphabet,

is performed by connecting the quantities together by

their proper signs, and uniting or reducing such as are

susceptible of it, namely similar quantities, by adding

their co-efficients together if the signs are the same, but

subtracting them when different. Thus the quantity

<hi

<hi rend="italics">a</hi> added to the quantity <hi rend="italics">b,</hi> makes <hi rend="italics">a</hi> + <hi rend="italics">b</hi>; and <hi rend="italics">a</hi> joined

rend="italics"

with-<hi rend="italics">b,</hi> makes <hi rend="italics">a</hi>-<hi rend="italics">b</hi>; also-<hi rend="italics">a</hi> and-<hi rend="italics">b</hi> make-<hi rend="italics">a</hi>-<hi rend="italics">b</hi>;

>a</hi> added to the quantity <hi

and 3<hi rend="italics">a</hi> and 5<hi rend="italics">a</hi> make 3<hi rend="italics">a</hi> + 5<hi rend="italics">a</hi> or 8<hi rend="italics">a,</hi> by uniting

rend="italics"

>b,</hi> makes <hi

rend="italics"

>a</hi> + <hi

rend="italics"

>b</hi>; and <hi

rend="italics"

>a</hi> joined

with-<hi

rend="italics"

>b,</hi> makes <hi

rend="italics"

>a</hi>-<hi

rend="italics"

>b</hi>; also-<hi

rend="italics"

>a</hi> and-<hi

rend="italics"

>b</hi> make-<hi

rend="italics"

>a</hi>-<hi

rend="italics"

>b</hi>;

and 3<hi

rend="italics"

>a</hi> and 5<hi

rend="italics"

>a</hi> make 3<hi

rend="italics"

>a</hi> + 5<hi

rend="italics"

>a</hi> or 8<hi

rend="italics"

>a,</hi> by uniting

the similar numbers 3 and 5 to make 8.

Thus also .<p

Thus also .In the addition of surd or irrational quantities, they

>In the addition of surd or irrational quantities, they

must be reduced to the same denomination, or to the

same radical, if that can be done; then add or unite

the rational parts, and subjoin the common surd.

Otherwise connect them with their own signs.<p

Otherwise connect them with their own signs.So ;

>So ;

but of √5 and √6 the sum is set down √5 + √6,

because the terms are incommensurable, and not reducible

to a common surd.<p

to a common surd.<hi rend="smallcaps">Addition</hi> <hi rend="italics">of Logarithms.</hi> See Logarithms.

><hi

<cb/><hi rend="smallcaps">Addition</hi> <hi rend="italics">of Ratios,</hi> the same as composition of

rend="smallcaps"

ratios; which see.</div2></div1><div1 part="n" n="ADDITIVE" org="uniform" sample="complete" type="entry"><head>ADDITIVE</head>, denotes something to be added to

>Addition</hi> <hi

rend="italics"

>of Logarithms.</hi> See Logarithms.

<cb

/><p

><hi

rend="smallcaps"

>Addition</hi> <hi

rend="italics"

>of Ratios,</hi> the same as composition of

ratios; which see.</div2></div1><div1

part="n"

n="ADDITIVE"

org="uniform"

sample="complete"

type="entry"

><head

>ADDITIVE</head><p

>, denotes something to be added to

another, in contradistinction to something to be taken

away or subtracted. So astronomers speak of additive

equations, and geometricians of additive rations.</div1><div1

equations, and geometricians of additive rations.</div1><div1 part="n" n="ADELARD" org="uniform" sample="complete" type="entry"><head>ADELARD</head>, or <hi rend="smallcaps">Athelard</hi>, was a learned monk

part="n"

n="ADELARD"

org="uniform"

sample="complete"

type="entry"

><head

>ADELARD</head><p

>, or <hi

rend="smallcaps"

>Athelard</hi>, was a learned monk

of Bath, in England, who flourished about the year

1130, as appears by some manuscripts of his in Corpus

Christi, and Trinity Colleges, Oxford. Vossius says he

Line 5637

Line 3385

Erichiafarim, upon the seven planets. He wrote a

book on the seven liberal arts, another on the astrolabe,

another on the causes of natural compositions, besides

several on physics and on medicine.<p

several on physics and on medicine.Although Vossius refers to Oxford for some of these

>Although Vossius refers to Oxford for some of these

manuscripts, it would yet seem they were not to be

found there in Wallis's time; for the Doctor, speaking

of this author, and other English authors and travellers

Line 5653

Line 3400

Vossius out of that manuscript copy. Whoever hath

them, would do a kindness (by some way or other) to

restore them, or at leaft a copy of them.” Wallis's

Algebra, pa. 6.</div1><div1

Algebra, pa. 6.</div1><div1 part="n" n="ADELM" org="uniform" sample="complete" type="entry"><head>ADELM</head>, <hi rend="smallcaps">Aldhelmus</hi>, or <hi rend="smallcaps">Althelmus</hi>, a learned

part="n"

n="ADELM"

org="uniform"

sample="complete"

type="entry"

><head

>ADELM</head><p

>, <hi

rend="smallcaps"

>Aldhelmus</hi>, or <hi

rend="smallcaps"

>Althelmus</hi>, a learned

Englishman, who flourished about the year 680. He

was sirst abbot of Malmsbury, and afterward bishop of

Shirburn. He died in the year 709, in the monastery

of Malmsbury.<p

of Malmsbury.Adelm was the son of Kenred or Kenten, who was

>Adelm was the son of Kenred or Kenten, who was

the brother of Ina, king of the West Saxons in England.

Beside certain books in theology, he composed

several on the mathematical sciences &c; as Arithmetic,

and Astrology, and librum de philosophorum disciplinis.

See Bede's History, lib. 5. cap. 19. He is also mentioned

by Bale and William of Malmsbury.</div1><div1

by Bale and William of Malmsbury.</div1><div1 part="n" n="ADERAIMIN" org="uniform" sample="complete" type="entry"><head>ADERAIMIN</head>, or <hi rend="smallcaps">Alderaimin</hi>, the Arabic name

part="n"

n="ADERAIMIN"

org="uniform"

sample="complete"

type="entry"

><head

>ADERAIMIN</head><p

>, or <hi

rend="smallcaps"

>Alderaimin</hi>, the Arabic name

of a star of the third magnitude, in the left shoulder of

Cepheus, marked <foreign

Cepheus, marked <foreign lang="greek">a</foreign> by Bayer. Its longitude for 1761,

lang="greek"

<foreign lang="greek">g</foreign> 9° 30′ 8″ north latitude 68° 56′ 20″.</div1><div1 part="n" n="ADFECTED" org="uniform" sample="complete" type="entry"><head>ADFECTED</head>, see <hi rend="smallcaps">Affected.</hi></div1><div1 part="n" n="ADHESION" org="uniform" sample="complete" type="entry"><head>ADHESION</head>, <hi rend="smallcaps">Adherence</hi>, in <hi rend="italics">Physics,</hi> is the state

>a</foreign> by Bayer. Its longitude for 1761,

<foreign

lang="greek"

>g</foreign> 9° 30′ 8″ north latitude 68° 56′ 20″.</div1><div1

part="n"

n="ADFECTED"

org="uniform"

sample="complete"

type="entry"

><head

>ADFECTED</head><p

>, see <hi

rend="smallcaps"

>Affected.</hi></div1><div1

part="n"

n="ADHESION"

org="uniform"

sample="complete"

type="entry"

><head

>ADHESION</head><p

>, <hi

rend="smallcaps"

>Adherence</hi>, in <hi

rend="italics"

>Physics,</hi> is the state

of two bodies, joined or fastened together, whether by

mutual attraction, the interposition of their own parts,

or the impulse or pressure of external bodies. See

<hi

<hi rend="smallcaps">Cohesion.</hi>Thus two hollow hemispheres, exhausted of air, are

rend="smallcaps"

>Cohesion.</hi><p

>Thus two hollow hemispheres, exhausted of air, are

made to adhere firmly together by the pressure of the

atmosphere on their convex or external surfaces; for

if they are introduced into an exhausted receiver, they

presently fall asunder. Also two very well polished

<pb

n="31"

/><cb

planes adhere firmly together, partly by the external

pressure of the atmosphere, and partly by the attraction

of their parts.<p

of their parts.In No. 389 of the Philos. Trans. Dr. Desaguliers

>In No. 389 of the Philos. Trans. Dr. Desaguliers

has given experiments of the adhesion of leaden bullets

to each other: the cause of which he resolves into the

principle of attraction.<p

principle of attraction.M. Musschenbroeck, in his Essai de Physique, has

>M. Musschenbroeck, in his Essai de Physique, has

given a great many remarks on the adhesion of bodies,

and relates various experiments which he had made

upon this matter, but chiefly relative to the resistance

Line 5749

Line 3439

as well as to the bodies they touch. The same may be

said of the particles of air, on which M. Petit has a

memoir among those of the Paris Academy of Sciences

for the year 1731.<p

for the year 1731.Some authors however are not willing to admit that

>Some authors however are not willing to admit that

the adhesion of the parts of water, or indeed of bodies

in general, is to be attributed to the attraction of their

parts, and they reason thus: suppose, say they, that

Line 5762

Line 3451

within the circle; but as these particles act in contrary

directions, their mutual effects must destroy one another,

and there can be no attraction of the particle, since it

will have no more tendency one way than another.</div1><div1

will have no more tendency one way than another.</div1><div1 part="n" n="ADHIL" org="uniform" sample="complete" type="entry"><head>ADHIL</head>, in <hi rend="italics">Astronomy,</hi> a star, of the sixth magnitude,

part="n"

n="ADHIL"

org="uniform"

sample="complete"

type="entry"

><head

>ADHIL</head><p

>, in <hi

rend="italics"

>Astronomy,</hi> a star, of the sixth magnitude,

upon the garment of Andromeda, under the

last star in her foot.</div1><div1

last star in her foot.</div1><div1 part="n" n="ADJACENT" org="uniform" sample="complete" type="entry"><head>ADJACENT</head>, whatever lies immediately by the side

part="n"

of another.<hi rend="smallcaps">Adjacent</hi> <hi rend="italics">Angle,</hi> in <hi rend="italics">Geometry,</hi> is said of an angle

n="ADJACENT"

org="uniform"

sample="complete"

type="entry"

><head

>ADJACENT</head><p

>, whatever lies immediately by the side

of another.<p

><hi

rend="smallcaps"

>Adjacent</hi> <hi

rend="italics"

>Angle,</hi> in <hi

rend="italics"

>Geometry,</hi> is said of an angle

when it is immediately contiguous to another, so that

they have both one common side. And the term is

more particularly used when the two angles have not

only one common side, but also when the other two

sides form one continued right line.<p

sides form one continued right line.<hi rend="smallcaps">Adjacent</hi> <hi rend="italics">bodies, in Physics,</hi> are understood of those

><hi

that are near, or next to, some other body.</div1><div1 part="n" n="ADJUTAGE" org="uniform" sample="complete" type="entry"><head>ADJUTAGE</head>, or rather AJUTAGE; which see.</div1><div1 part="n" n="ADSCRIPTS" org="uniform" sample="complete" type="entry"><head>ADSCRIPTS</head>, in <hi rend="italics">Trigonometry,</hi> is used by some

rend="smallcaps"

>Adjacent</hi> <hi

rend="italics"

>bodies, in Physics,</hi> are understood of those

that are near, or next to, some other body.</div1><div1

part="n"

n="ADJUTAGE"

org="uniform"

sample="complete"

type="entry"

><head

>ADJUTAGE</head><p

>, or rather AJUTAGE; which see.</div1><div1

part="n"

n="ADSCRIPTS"

org="uniform"

sample="complete"

type="entry"

><head

>ADSCRIPTS</head><p

>, in <hi

rend="italics"

>Trigonometry,</hi> is used by some

mathematicians, for the tangents of arcs. Vieta calls

them also prosines.<p

them also prosines.ADVANCE-<hi rend="smallcaps">Fosse</hi>, in Fortification, a ditch thrown

>ADVANCE-<hi

rend="smallcaps"

>Fosse</hi>, in Fortification, a ditch thrown

round the esplanade or glacis of a place, to prevent its

being surprised by the besiegers.<p

being surprised by the besiegers.The ditch sometimes made in that part of the lines

>The ditch sometimes made in that part of the lines

or retrenchments nearest the enemy, to prevent him

from attacking them, is also called the advance-fosse.<p

from attacking them, is also called the advance-fosse.The advance-fosse should always be full of water,

>The advance-fosse should always be full of water,

otherwise it will serve to cover the enemy from the fire

of the place, if he should become master of the fosse.

Beyond the advance-fosse it is usual to construct lunettes,

redouts, &c.</div1><div1

redouts, &c.</div1><div1 part="n" n="ADVENT" org="uniform" sample="complete" type="entry"><head>ADVENT</head>, <hi rend="italics">Adventus,</hi> in the Calendar, the time immediately

part="n"

n="ADVENT"

org="uniform"

sample="complete"

type="entry"

><head

>ADVENT</head><p

>, <hi

rend="italics"

>Adventus,</hi> in the Calendar, the time immediately

preceding Christmas; and was anciently employed

in pious preparation for the <hi

in pious preparation for the <hi rend="italics">adventus,</hi> or coming

rend="italics"

>adventus,</hi> or coming

on, of the feast of the Nativity.

<cb

<cb/>Advent includes four Sundays, or weeks; commencing

/><p

>Advent includes four Sundays, or weeks; commencing

either with the Sunday which falls on

St. Andrew's day, namely the 30th day of November,

or the nearest Sunday to that day, either before or

after.<p

after.ÆOLIPILE, <hi rend="italics">Æolipile,</hi> in Hydraulics, a hollow ball

>ÆOLIPILE, <hi

rend="italics"

>Æolipile,</hi> in Hydraulics, a hollow ball

of metal, with a very small hole or opening; chiefly

used to shew the convertibility of water into elastic

steam. The best way of fitting up this instrument, is

Line 5885

Line 3504

very little water in it, and that the small pipe be not

stopped with any thing; for in such case, the included

elastic steam will suddenly burst the ball with a very

dangerous explosion.<p

dangerous explosion.This instrument was known to the ancients, being

>This instrument was known to the ancients, being

mentioned by Vitruvius, lib. 1. cap. 6. It is also

treated of, or mentioned, by several modern authors,

as Descartes, in his Meteor. cap. 4; and Father Mersennus,

in prop. 29 Phædom. Pneumat. uses it to weigh

the air, by first weighing the instrument when red hot,

and having no water in it; and afterwards weighing

the same when it becomes cold. But the conclusion

Line 5901

Line 3519

raresied but about 70 times; and consequently the

weight obtained by the above process, will be about

one-70th too small, or more or less according to the

intensity of the heat.<p

intensity of the heat.In Italy it is said that the Æolipile is often used to

>In Italy it is said that the Æolipile is often used to

cure smoaky chimneys: for being hung over the fire,

the blast arising from it carries up the loitering smoke

along with it.<p

along with it.And some have imagined that the æolipile might

>And some have imagined that the æolipile might

be employed as bellows to blow up a fire, having the

blast from the pipe directed into the fire: but experience

would soon convince them of their mistake; for

it would rather blow the sire <hi

it would rather blow the sire <hi rend="italics">out</hi> than <hi rend="italics">up,</hi> as it is not

rend="italics"

>out</hi> than <hi

rend="italics"

>up,</hi> as it is not

air, but rarefied water, that is thus violently blown

through the pipe.<p

through the pipe.ÆOLUS, in Mechanics, a small portable machine,

>ÆOLUS, in Mechanics, a small portable machine,

not long since invented by Mr. Tidd, for refreshing

and changing the air in rooms which are made too

close.<p

close.The machine is adapted to supply the place of a

>The machine is adapted to supply the place of a

<pb

n="32"

/><cb

square of glass in a sash-window, where it works with

little or no noise, on the principle of the sails of a mill,

or a smoke-jack; and thus admitting an agreeable

quantity of air, at a convenient part of the room.<p

quantity of air, at a convenient part of the room.Æ<hi rend="smallcaps">OLUS</hi>'<hi rend="italics">s Harp,</hi> or <hi rend="italics">Æolian Harp,</hi> an instrument so

>Æ<hi

rend="smallcaps"

>OLUS</hi>'<hi

rend="italics"

>s Harp,</hi> or <hi

rend="italics"

>Æolian Harp,</hi> an instrument so

named, from its producing an agreeable melody, merely

by the action of the wind.<p

by the action of the wind.Neither the age nor inventor of this instrument are

>Neither the age nor inventor of this instrument are

very well known. It is not mentioned by Mersennus

in his Harmonics, where he describes most sorts of

in his