A Mathematical and Philosphical Dictionary
, the art or act of measuring the capacities or contents of all kinds of vessels, and determining the quantity of fluids, or other matters contained in them. These are principally pipes, tuns, barrels, rundlets, and other casks; also backs, coolers, vats, &c.
As to the solid contents of all prismatical vessels, as cubes, parallelopipedons, cylinders, &c, they are found by multiplying the area of the base by their altitude. And the contents of all pyramidal bodies, and cones, are equal to 1 3d of the same.
In Gauging, it has been usual to divide casks into four varieties or forms, denominated as follows, from the supposed resemblance they bear to the frustums of solids of the same names: viz,
1. The middle frustum of a spheroid,
2. The middle frustum of a parabolic spindle,
3. The two equal frustums of a paraboloid,
4. The two equal frustums of a cone.
And particular rules, adapted to each of these forms, may be found in most books of Gauging, and in my Mensuration, p. 575 &c. But as the form is imaginary, and only guessed at, it hardly ever happens that a true solution is brought out in this way; beside which, it is very troublesome and inconvenient to have so many rules to put in practice. I shall therefore give here one rule only, from p. 592 of that book, which is not only general for all casks that are commonly met with, but quite easy, and very accurate, as having been often verified and proved by filling the casks with a true gallon measure.
General Rule. Add into one sum, 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the product of those diameters; multiply the sum by the length of the cask, and the product by the number .00034; then this last product divided by 9 will give the wine gallons, and divided by 11 will give the ale gallons. Or, is the content in inches; which being divided by 231 for wine gallons, or by 282 for ale gallons, will be the content.
For Ex. If the length of a cask be 40 inches, the bung diameter 32, and the head diameter 24. Here 322 × 39=39936and 242 × 25 =14400and 32 × 24 × 26=19968the sum74304multiplied by40and divid. by114)2972160gives26071cubic inches; this divided by 231 gives 112 wine gallons, or divided by 282 gives 92 ale gallons.
But the common practice of Gauging is performed mechanically, by means of the Gauging or Diagonal Rod, or the Gauging Sliding Rule, the description and use of which here follow.Gauging
, or Diagonal, Rod, is a rod or rule adapted for determining the contents of casks, by measuring the diagonal only, viz the diagonal from the bung to the extremity of the opposite stave next the head. It is a square rule, having 4 sides or faces, being usually 4 feet long, and folding together by means of joints.
Upon one face of the rule is a scale of inches, for taking the measure of the diagonal; to these are adapted the areas, in ale gallons, of circles to the corresponding diameters, like the lines on the under sides of the three slides in the sliding rule, described below. And upon the opposite face are two scales, of ale and wine gallons, expressing the contents of casks having the corresponding diagonals; and these are the lines which chiefly constitute the difference between this instrument and the sliding rule; for all the other lines upon it are the same with those in that instrument, and are to be used in the same manner.
To use the Diagonal Rod. Unfold the rod straight out, and put it in at the bung hole of the cask to be gauged, till its end arrive at the intersection of the head and opposite stave, or to the farthest possible distance from the bung-hole, and note the inches and parts cut by the middle of the bung; then draw out the rod, and look for the same inches and parts on the opposite face of it, and annexed to them are found the contents of the cask, both in ale and wine gallons.
For Ex. Let it be required to find, by this rod, the content of a cask whose diagonal measures 34.4 inches; which answers to the cask in the foregoing example, whose head and bung diameters are 32 and 24, and length 40 inches; for if to the square of 20, half the length, be added the square of 28, half the sum of the diameters, the square root of the sum will be 34.4 nearly.
Now, to this diagonal 34.4, corresponds, upon the rule, the content 91 ale gallons, or 111 wine gallons; which are but 1 less than the content brought out by the former general rule above given.
Gauging Rule, or Sliding Rule, is a sliding rule particularly adapted to the purposes of Gauging. It is a square rule, of four faces or sides, three of which are furnished with sliding pieces running in grooves. The lines upon them are mostly logarithmic ones, or distances which are proportional to the logarithms of the numbers placed at the ends of them; which kind of lines was placed upon rulers, by Mr. Edmund Gunter, for expeditiously performing arithmetical operations, using a pair of compasses for taking off and applying the several logarithmic distances: but instead of the compasses, sliding pieces were added, by Mr. Thomas Everard, as more certain and convenient in practice, from whom this sliding rule is often called Everard's Rule. For the more particular description and uses of this rule, see my Mensuration, p. 564, 2d edition.
The writers on Gauging are, Beyer, Kepler, Dechales, Hunt, Everard, Dougherty, Shettleworth, Shirtcliffe, Leadbetter, &c.