Archimedes Texts

520
continued, the thicker the ice becomes upon the water in ponds, and the deeper into the earth the ground is frozen. In about 16 or 17 days Frost, Mr. Boyle found it had penetrated 14 inches into the ground. At Moscow, in a hard season, the Frost will penetrate 2 seet deep in the ground; and Capt. James found it penetrated 10 feet deep in Charlton island, and the water in the same island was frozen to the depth of 6 feet. Scheffer assures us, that in Sweden the Frost pierces 2 cubits, or Swedish ells into the earth, and turns what moisture is found there into a whitish substance, like ice; and standing waters to 3 ells, or more. The same author also mentions sudden cracks or rifts in the ice of the lakes of Sweden, 9 or 10 feet deep, and many leagues long; the rupture being made with a noise not less loud than if many guns were discharged together. By such means however the fishes are surnished with air; so that they are rarely found dead.

The natural histories of Frosts furnish very extraordinary esfects of them. The trees are often scorched, and burnt up, as with the most excessive heat; and split or shattered. In the great Frost in 1683, the trunks of oak, ash, walnut, &c, were miserably split and cleft, so that they might be seen through, and the cracks often attended with dreadful noises like the explosion of fire-arms. Philos. Trans. number 165.

The close of the year 1708, and the beginning of 1709, were remarkable, throughout the greatest part of Europe, for a severe Frost. Dr. Derham says, it was the greatest in degree, if not the most universal, in the memory of man; extending through most parts of Europe, though scarcely felt in Scotland or Ireland.

In very cold countries, meat may be preserved by the Frost 6 or 7 months, and prove tolerable good eating. See Capt. Middleton's observations made in Hudson's bay, in the Philos. Trans. no. 465, sect. 2. In that climate the Frost seems never out of the ground, it having been found hard frozen in the two summer months. Brandy and spirit of wine, set out in the open air, freeze to solid ice in 3 or 4 hours. Lakes and standing waters, not above 10 or 12 feet deep, are frozen to the ground in winter, and all their fish perish. But in rivers, where the current of the tide is strong, the ice does not reach so deep, and the fish are preserved. Id. ib.

Some remarkable instances of Frost in Europe, and chiesly in England, are recorded as below: In the year

220, Frost in Britain that lasted 5 months.

250, The Thames frozen 9 weeks.

291, Most rivers in Britain srozen 6 weeks.

359, Severe Frost in Scotland for 14 weeks.

508, The rivers in Britain frozen for 2 months.

558, The Danube quite frozen over.

695, Thames frozen 6 weeks; booths built on it.

759, Frost from Oct. 1 till Feb. 26, 760.

827, Frost in England for 9 weeks.

859, Carriages used on the Adriatic sea.

908, Most rivers in England frozen 2 months.

923, The Thames frozen 13 weeks.

987, Frost lasted 120 days: began Dec. 22.

998, The Thames frozen 5 weeks.

1035, Severe Frost on June 24: the corn and fruits destroyed.

1063, The Thames frozen 14 weeks.

1076, Frost in England from Nov. till April.

1114, Several wooden bridges carried away by ice.

1205, Frost from Jan. 14 till March 22.

1407, Frost that lasted 15 weeks.

1434, From Nov. 24 till Feb. 10. Thames frozen down to Gravesend.

1683, Frost for 13 weeks.

170 8/9, Severe Frost for many weeks.

1715, The same for many weeks.

1739, One for 9 weeks. Began Dec. 24.

1742, Severe Frost for many weeks.

1747, Severe Frost in Russia.

1754, Severe one in England.

1760, The same in Germany.

1776, The same in England.

1788, Thames frozen below bridge; booths on it.

Hoar Frost, is the dew frozen or congealed, early in cold mornings; chiefly in autumn. Though many Cartesians will have it formed of a cloud; and either congealed in the cloud, and so let fall; or ready to be congealed as soon as it arrives at the earth.

Hoar Frost, M. Regis observes, consists of an assemblage of little parcels of ice crystals; which are of various figures, according to the different disposition of the vapours, when met and condensed by the cold.

FRUSTUM

, in Geometry, is the part of a solid next the base, left by cutting off the top, or segment, by a plane parallel to the base: as the Frustum of a pyramid, of a cone, of a conoid, of a spheroid, or of a sphere, which is any part comprised between two parallel circular sections; and the Middle Frustum of a sphere, is that whose ends are equal circles, having the centre of the sphere in the middle of it, and equally distant from both ends.

For the Solid Content of the Frustum of a cone, or of any pyramid, whatever figure the base may have. Add into one sum, the areas of the two ends and the mean proportional between them; then 1/3 of that sum will be a mean area, or the area of an equal prism, of the same altitude with the Frustum; and consequently that mean area being multiplied by the height of the Frustum, the product will be the solid content of it. That is, if A denote the area of the greater end, a that of the less, and h the height; then is the solidity.

Other rules for pyramidal or conic Frustums may be seen in my Mensuration, p. 189, 2d edit. 1788.

The curve Surface of the Zone or Frustum of a sphere, is had by multiplying the circumference of the sphere by the height of the Frustum. Mensur. p. 197.

And the Solidity of the same Frustum is found, by adding together the squares of the radii of the two ends. and 1/3 of the square of the height of the Frustum, then multiplying the sum by the said height and by the number 1.5708. That is, is the solid content of the spheric Frustum, whose height is h, and the radii of its ends R and r, p being = 3.1416. Mensur. p. 209.

For the Frustums of spheroids, and conoids, either parabolic or hyperbolic, see Mensur. p. 326, 328, 332, 382, 435. And in p. 486 &c, are general theorem<*> concerning the Frustum of a sphere, cone, spheroid, or