the density of the former to that of the latter, as 99 to 68, or as 10 to 7 nearly, and their mean distance 30 of the earth's diameters? Ans. at parts of a diameter from the earth's centre, 4 I or parts of a diameter, or 648 miles below the surface. QUEST. 40. Whereabouts, between the earth and moon, are their attractions equal to each other? Or where must another body be placed, so as to remain suspended in equi librio, not being more attracted to the one than to the other, or having no tendency to fall either way? Their dimensions being as in the last question. Ans. From the earth's centre 26 of the earth's diameters. QUEST. 41. Suppose a stone dropt into an abyss, should be stopped at the end of the 11th second after its delivery; what space would it have gone through? Ans. 1946 feet. QUEST. 42. What is the difference between the depths of two wells, into each of which should a stone be dropped at the same instant, the one will strike the bottom at 6 seconds, the other at 10? Ans. 1029 feet. QUEST. 43. If a stone be 19 seconds in descending from the top of a precipice to the bottom, what is its height? Ans. 6115 feet. QUEST. 44. In what time will a musket ball, dropped from the top of Salisbury steeple, said to be 400 feet high, reach the bottom? Ans. 5 seconds nearly. QUEST. 45. If a heavy body be observed to fall through 100 feet in the last second of time, from what height did it fall, and how long was it in motion? Ans. time 333 sec. and height 2094273 feet. QUEST. 46. A stone being let fall into a well, it was observed that, after being dropped, it was 10 seconds before the sound of the fall at the bottom reached the ear. What is the depth of the well? Ans. 1270 feet nearly. QUEST. 47. It is proposed to determine the length of a pendulum vibrating seconds, in the latitude of London, where a heavy body falls through 16 feet in the first second of time? Ans. 39 11 inches. By experiment this length is found to be 394 inches. QUEST. 48. top, but its side next the bank of earth perpendicular QUEST. 31. But if the earth will only stand at a 30 degrees to the horizontal line; it is required to the thickness of wall in both the preceding cases Ans. the breadth of the rectangle 12, but the base of the triangular bank 12√ QUEST.32. To find the thickness of an gular wall, necessary to support a body of being 10 feet deep, and the wall 12 feet hi fic gravity of the wall to that of the wate 4 L be of wood, floating in common water, dry above the water, and 485 *; it is proposed to determine "hat sort of wood it is made nd each side 40 inches. ore weighs, in air her fragment uired their >. as 145 to 132. glass, in the scale, gnet 102 grains; but re than 120 grains, and r specific gravities turn out ass to magnet as 3933 to 5202 or nearly as 10 to 13. ig of Sicily, ordered his jeweller to Containing, 63 ounces of gold. The hat substituting part silver was only a ; which taking air, Archimedes was apine it; who, on putting it into a vessel of it raised the fluid 8-2245 cubic inches: and covered that the inch of gold more critically 10:36 ounces, and that of silver but 5.85 ounces, he by calculation what part of the king's gold had been ged. And you are desired to repeat the process. Ans. 28.8 ounces. QUEST. 60. Supposing the cubic inch of common glass weigh 1.4921 ounces troy, the same of sea-water 59542, and of brandy 5368; then a seaman having a gallon of this liquor in a glass bottle, which weighs 3.84lb out of water, and, to conceal it from the officers of the customs, throws it overboard. It is proposed to determine, if it will ṣink, how much force will just buoy it up? Ans. 14 1496 ounces. QUEST. 61. Another person has half an anker of brandy, of the same specific gravity as in the last question; the wood of the cask suppose measures of a cubic foot; it is proposed to assign what quantity of lead is just requisite to keep the cask and liquor under water? Ans. 89-743 ounces. QUEST. 62. Suppose, by measurement, it be found that a man-of-war, with its ordnance, rigging, and appointments, QUEST. 48. What is the length of a pendulum vibrating in 2 seconds; also in half a second, and in a quarter second Ans. the 2 second pendulum 156 the second pendulum 93 QUEST. 49. What difference will there be in the number of vibrations, made by a pendulum of 6 inches long, and another of 12 inches long, in an hour's time? Ans. 26924. QUEST 50. Observed that while a stone was descending, to measure the depth of a well, a string and plummet, that from the point of suspension, or the place where it was held, to the centre of oscillation, measured just 18 inches, had made 8 vibrations, when the sound from the bottom returned. What was the depth of the well? Ans. 412.61 feet. QUEST. 51. If a ball vibrate in the arch of a circle, 10 degrees on each side of the perpendicular; or a ball roll down the lowest 10 degrees of the arch; required the velocity at the lowest point? the radius of the circle, or length of the pendulum, being 20 feet. Ans. 4.4213 feet per second. QUEST. 52. If a ball descend down a smooth inclined plane, whose length is 100 feet, and altitude 10 feet; how long will it be in descending, and what will be the last velocity? Ans. the veloc. 25 364 feet per sec. and time 7.8852 sec. QUEST. 53. If a cannon ball, of 1lb weight, be fired against a pendulous block of wood, and, striking the centre of oscillation, cause it to vibrate an arc whose chord is 30 inches; the radius of that arc, or distance from the axis to the lowest point of the pendulum, being 118 inches, and the pendulum vibrating in small arcs 40 oscillations per minute. Required the velocity of the ball, and the velocity of the centre of Oscillation of the pendulum, at the lowest point of the arc; the whole weight of the pendulum being 500lb ? Ans. veloc. ball 1956.6054 feet per sec. and veloc. cent. oscil. 3.9054 feet per sec. QUEST. 54. How deep will a cube of oak sink in common water; each side of the cube being 1 foot? Ans. 11 inches. QUEST. 55. How deep will a globe of oak sink in water; the diameter being 1 foot? Ans 9.9867 inches. QUEST QUEST. 56. If a cube of wood, floating in common water, have three inches of it dry above the water, and 4 inches dry when in sea-water; it is proposed to determine the magnitude of the cube, and what sort of wood it is made of? Ans. the wood is oak, and each side 40 inches. QUEST. 57. An irregular piece of lead ore weighs, in air 12 ounces, but in water only 7; and another fragment weighs in air 14 ounces, but in water only 9; required their comparative densities, or specific gravities? Ans. as 145 to 132. QUEST. 58. An irregular fragment of glass, in the scale, weighs 171 grains, and another of magnet 102 grains; but in water the first fetches up no more than 120 grains, and the other 79: what then will their specific gravities turn out to be? Ans. glass to magnet as 3933 to 5202 or nearly as 10 to 13. QUEST. 59. Hiero, king of Sicily, ordered his jeweller to make him a crown, containing 63 ounces of gold. The workmen thought that substituting part silver was only a proper perquisite; which taking air, Archimedes was appointed to examine it; who, on putting it into a vessel of water, found it raised the fluid 8.2245 cubic inches: and having discovered that the inch of gold more critically weighed 10.36 ounces, and that of silver but 5.85 ounces, he found by calculation what part of the king's gold had been changed. And you are desired to repeat the process. Ans. 28.8 ounces. QUEST. 60. Supposing the cubic inch of common glass weigh 14921 ounces troy, the same of sea-water 59542, and of brandy 5368; then a seaman having a gallon of this liquor in a glass bottle, which weighs 3.84lb out of water, and, to conceal it from the officers of the customs, throws it overboard. It is proposed to determine, if it will sink, how much force will just buoy it up? Ans. 14 1496 ounces. QUEST. 61. Another person has half an anker of brandy, of the same specific gravity as in the last question; the wood of the cask suppose measures of a cubic foot; it is proposed to assign what quantity of lead is just requisite to keep the cask and liquor under water? Ans. 89.743 ounces. QUEST. 62. Suppose, by measurement, it be found that a man-of-war, with its ordnance, rigging, and appointments, |