97. Let the weight be 2240lb. the power 11.881b. and the lever 30 inches: Required the distance between the threads? lb. lb. in. in. As 2240 11-88 :: 288-496: 1 nearly, Ans. 98. Let the power be 11.88lb. the weight 2240lb. and the threads an inch asunder, to find the length of the lever. As 11.88 2240 :: 1: 188*5; then, as 355 : 113 :: 188·5 : 60 inches nearly, the diameter, and 60÷2-30 inches, Ans. 99. Suppose one of those meteors, called fire balls, to move parrallel to the earth's surface, and 50 miles from it, at the rate of 20 miles per second: In what time would it move round the earth? The Earth's diameter is. 7964 English miles; then, 7964+50x2= 8064 the diameter of the circle, described by the ball. Then, 8064×3·1416=25333-8624 miles, its circumference, and 25333-8624 +20=1266.69312 seconds=21′ 6′′ 41′′ 35′′" 13′′" 55" 12""", Ans. 100. Sound, uninterrupted, moves about 1142 feet in a second: How long, then, after firing a cannon at Newburyport, before it will be heard at Ipswich, estimating the distance at 10 miles in a right line? 10 miles = 52800 feet, and 52800÷1142=46334 seconds, Ans. 101. In a thunder storm I observed by my clock that it was 6 seconds between the lightning and thunder: at what distance was the explosion? 1142×6=6852 feet = 1448 13 mile, Ans. 102. Tubes may be made of gold, weighing not more than at the rate of rs of a grain per foot: What would be the weight of such a tube, which would extend across the Atlantick, from Boston to London, estimating the distance at 1000 leagues? 1000x3=3000 miles, and 3000x5280=15840000 feet, and 15840000 X1625=974785gr. or rather, 1lb. 8oz. 6pwt. 3gr. Ans. 103. The mean distances of the Planets from the Sun, in English miles, are as follow: viz. Mercury 36686617·5; Venus 68552135-83; Earth 94772980; Mars 144404783-33; Jupiter 492912533-33; Saturn 903957657.5: Now, as a cannon ball, at its first discharge, flies about a mile in 8 seconds, and sound 1142 feet in a second: In what time, at the above rate, would a bullet pass from the Earth to the Sun? and sound move from the Sun to Saturn? 94772980×8"=758183840=24 years, 15 days, 6 hours, 27 minutes, 20 seconds, for the passage of the ball. And 903957657-5x5280= 4772896431600 feet, and 4772896431600÷1142=132 years, 192 days, 21h. 42m. 21s. sound passing from the Sun to Saturn, Ans. 104. Light passes from the Sun to the Earth in 8-2 minutes: In what time would it pass from the sun to the Georgium Sidus, it being 1803930416.66 English miles? As 94772980: 8+2: 1803930416-66: 2h. 36m. 4" 50′′, Ans. 105. The Sun's diameter is 883217.58 English miles; Jupiter's is 89170-81; Saturn's 79042-35; Georgium 35109; Mercury's 3222-48; Venus' 7687·85; Earth's 7964-12; Mars' 4189-69; and and the Moon's 2180: Required the comparative magnitude between each of those bodies and the Earth? N. B. The above diameters and mean distances in English miles answer to the same in geographical miles, as they were deduced from observations on the transits of Venus over the Sun in 1761 and 1769. 106. Suppose the density of the Moon 464, and that of the Earth 392-5 Required the proportion between the quantity of matter in the Earth and in that of the Moon, allowing the Earth's diameter to be 7964-12, and the Moon's 2180 miles, and supposing the Earth a complete sphere, which, however, it is not? There is 7964-12x7964·12x7964·12x392.5 2180 X2180 X2180 X464 — 41.24 times the quan tity of matter in the Earth that there is in the Moon; or, the Earth's weight is so many times that of the Moon. 107. The mean diameter of the Earth's orbit, (or annual path round the Sun) supposing it truly spherical, is, in English miles, 190437141-7: Required its mean motion, (or the space through which it moves in its orbit,) per minute? 190437141-7X3·1416=598277324-36 miles in circumference; then, Days. As 365-25: 598277324-36:: 1': 1137.49 miles, Ans. N. B. The Earth's diurnal motion round its axis is 174 miles per minute, at the equator. OF THE SPECIFICK GRAVITIES OF BODIes. The specifick gravities of bodies are as their densities, or weights, bulk for bulk; thus, a body is said to have two or three times the specifick gravity of another, when it contains two or three times as much matter in the same space. A body, immersed in a fluid, will sink, if it be heavier than its bulk of the fluid. If it be suspended therein, it will lose so much of what it weighed in the air, as its bulk of the fluid weighs. Hence, all bodies of equal bulk, which will sink in fluids, lose equal weights when suspended therein, and unequal bodies lose in proportion to their bulks. The hydrostatick balance differs very little from a common balance that is nicely made; only it has a hook at the bottom of each scale, bn which small weights may be hung by horse hairs, so that a body suspended by the hair, may be immersed in water without wetting the scales. How How to find the Specifick Gravities of Bodies. If the body, thus suspended under the scale, at one end of the balance, be first counterpoised in air by weights in the opposite scale, and then immersed in water, the equilibrium will be immediately de stroyed; then, if as much weight be put into the scale, to which the body is suspended, as will restore the equilibrium, (without altering the weights in the opposite scale) that weight, which restores the equilibrium, will be equal to a quantity of water as big as the immersed body; and if the weight of the body in air be divided by what it loses in water, the quotient will shew how much that body is heav ier than its bulk of water. Thus, if a guinea, suspended in air, be counterbalanced by 129 grains in the opposite scale, and then, upon being immersed in water, it becomes so much lighter as to require 7 grains to be put into the scale over it, to restore the equilibrium, it shews that a quantity of water, of equal bulk with the guinea, weighs 7.25 grains; by which divide 129 (the weight of the guinea in air) and the quotient will be 17.793; which shews that the guinea is 17.793 times as heavy as its bulk of water. Thus may any piece of gold be tried, by weighing it first in air, and then in water; and if, upon dividing the weight in air by the loss in water, the quotient comes out 17-793, the gold is good: If the quotient be 18, or between 18 and 19, the gold is very fine: but, if it be less than 17, the gold is too much alloyed by being mixed with some other metal. If silver be tried in this manner and found to be 11 times as heavy as water, it is very fine: If it be 10 times as heavy, it is standard; but if it be of any less weight compared with water, it is mixed with some lighter metal, such as tin, &c. If a piece of brass, glass, lead, or silver, be immersed and suspended in different sorts of fluids, the different losses of weight therein will shew how much heavier it is than its bulk of the fluid; that fluid being lightest, in which the immersed body loses least of its aerial weight. Common clear water, for common uses, is generally made a standard for comparing bodies by, whose gravity may be represented by unity, or 1, or, in case great accuracy be required, by 1.000, where 3 cyphers are annexed to give room to express the ratios of other gravities in larger numbers in the table. In doing this there is a twofold advantage; the first is, that, by this mean, the specifick gravities of bodies may be expressed to a much greater degree of accuracy.— The second is, that the numbers of the Table, considered as whole numbers, do also express the ounces Avoirdupois contained in a cubick foot of every sort of matter therein specified; because a cubick foot of common water, is found by experiment to weigh very nearly 100,0 ounces Avoirdupois, or 624 pounds. A TABLE ATABLE of the Specifick Gravities of several solid and fluid Bodies; where the second column contains their Absolute weight, and the third, their Relative Weight, in Avoirdupois Ounces. The use of the Table of Specifick Gravities will best appear by sev. eral Examples. How to discover the quantity of adulteration in metals. Suppose a body be compounded of gold and silver, and it be required to find the quantity of each metal in the compound. First, find the specifick gravity of the compound, by weighing it in air and in water, and dividing its aerial weight by what it loses thereof in water, and the quotient will shew its specifick gravity, or how many times heavier it is than its bulk of water. Then, subtract the specifick gravity of silver (found in the Table) from that of the compound, and the specifick gravity of the compound from that of the gold: the first remainder will shew the bulk of gold, and the latter, the bulk of silver in the whole compound; and if these remainders be multiplied by the respective specifick gravities, the products will shew the proportional weights of cach metal in the body. Suppose Suppose the specifick gravity of the compounded body be 14; that of standard silver (by the Table) is 10-535, and that of standard gold 18.888; therefore, 10:535 from 14, remains 3.465, the proportional bulk of the gold in the compound; and 14 from 18.888, remains 4-888, the proportional bulk of silver in the compound: then, 18.888, the specifick gravity of gold, multiplied by the first remainder 3.465, produces 65.447 for the proportional weight of gold; and 10-535, the specifick gravity of silver, multiplied by the last remainder, produces 51-495 for the proportional weight of silver in the whole body: So that for every 65.447 ounces or pounds of gold, there are 51.495, ounces or pounds of silver in the body. Hence it is easy to know whether any suspected metal be genuine, or alloyed or counterfeit, by finding how much heavier it is than its bulk of water, and comparing the same with the Table; if they agree, the metal is good; if they differ, it is alloyed or counterfeited. How to try Spirituous Liquors. A cubick inch of good brandy, rum, or other proof spirits, weighs 234 grains; therefore, if a true inch cube of any metal weighs 234 grains less in spirits than in air, it shews the spirits are proof: If it lose less of its aerial weight in spirits, they are above proof; if it lose more, they are under proof; for, the better the spirits are, the lighter they are, and the worse, the heavier. Or, let any solid, of sufficient specifick gravity, be, weighed first in air, then in water, and then in another liquid; from its weight in the air take its weight in water, and the remainder is the weight of its bulk of water. From its weight in air take its weight in the other liquid, and the remainder is the weight of the same quantity of that liquid. Divide the weight of this quantity of liquid by the weight of the same quantity of water, and the quotient will be the specifick gravity of the liquid. All bodies expand with heat and contract with cold; but some more, and some less than others: therefore, the specifick gravities of bodies are not precisely the same in summer as in winter. The four following Problems, relating to spirituous liquors, are wrought by Alligation. 108. What proportion of rectified spirits of wine must be mixed with water, to make proof spirit, the specifick gravity of the rectified spirits being 850, that of proof spirit 925, and of water 1000? 1000 925 {1990)75} Or equal measures. 109. What proportional weight of rectified spirits of wine and wa ter must be mixed, to make proof spirit, the specifick gravities as before? Ans.. 1000 20 ——, or as 20 to 17. 850 17 110. What is the specifick gravity of best French brandy, consisting of 5 parts, measure, of rectified spirits of wine, and 3 parts water? 850x |