and the Moon's 2180: Required the comparative magnitude between each of those bodies and the Earth? 3222-48X3222·48 × 3222·48-93·12 less. 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 7964-12X7964·12×7964·12×392.5 41.24 times the 2180 X2180 X2180 X464 quantity 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 a circle, is in English miles 190437141-7: Required its mean motion, (or the space through which it moves in its orbit,) per minute? 190437141 7×3·1416-598277324-36 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 17 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, on 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 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 destroyed; 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 heavier 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 74 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 tinies 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 accuaracy 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 1000 ounces Avoirdupois, or 621 pounds. A TABLE 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 several 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 each metal in the body. 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 Spiritous 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 spiritous 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 recti fied spirits being 850, that of proof spirit 925, and of water 1000? 925 (1000)75 Or equal measures. 850/75 109. What proportional weight of rectified spirits of wine and water must be mixed, to make proof spirit, the specifick gravities. as before? 1000 20 110. What is the specifick gravity of best French brandy, consisting of 5 parts, measure, of rectified spirits of wine, and 3 parts water? 850x5=4250 1000x3=3000 5+3= 8) 7250 906.25 specifick gravity. 111. A retailer has 30 gallons of rum, whose specifick gravity is 900: How much water must he add to reduce it to standard proof? 925 75 A5 75 (1000) 25} 8. rum. g. wat. g. rum. g. wat. g. As 25 :: 30 : 10 to be added. 112. The cubick inch of common glass weighs about 1.360z. Troy ditto of salt water 5427oz. ditto of brandy 48927oz. Suppose then, a seaman has a gallon of brandy in a bottle, which weighs 4th Troy, out of water, and to conceal it, throws it overboard into salt water: Pray, will it sink or swim, and by how much is it heavier or lighter than the same bulk of salt water? 454oz. weight of bottle 54 —— 1.36 =39.7059 cub. in. in the bottle. Add 231. do. in the brandy. 270.7059 ditto in both. Then, 270 7059×·5427=146·912oz.weight of salt water occupied by the bottle and brandy. And 48927 (=weight of a cubick inch of brandy) ×231=113·02+oz. and 113 02+54=167·02oz, weight of the bottle and brandy. From this take the weight of the salt water, viz. 146-192oz. Ans. Supposing the bottle full, it is 20-11oz. heavier than the same bulk of salt water, and therefore will sink. Given the weight to be raised by a balloon, to find its diameter. RULE. 1. As the specific difference between common and inflammable air, is to one cubick foot: so is any weight to be raised, to the cubick feet contained in the balloon. 2. Divide the cubick feet by 5236, and the cube root of the quotient will be the diameter required, to balance it with common air; but, to raise it, the diameter must be somewhat greater, or the weight somewhat less. 113. I would construct a spherical balloon, of sufficient capacity to ascend with 4 persons, weighing, one with another, 160, and the balloon and a bag of sand weighing 60: Required the diame. ter of the balloon? By the Table of Specifick Gravities, page 388, I find a cubick foot of common air weighs 1.25 ounces Avoirdupois, and a cubick foot of inflammable air 12 of an ounce Avoirdupois; therefore, |