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For, if the fluid EF be twice or thrice as light as CD; it must have twice or thrice the beight, to have an equal pressure, to counterbalance the other.
PROP. 5.-If a body, of the same specific gravity of a fluid, be immersed in it will rest in any place of it. A body of greater density will sink, and one of a less density will swim.
Let A, B, C, fig. 4, be three bodies ; whereof A is lighter bulk for bulk than the fluid; B is equal; and C heavier. The body B, being of the same density, or equal in weight as so much of the fluid, it will press the Quid under it just as much as if the space was filled with the Guid. The pressure then will be the same all around it, as if the fluid was there, and consequently there is no force to put it ont of its place. But, if the body be lighter, the pressure of it downwards will be less than before, and less than in other places at the same depth ; and consequently the lesser force will give way, and it will rise to the top. And, if the body be heavier, the pressure downwards will be greater than before; and the greai. er pressure will prevail and carry it to the bottom.
Cor. 1.-Hence, if several bodies of different specific gravity be inimer. sed in a fluid, the heaviest will get the lowest.
For the heaviest are impelled with a greater force and therefore will go fastest down.
Cor. 2.-A body, immersed in a fuid, loses as much weiglit as an equal qnantity of the fluid weighs; and the fluid gains it.
For, if the body is of the same specific gravity as the thuid, then it will lose all its weight. And, if it be lighter or heavier, there remains only the difference of the weights of the body and fluid to move the body.
Cor. 3.- All bodies of equal magnitudes lose equal weights in the same Ouid. And bodies of different magnitudes lose weights propor:ional to the magnitudes.
Cor. 4.-The weights lost in different Quids, by immerging the same borly thercin, are as the specific gravities of the fluids. Anil bodies of equal weight, lose weights, in the same fluid, reciprocally as the specific gravities of the bodies.
Cor 5.- The weight of a hody swimming in a fluid is equal to the weiglit of as much of the fluid as the immersed part of the body takes up.
For the pressure underneath the swimming body is just the same us so much of the immersed fluid ; and therefore the weighits are the same.
Cor. 6.-Hence a hody will sink deeper in a lighter fluid than in a lieavier.
Cor. 7.—llence appears the reason why we do not feel the whole weight of an immersed boils, till it be drawn quite out of the water
SPECIFIC GRAVITIES. By the specific gravities of bodies, is meant the relative weights which equal bulks of different bodies have in regard to each other.
Obs.-1. Tbus a cubic foot of cork is not of eqnal weight with a cubic foot of water, or marble, or lead; but the water is four times heavier than the cork, the marble 11 times, and the lead 45 times; or, in other words, a cubic foot of lead would weigh as much as 45 of cork, &c. &c.
2. 'The terms absolute gravity and specific gravity very frequently occur in physics. The first is what we express in cummon life by the word weight, and signifies the whole of the power with which a body is carried to the earth. Every particle in every substance is heavy; that is, it has a tendency to fali toward the earth, or is attracted by the earth. Now, the greater the number of particles a substance has, the greater will be its momentum, and the more powerful will be its tendency toward the centre of the earth's motions.
PROP. 10.-To find the specific grarity of solids or fluids. For a solid heavier than water. Weigh the boily separately, first out of water, and then suspended in water. And divide the weight out of water by the difference of the weights, gives the specific gravity: reckoning the specific gravity of water 1.
For the dillisence of the weights is equal to the weight of as much water (by Cor. 2. Prop. 5); and the weights of equal magnitudes are as the specilic gravities; therefore, the difference of these weights, is te the weight of the body, as the specific gravity of water 1, to the specific gravity of the body.
For a body lighter than water.--Take a piece of any heary body, so big as, being tied to the light body, it may siok it in water. Weigh the heavy body in and out of water, and find the loss of weight. Also weigh the compound both in and out of water, and find also the loss of weight. Then divide the weight of the light body (out of water,) by the difference of these losses, gives the specific gravity; the specific gravings of water being 1. For the last loss is = weight of water equal in magnitude to the
compound, And the first loss is = weight of water equal in magnitude to the
heavy body, Whence the diff. losses is = weight of water equal in magnitude to the
light body; and the weights of equal magnitudes being as the specific gravities; therefore the difference of the losses (or the weight of water equal to the light body) : weight of the light body :: specific gravity of wae ter 1 : specific gravity of the light body.
For a fluid of any sort.-Take a piece of a body whose specific gravity you know; weigh it both in and out of the fluid ; take the difference of the weighits, and multiply it by the specific gravity of the solid body, and divide the product by the weight of the body (out of water), for the specific gravity of the fluid.
For the difference of the weights in and out of water, is the weight of so much of the fluid as equals the magnitude of the body. And the weight of equal magnitudes being as the specific gravities; therefore, weight of the solid : difference of the weights (or the weight of so much of the fluid) :: specific gravity of the solid : the specific gravity of the duid.
Example to Case 1. A piece or lead ore was weighed, which was 124 grains; and in water it
124 weighed 104 grains, the difference is 20; tben =6:2, the specific
20 gravity of ore.
Cor. 1. As the weight lost in a fluid, is to the absolute weight of the body; so is the specific gravity of the fluid to the specific gravity of the body.
Cor. 2. Having the specific gravity of a body, and the weight of it, the solidity may be found thus: multiply the weight in pounds by 62}; then say, as that product is to one, so is the weight of the body in pounds to the content in feet. And, having the content given, one may ind the weight by working backwards.
For a cubic foot of water weighs 62} lb. avoirdupois; and therefore a cubic foot of the body weighs 624 X by the specific gravity of the boly. Whence the weight of the body, divided by that product, gives the number of feet in it. Or, as 1 to that product, so is the content to the weight.
SCHOLIUM.–The specific gravities of bodies may be found with a pair of scales, suspending the body in water by a horsehair. But there is an jystrument for this purpose, called the Hydrostatical Balance, (fig. 13,) the construction of which is thus. AB is the stand and pedestal, having at the top two cheeks of steel, on which the beam CD is suspended, which is like the beam of a pair of scales, and must play freely, and be itself exactly in equilibrio. "To this belongs the glass bubble G, and the glass bucket H, and four other parts E, F, I, L. To these are loops fastened to hang them by. And the weights of all these are so adjusted that E=F + the bubble in the water, or= I + the bucket out of water, or=I+L + the bucket in water. Whence L = difference of the weights of the bucket in and out of water. And, if you please, you may have a weight K, so that K + bubble in water = bubble out water; or else find it in grains. The piece L has a slit in it to slip it upon tbe sbank of I.
It is plain the weight K = weight of water as big as the bubble, or a water bubble.
Then to find the specific gravily of a solid.-Hang E at one end of the
balance, and I and the bucket with the solid in it, at the other end; and und lat weight is a balance to it.
Then slip L iipon I, and immerge the bucket and solid in the water and find again what weight balances it. Then the first weight divideo by the difference of the weights, is the specific gravity of the body; thia of water being 1.
For fluids.--Hang E at one end, and F with the bubble at the other plunge the bubble into the fluid in the vessel MN. Then find the weight ', which makes a balance. Then the specific gravity of the fluid is K+P
K-P when P is laid on F; or
when P is laid on E. K
K For E being equal to I + the bucket; the first weight found for a baJance, is the weight of the solid. Again E being equal to I + L + the bucket in water; the weight to balance that, is the weight of the solid in water; and the difference is = to the weight of as much water. Therefore (Cor 1.) the first weight divided by that difference, is the specific gravity of the body.
Again, since E'is = to F + the bubble in water, therefore P is the difference of the weights of the fuid and so much water; that is, P=ditference of K and a fluid bubble; or P= fluid - K, when the fluid is heavier than water, or when P is laid on F. And therefore P=kthe fluid bubble, when contrary. Whence the fluid bubble=KÉP, for a heavier or a lighter fuid. And the specific gravities being as the weights of these equal bubbles; specific gravity of water : specific gra
K+P vity of the fluid ::K: KEP :: 1 : the specific gravity of
K the fluid. Where if P be 0, it is the same as that of water.
Obs.—The method of ascertaining the specific gravities of bodies was discovered accidentally by Archimedes. He had been employed by the king of Syracuse to investigate the metals of a golden crown, which, he suspected, had been adulterated by the workman. The philosopher Jaboured at the problem in vain, till, going one day into the bath, he perceived that the water rose in the bath in proportion to the bulk of his body; be instantly saw that any other substance of equal size would have raised the water just as much, though one of equal weight and of less bulk could not have produced the same effect. He immediately felt that the solution of the king's question was within bis reach, and he was so transported with joy, that he leaped from the bath, and, running naked through the streets, cried out, “ Eupora, Eupnxa,”—“ I have found it out,
I have found it out!” He then got two'masses, one of gold and one of silver, each equal in weight to the crown, and, having filled a vessel very accurately with water, he first plunged the silver mass into it, and observed the quantity of water that flowed over; he then did the same with the gold, and found that a less quantity had passed over than before. Hence he inferred that, though of equal weight, the bulk of the silver was greater than that of the gold, and that the quantity of water displaced was, in each experiment, equal to the bulk of the metal. He next made a like trial with the crown, and found it displaced more water than the gold, and less than the silver, which led him to conclude that it was neither pire gold nor purr silver.
TABLES OF SPECIFIC CRAVITIES.
.20,722 Marble, green, Campanian 2,742 Gold, pure, hammered .19,362
2 837 Guinea of George III. ..17,629
2,668 Mercury, at 320 Fahrenheit 13,598 Emerald
2,775 Lead.. 11,352 | Pearl..
2,752 Palladium .11,3300 Chaik, British
2,784 Rhodium .11,000 Jasper
2,710 Virgin Silver 10,744 | Coral
2,680 Shilling of George III. . 10,534 Rock Crystal
2,653 Bismuth, niolten... 9,822 | English Pebble
2,619 Copper, wire-drawn 8,878 Limpid Feldspar
2,564 Red Copper, molten 8,788 Glass, green.
2,73: Nickel, molten 8,279 Porcelaine, China
- Limoges 2,341 Stecl .... from 7,769 to 7,816 Native Sulphur
2,033 Cobalt, molten 7,812 Ivory
1,917 Bar Iron 7,788 Alabaster.
1,874 Pure Cornish Tin 7,291 Alum
1,720 Do, harilened 7,299 Copal, opaque
1,140 Cast Iron ... 7,207 Sodium..
973 Ziuc 6,862 Oak, heart of
950 Antimony. 6,712 Ice
930 Tellurium 6,115 Potassium
866 Chiromium 5,900 Beech
852 Spar, heavy 4,430 Ash
845 Jargon of Ceylon 4.410 Apple-Tree
793 Oriental Ruby... 4,283 Orange-Wood
705 Sapphire, Oriental 3,994 Pear Tree
661 Do. Brazilian 3,131 Linden-Tree
604 Oriental Topaz 4,019 Cypress
598 Oriental Beryl 3,549 Cedar
561 Diamond .... from 3,501 to 3,531 Fir
350 English Flint Glass 3,329 Poplar
383 Tourmalin 3,155 Cork...
LIQUIDS. Sulphuric Acid 1,841 | Burgundy Wine
991 Nitrous Acid 1,550 | Olive Oil
915 Water from the Dead Sea .. 1,240 Muriatic Ether.
874 Nitric Acid 1,218 | Oil of Turpentine
870 Sea-Waler 1,026 Liquid Bitumen
848 Milk... 1,030 | Alcohol, absolute
792 Distilled Water 1,000 Sulphuric Ether
716 Wine of Bourdeaux
944 | Air at the Earth's surface, about 13 Since a cubic foot of water, at the temperature of 40° Fahrenheit, weiglıs 1000 ounces, avoirdapois, or 62° pounds, the numbers in the preoeding tables exhibit very nearly the respective weights of a cubic foot of the several substances tabulated.