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For, if the fluid EF be twice or thrice as light as CD; it must have twice or thrice the height, 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, 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 fluid under it just as much as if the space was filled with the fluid. 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 out 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 greater pressure will prevail and carry it to the bottom.
Cor. 1.-Hence, if several bodies of different specific gravity be immersed 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 fluid, loses as much weight as an equal quantity of the fluid weighs; and the fluid gains it.
For, if the body is of the same specific gravity as the fluid, then it will lose all its weight. And, if it be lighter or heavier, there remains ouly 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 fluid. And bodies of different magnitudes lose weights propor sional to the magnitudes.
Cor. 4.-The weights lost in different fluids, by immerging the same. body therein, are as the specific gravities of the fluids. And bodies of equal weight, lose weights, in the same fluid, reciprocally as the specific gravities of the bodies.
Cor 5. The weight of a body swimming in a fluid is equal to the. weight 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 as so much of the immersed fluid; and therefore the weights are the same. Cor. 6. Hence a body will sink deeper in a lighter fluid than in a heavier.
Cor. 7-Hence appears the reason why we do not feel the whole weight of an immersed body, till it be drawn quite out of the water
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. Thus a cubic foot of cork is not of equal 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 common 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 gravity of solids or fluids. For a solid heavier than water.—Weigh the body separately, first out of water, and then suspended in water. And divide the weight cut of water by the difference of the weights, gives the specific gravity: reckoning the specific gravity of water 1.
For the difference 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 specific 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 heavy body, so big as, being tied to the light body, it may sink 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 gravity of water being 1.
For the last loss is
And the first loss is
Whence the diff. losses is =
weight of water equal in magnitude to the compound,
weight of water equal in magnitude to the heavy body,
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 wa 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 weights, 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 Auid.
Example to Case 1.
A piece of lead ore was weighed, which was 124 grains; and in water it
weighed 104 grains, the difference is 20; then
gravity of ore.
6.2, the specific
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 find 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 body. 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 horse-hair. But there is an instrument 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 EF+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 the shank 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 gravity 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 find what weight is a balance to it.
Then slip L upon I, and immerge the bucket and solid in the water and find again what weight balances it. Then the first weight divides by the difference of the weights, is the specific gravity of the body; tha 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 P, which makes a balance. Then the specific gravity of the fluid is when P is laid on F; or KP, when P is laid on E.
K+P K For E being equal to I + the bucket; the first weight found for a balance, 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. There fore (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 fluid and so much water; that is, P = difference of K and a fluid bubble; or Pfluid-K, when the fluid is heavier than water, or when P is laid on F. And therefore P=K— the fluid bubble, when contrary. Whence the fluid bubble=K ± P, for a heavier or a lighter fluid. And the specific gravities being as the weights of these equal bubbles; specific gravity of water: specific graK± P vity of the fluid :: K: KP :: 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 laboured 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; he 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 his reach, and he was so transported with joy, that he leaped from the bath, and, running naked through the streets, cried out, "Evpnna, Evpnxa,”—“ 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 pure gold nor pure silver.
Water from the Dead Sea .. 1,240 | Muriatic Ether.
1,218 Oil of Turpentine
1,026 Liquid Bitumen
Wine of Bourdeaux
944 Air at the Earth's surface, about 14
Since a cubic foot of water, at the temperature of 40° Fahrenheit, weighs 1000 ounces, avoirdupois, or 62 pounds, the numbers in the preceding tables exhibit very nearly the respective weights of a cubic foot of the several substances tabulated.