gravities, determined at any temperature, may be readily reduced to what they would have been had they been determined at any other temperature.

The densities of pure water at different temperatures has been determined with great accuracy by experiment, and the results arranged in tables, the density at 38°75 being taken as 1.

Since the specific gravity of a body increases as the density of the standard diminishes, it will be a little less when referred to water at 38°75 than at any other tempe

rature.

Let d and d' denote the densities of water at any two temperatures t and t'; let s and s' denote the specific gravities of the same body, referred to water at these temperatures; then,

This formula is applicable in any case where it is necessary to reduce the specific gravity taken at the temperature t' to what it would have been if taken at the temperature t. If t = 38°75, we have d = 1, and the formula becomes,

Hence, to reduce the specific gravity taken at the temperature t', to the standard temperature, multiply it by the tabular density of water at the temperature t'.

The specific gravity should also be corrected for expansion. This correction is made in a manner entirely similar to the last. Denote the volumes of the same body at the temperatures t and t', by v and v', and the apparent specific gravities, after the last correction, by S and S', then,

If t is the standard temperature, and the unit of volume, we have,

In what follows, we shall suppose that the specific gravities are taken at the standard temperature, in which case no correction will be necessary.

Gases are generally referred to atmospheric air as a standard, but, as air may be readily referred to water as a standard, we shall, for the purpose of simplification, suppose that the standard for all bodies is distilled water at 38°75 Fahrenheit.

Hydrostatic Balance.

160. This balance is similar to that described in Article 81, except the scale-pans have hooks attached to their lower surfaces for the purpose of suspending bodies. The suspension is effected by a fine platinum wire, or by some other material not acted upon by the liquids employed.

Fig. 144.

To determine the Specific Gravity of an Insoluble Body.

161. Attach the suspending wire to the first scale-pan, and after allowing it to sink in a vessel of water to a certain depth, counterpoise it by an equal weight, attached to the hook of the second scale-pan. Place the body in the first scale-pan, and counterpoise it by weights in the second pan. These weights will give the weight of the body in air. Next, attach the body to the suspending wire, and immerse it in the water. The buoyant effort of the water will be equal to the weight of a volume of water equivalent to that of the body (Art. 157); hence, the second pan will descend. Restore the equilibrium by weights placed in the first pan. These weights will give the weight of the displaced water.

Divide the weight of the body in air by the weight just found, and the quotient will be the specific gravity sought. If the body will not sink in water, determine its weight in air as before; then attach to it a body so heavy, that the combination will sink; find, as before, the loss of weight of the combination, and also the loss of weight of the heavier body; take the latter from the former, and the difference will be the loss of weight of the lighter body; divide its weight in air by this weight, and the quotient will be the specific gravity sought.

If great accuracy is required, account must be taken of the buoyant effort of the air, which, when the body is very light, and of considerable dimensions, will render the apparent weight less than the true weight, or the weight in vacuum. Since the weights used in counterpoising are always very dense, and of small dimensions, the buoyant effort of the air upon them may always be neglected.

To determine the true weight of a body in vacuum: let w denote its weight in air, w' its weight in water, and W its weight in vacuum; then will W w, and W-w', denote its loss of weight in air and water; denote the specific gravity of air referred to water, by s. Since the losses of weight in air and water are proportional to their specific gravities, we have,

This weight should be used, instead of the weight in air.

To determine the Specific Gravity of Liquids.

162. FIRST METHOD.-Take a vial with a narrow neck, and weigh it; fill it with the liquid, and weigh again; empty out the liquid, and fill with water, and weigh again; deduct from the last two weights, respectively, the weight of the vial; these results will give the weights of equal

volumes of the liquid and of water. Divide the former by the latter, and the quotient will be the specific gravity sought.

SECOND METHOD. Take a heavy body, that will sink both in the liquid and in water, and which will not be acted upon by either; determine its loss of weight, as already explained, first in the liquid, then in water; divide the former by the latter, and the quotient will be the specific gravity sought. The reason is evident.

F

B D

Fig. 145.

E

THIRD METHOD.-Let AB and CD represent two graduated glass tubes of half an inch in diameter, open at both ends. Let their upper ends communicate with the receiver of an air-pump, and their lower ends dip into two cisterns, one containing distilled water, and the other the liquid whose specific gravity is to be determined. Let the air be partially exhausted from the receiver by means of an air-pump; the liquids will rise in the tubes, but to different heights, these being inversely as the specific gravities of the liquids. If we divide the height of the column of water by that of the other liquid, the quotient will be the specific gravity sought. By creating different degrees of rarefaction, the columns will rise to different heights, but their ratios ought to be the same. We are thus enabled to make a series of observations, each corresponding to a different degree of rarefaction, from which a more accurate result can be had than from a single observation.

To determine the Specific Gravity of a Soluble Body.

163. Find its specific gravity by the method already given, with respect to some liquid in which it is not soluble, and find also the specific gravity of this liquid referred to water; take the product of these specific gravities, and it will be the specific gravity sought. For, if the body is m times heavier than an equivalent volume of the liquid used,

and this is n times heavier than an equivalent volume of water, it follows that the body is mn times heavier than its volume of water, whence the rule.

The auxiliary liquid, in some cases, might be a saturated solution of the given body in water; the rule remains unchanged.

To determine the Specific Gravity of the Air.

164. Take a hollow globe, fitted with a stop-cock, to shut off communication with the external air, and, by means of the air-pump or condensing syringe, pump in as much air as is convenient, close the stop-cock, and weigh the globe thus filled. Provide a glass tube, graduated so as to show cubic inches and decimals of a cubic inch, and, having filled it with mercury, invert it over a mercury bath. Open the stopcock, and allow the compressed air to escape into the inverted tube, taking care to bring the tube into such a position that the mercury without the tube is at the same level as within. The reading on the tube will give the volume of the escaped air. Weigh the globe again, and subtract the weight thus found from the first weight; this difference will indicate the weight of the escaped air. Having reduced the measured volume of air to what it would have occupied at a standard temperature and barometric pressure, by means of rules yet to be deduced, compute the weight of an equivalent volume of water; divide the weight of the corrected volume of air by that of an equivalent volume of distilled water, and the quotient will be the specific gravity sought.

Fig. 146.

To determine the Specific Gravity of a Gas.

165. Take a glass globe of suitable dimensions, fitted with a stop-cock for shutting off communication with the atmosphere. Fill the globe with air, and determine the weight of the globe thus filled referred to a vacuum, as already explained. From the known volume of the globe