(2) Direct Weighing

The balance which is necessary in both the methods described under this head should be capable of giving results accurate to milligrams, i.e. the thousandth part of a gram, and consistent with that restriction the beam may be as short as possible so as to give rapid swings and thus shorten the time taken in the observations. A good assay balance answers the purpose admirably. Of course, it is never necessary to wait till the balance has come to rest. The mean of the extreme readings of the pointer attached to the beam will give the position in which it would ultimately come to rest. Thus, if the pointer just touches the eighth division on the right-hand side and the second on the other, the mean position is the third division on the right-hand side (½(8 − 2) = 3). Instead of the ordinary form of chemical balance, Westphal’s form or Joly’s spring-balance may be employed. Weighings are made more quickly, but are not so accurate.

In refined physical work the practice known as double-weighing is employed to obviate any slight error there may be in the suspension of the balance. A counterpoise which is heavier than anything to be weighed is placed in one pan, and weighed. The counterpoise is retained in its pan throughout the whole course of the weighings. Any substance whose weight is to be found is placed in the other pan, and weights added till the balance swings truly again. The difference between the two sets of weights evidently gives the weight of the substance. Balances, however, are so accurately constructed that for testing purposes such refined precautions are not really necessary.

It is immaterial in what notation the weighings are made, so long as the same is used throughout, but the metric system of weights, which is in universal use in scientific work, should preferably be employed. Jewellers, however, use carat weights, and a subdivision to the base 2 instead of decimals, the fractions being ½, ¼, ⅛, ¹/₁₆, ¹/₃₂, ¹/₆₄. If these weights be employed, it will be necessary to convert these fractions into decimals, and write ½ = ·500, ¼ ·250, ⅛ = ·125, ¹/₁₆ = ·062, ¹/₃₂ = ·031, ¹/₆₄ = ·016.

(a) Hydrostatic Weighing

The principle of this method is very simple. The stone, the specific gravity of which is required, is first weighed in air and then when immersed in water. If W and W´ be these weights respectively, then W − W´ is evidently the weight of the water displaced by the stone and having therefore the same volume as it, and the specific gravity is therefore equal to ^W/_{W − W^r}.

If the method of double-weighing had been adopted, the formula would be slightly altered. Thus, suppose that c corresponds to the counterpoise, w and w´ to the stone weighed in air and water respectively; then we have W = c − w and W´ = c − w´, and therefore the specific gravity is equal to ^{c − w}/_{w´ − w}.

Fig. 33.—Hydrostatic Balance.

Some precautions are necessary in practice to assure an accurate result. A balance intended for specific gravity work is provided with an auxiliary pan (Fig. 33), which hangs high enough up to permit of the stone being suspended underneath. The weight of anything used for the suspension must, of course, be determined and subtracted from the weight found for the stone, both when in air and when in water. A piece of fine silk is generally used for suspending the stone in water, but it should be avoided, because the water tends to creep up it and the error thus introduced affects the first place of decimals in the case of a one-carat stone, the value being too high. A piece of brass wire shaped into a cage is much to be preferred. If the same cage be habitually used, its weight in air and when immersed in water to the customary extent in such determinations should be found once for all.

Care must also be taken to remove all air-bubbles which cling to the stone or the cage; their presence would tend to make the value too low. The surface tension of water which makes it cling to the wire prevents the balance swinging freely, and renders it difficult to obtain a weighing correct to a milligram when the wire dips into water. This difficulty may be overcome by substituting a liquid such as toluol, which has a much smaller surface tension.

As has been stated above, the density of water at 4° C. is taken as unity, and it is therefore necessary to multiply the values obtained by the density of the liquid, whatever it be, at the temperature of the observation. In Table IX, at the end of the book, are given the densities of water and toluol at ordinary room-temperatures. It will be noticed that a correct reading of the temperature is far more important in the case of toluol.

Example of a Hydrostatic Determination of Specific Gravity—

Weight of stone in air = 1·471 gram

Weight of stone in water = 1·067 „

Specific gravity = ^1·471/_{1·471 − 1·067} = ^1·471/_0·404.

Allowing for the density of water at the temperature of the room, which was 16° C., the specific gravity is 3·637. Had no such allowance been made, the result would have been four units too high in the third place of decimals. For discriminative purposes, however, such refinement is unnecessary.

(b) Pycnometer, or Specific Gravity Bottle

The specific gravity bottle is merely one with a fairly long neck on which a horizontal mark has been scratched, and which is closed by a ground glass stopper. The pycnometer is a refined variety of the specific gravity bottle. It has two openings: the larger is intended for the insertion of the stone and the water, and is closed by a stopper through which a thermometer passes, while the other, which is exceedingly narrow, is closed by a stopper fitting on the outside, and is graduated to facilitate the determination of the height of the water in it.

The stone is weighed as in the previous method. The bottle is then weighed, and filled with water up to the mark and weighed again. The stone is now introduced into the bottle, and the surplus water removed with blotting-paper or otherwise until it is at the same level as before, and the bottle with its contents is weighed. Let W be the weight of the stone, w the weight of the bottle, W´ the weight of the bottle and the water contained in it, and W″ the weight of the bottle when containing the stone and the water. Then W´ − w is the weight of the water filling the bottle up to the mark, and W″ − w − W is the reduced weight of water after the stone has been inserted; the difference, W + W´ − W″, is the weight of the water displaced. The specific gravity is therefore ^W/_{W + W´ − W″}. As in the previous method, this value must be multiplied by the density of the liquid at the temperature of the experiment. If the method of double-weighing be adopted, the formula will be slightly modified.

Of the above methods, that of heavy liquids, as it is usually termed, is by far the quickest and the most convenient for stones of ordinary size, the specific gravity of which is less than the density of pure methylene iodide, namely, 3·324, and by its aid a value may be obtained which is accurate to the second place of decimals, a result quite sufficient for a discriminative test. The method is applicable no matter how small the stone may be, and, indeed, for very small stones it is the only trustworthy method; for large stones it is inconvenient, not only because of the large quantity of liquid required, but also on account of the difficulty in estimating with sufficient certainty the position of the centre of gravity of the stone. A negative determination may be of value, especially if attention be paid to the rate at which the stone falls through the liquid; the denser the stone the faster it will sink, but the rate depends also upon the shape of the stone. Retgers’s salt is less convenient because of the delay involved in warming it and of the almost inevitable staining of the hands, but its use presents no difficulty whatever.

Hydrostatic weighing is always available, unless the stone be very small, but the necessary weighings occupy considerable time, and care must be taken that no error creeps into the computation, simple though it be. Even if everything is at hand, a determination is scarcely possible under a quarter of an hour.

The third method, which takes even longer, is intended primarily for powdered substances, and is not recommended for cut stones, unless there happen to be a number of tiny ones which are known to be exactly of the same kind.

The specific gravities of the gem-stones are given in [Table VII] at the end of the book.