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 scale divided into equal parts, so that the divisions do not correspond as they ought to do with the numbers which express specific gravities.

In the aræometer of Fahrenheit, the uncertainty arising from the erroneous division of the scale is obviated, no division being required. The form of the instrument is the same as that just described, only at the top there is a small cup, into which weights are put, so as to bring the surface of the denser liquid to a fixed mark on the stalk; when the instrument is placed in a liquid of jess density, some of the weights are taken out till the mark again comes to the surface.

Suppose the weight of the instrument and of the weights in the cup together equal to 1000, when sunk to the mark in distilled water at a certain temperature; the instrument is now taken out of the water and immersed in a liquid, where 10 must be taken out of the cup in order to bring the mark to the surface; the immersion in water indicates that a volume of water weighs 1000; the immersion in the second liquid, shows that an equal volume of this liquid weighs 990; when the volumes of bodies are equal, the specific gravities are directly as the absolute weights $$\frac{G}{g}=\frac{W}{w}$$, consequently the specific gravity of the second liquid is 990, that of water being 1000. To save computation, it is convenient that the whole weight of the apparatus, when in distilled water, at a certain temperature, should be represented by 1000; for this purpose, the instrument-maker divides the weight of the apparatus into 1000 parts, and forms small weights consisting of one, two, three, &c. of these thousandth parts, the relation of which to the ounce or pound, does not require to be known; the weights thus formed are to be used with the instrument.

The aræometer of Nicholson is like that of Fahrenheit, with the addition of an immersed cup, whereby it is rendered proper for ascertaining

the specific gravity of solids. Suppose that it requires 400 grains in the exterior cup to sink the instrument to the mark in distilled water, at 60 degrees of Fahrenheit’s thermometer; 1st, The body under examination is put into the exterior cup, and weights (say 300 grains) are taken out till the mark again stands at the surface; this gives the absolute weight of the body 300 grains. 2dly, The body is then put into the immersed cup S, taking care to brush off any air-bubbles with a hair pencil, and in order to bring the mark to the surface, a weight (say 100 grains) must be put into the exterior cup, that is, the weight of a volume of water equal to the body, is 100 grains. The first part of the process gave the absolute weight of the body 300 grains, and the volumes being equal, the specific gravities are as the absolute weights, consequently the specific gravity of the body is 300, that of water being 100. This aræometer may be used to find the specific gravity of liquids; the process, in that case, is the same as that described above in speaking of the aræometer of Fahrenheit. The aræometer of Nicholson is useful to the mineralogist for ascertaining the specific gravity of minerals; the specific gravity being a convenient character for distinguishing one kind of mineral from another. It is sometimes made of tinned iron, but where more accuracy is required, copper is the material employed. When put together, it does not exceed a foot in length, and therefore is suited to form a part of the travelling mineralogist’s apparatus.

Some aræometers have been constructed with the exterior cup C placed underneath, and supported by a stirrup, whose upper part is fixed to the stalk of the aræometer, as represented on the margin; this is done in order to place the centre of gravity low, that the aræometer may thereby float mere steadily. The aræometer floats in a cylindrical vessel fitted to the size of the stirrup, and this vessel is supported on a stand so formed as not to interfere with the free motion of the stirrup.

The aræometer of Deparcieux is like the common hydrometer, only the ball is much more voluminous; this renders it capable of indicating the small difference which exists in the specific gravity of the water of different springs, for which purpose Deparcieux proposed it. The dilatation of the large glass bulb by heat, has a considerable effect on the operation of this instrument, and this dilatation being differont in different instruments, renders the results inaccurate. The different aræometers above-mentioned, have the advantages of being easily made and easily carried about; but where the specific gravity of a body is required with the greatest accuracy, recourse must be had to the hydrostatic balance, which ought to be constructed with the utmost care by the most skilful artist.

The following algebraic expressions may serve to elucidate some of the properties of the aræometers hitherto spoken of:

$$g$$ is the specific gravity of water, which is 1000 ounces when the ounce and foot are taken as unities, 1000 ounces avoirdupois being the weight of a cubic foot of water.

$$z$$ is the diameter of the wire-stalk of the aræometer.

$$\pi$$ is 3.1415, &c. the number expressing the periphery of a circle whose diameter is 1. Rh