A class of animals of the type Annulosa. See Index to Annulosa.

ARÆOMETER (composed of aquæ, levis, tenuis, and justæ mensura), a measure of the comparative density and rarity of bodies. The name does not occur in ancient authors; hydroscopium and baryllium being the ancient names of the instrument. This instrument was known in the civilized part of the Roman empire, about the year 400, as appears from the fifteenth epistle of Synesius, addressed to Hypatia, daughter of Theon; and to Hypatia some modern writers have erroneously ascribed its invention. The instrument is also described in some verses annexed to Priscian; and the principles on which its operation is founded, are to be seen in the treatise of Archimedes on floating bodies (De Humido In-

sidentibus). The term, as used by writers on natural philosophy, is chiefly applied to instruments which are made to float, so as to indicate the specific gravity of the liquids in which they are placed: the pèse liqueur, and hydrometer, in common use for measuring the specific gravity of vinous spirits, are instruments of this kind.

A floating body displaces a portion of the liquid, the weight of which is equal to its own weight, the liquid acting upwards with a force equal to this weight, and the weight of the body acting downwards with the same force, equilibrium takes place. If the body be afterwards placed in a liquid of less density, the part of the body immersed, will be greater than when the body was in the more dense liquid, because it requires a greater volume of this less dense liquid to equal the weight of the floating body. The absolute weights of two bodies being the same, their specific gravities are in the inverse ratio of their volumes \( \frac{G}{g} = \frac{v}{V} \), when \( G \) is put for the specific gravity of the first body, \( g \) for that of the second; \( V \) for the volume of the first, and \( v \) for the volume of the second. On this principle the common hydrometer is constructed; the instrument described by Synesius, is also of this kind. In order that a small difference in the volume immersed may be sensible, the part which is intersected by the surface of the fluid is in the form of a very slender cylinder, the great bulk of the instrument being always immersed in the liquid. At the inferior part is a small ball, containing mercury or small lead shot, which serves as ballast, bringing the centre of gravity low, so that the instrument may float erect, and without much lateral oscillation. The common hydrometers are made of glass, and sometimes of brass, or tin or pewter, and some have been made of amber as objects of curiosity: when made of glass, a scale, inscribed upon paper, is inserted in the cylindrical stalk; the division of the scale at which the surface of any liquid intersects the stalk, denotes the specific gravity of that liquid. The divisions of the scale should be formed by immersing the instrument in liquids of known specific gravity, and marking a number corresponding to that specific gravity opposite to each division. The specific gravities of water and alcohol mixed in various proportions, have been accurately ascertained by Mr Gilpin (see his Tables, and Dr Blagden's paper in the Philosophical Transactions); on immersing the instrument in a mixture of known proportions of these two liquids, the point at which the surface intersects the stalk, is to be marked with the number expressing the specific gravity of the mixture taken from the table. Some hydrometers, such as that constructed by the French chemist Beaumé, and which is much used in France under the name of Aréometre de Beaumé, have the Aræmeter 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 aræmeter 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 less 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 aræmeter 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 Aræmeter 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 aræmeter 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 aræmeter of Fahrenheit. The aræmeter 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 aræmeters 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 aræmeter, as represented on the margin; this is done in order to place the centre of gravity low, that the aræmeter may thereby float more steadily. The aræmeter 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 aræmeter 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 different in different instruments, renders the results inaccurate. The different aræmeters 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 aræmeters hitherto spoken of:

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

\( z \) is the diameter of the wire-stalk of the aræmeter.

\( \pi \) is 3.1415, &c., the number expressing the periphery of a circle whose diameter is 1. When the small weight, the density of the liquid, and the length of that part of the stalk which is submerged on adding the small weight, are known, then this equation will give the diameter of the stalk in known quantities \( z = \frac{2}{\sqrt{\frac{w}{v + \frac{1}{3}x^2}}} \).

When the weight of the whole araeometer is known in ounces, &c., and the specific gravity of one of two liquids (water for instance) is known, the difference of specific gravity between that liquid and another liquid may be had in known quantities.

\( g \) is the specific gravity of water.

\( g' \) is the specific gravity of the second liquid, which is here supposed more dense.

\( w \) is the weight of the volume of water displaced by the araeometer.

\( s \) is a small additional weight placed on the exterior cup to keep the araeometer, when placed in the denser liquid, at the same point of immersion as when it floated in water.

\( w + s \) is the whole weight of the apparatus when floating in the denser liquid.

The equation \( g' = \frac{w + s}{v + \frac{1}{3}x^2} \) is obtained by substituting \( g' \) for \( g \), and \( w + s \) for \( w \) in the equation, \( g = \frac{w}{v + \frac{1}{3}x^2} \), which was given above. Divide by \( g = \frac{w}{v + \frac{1}{3}x^2} \) and there results \( \frac{g'}{g} = \frac{w + s}{w} \), which gives the proportion of the density of the second liquid to the density of water. By subtraction there results \( \frac{g' - g}{g} = \frac{s}{w} \) and \( g' - g = \frac{s}{w} \), that is, the difference between the density of the second liquid, and the density of water is found by multiplying the small weight by 1000 ounces, and dividing this product by the number of ounces, &c., which denote the weight of the araeometer unchanged.

Small bodies, whose specific gravities are known, serve to indicate the specific gravity of a liquid in Aræometer, which they just remain suspended. In this way, beads of glass, three or four tenths of an inch in diameter, are employed, each of which remains suspended in spirit of a certain specific gravity. The density of each of these beads, or rather bubbles, is regulated by the proportion between the quantity of glass and the cavity which the glass incloses. A piece of bees-wax, whose specific gravity, by the addition of lead, is such, that the body is just suspended in brine of a known density, is used as an araeometer in some salt works. The fresh egg of a common fowl is just sustained by brine of a certain specific gravity, and is employed as an araeometer.

The araeometer of Homberg, consists of a phial, Homberg's, with a slender neck and glass-stopper, so made, that it may be filled with the same volume of different liquids. It is employed in finding the specific gravity of liquids in the following way: 1st, The phial is filled with distilled water, and then weighed in a balance; 2dly, The phial is emptied, and again filled with the liquid, whose specific gravity is sought, and weighed in a balance, the proportion of the weight of the contents of the phial in the second process to the weight of its contents in the first, is the specific gra- The pressure of the atmosphere supports columns of different fluids, whose height is inversely as the densities of the fluids. An arrometer has been constructed on this principle. It is a curved tube, one leg of which has its extremity immersed in water, and the other in the spirit whose density is to be tried. On rarifying the air in the tube, by means of a pump fixed at the upper part of the tube, the water ascends in one leg, and the spirit in the other; the height of the column of each liquid being measured by a scale of equal parts applied to each branch of the tube. This instrument has never come into use, probably on account of the difficulty of ascertaining, with precision, the points at which the surfaces of the columns are terminated. See Encyclopaedia, Art. HYDRODYNAMICS, Part I. ch. 2. sect. 2. for some farther notice of Arrometers.