Fig. 1.

Fig. 2. 2d Position

Fig. 3.

SOILS Analysis of compresed than before, the increase of its volume being equal to the whole capacity of the tube from C to D, indicated by the second scale.

It is therefore known that the pressures are in proportion to the barometrical column, and to the same column —DE. The bulks of the air in these two states are inversely in the same proportion; and the difference between these bulks is the absolute quantity left void in the tube by the fall of the mercury; from which data the following rule is deduced. Multiply the number expressing the less pressure by that which denotes the augmentation of capacity, and divide the product by the number which denotes the difference of the pressures. The quotient is the bulk of the air when subject to the greater pressure.

Suppose the height of the mercury in the barometer to be 78 centimetres, and the instrument being empty to be plunged into the mercury to the point C. It is then covered and raised till the small column of mercury DE is suspended, say at the height of six centimetres. The internal air at first compressed by a force represented by 78 centimetres, is now only compressed by a force = 72 centimetres, or 78—6 = 72.

Suppose that the capacity of the part CD of the tube which the mercury has quitted is two cubic centimetres.

Then \( \frac{72}{6} \times 2 = 24 \) cubical centimetres, the volume of the air included in the instrument when the mercury rose as high as C in the tube.

The body of which the volume is to be ascertained must then be placed in the capsule, and the operation repeated. Let the column of mercury suspended be = 8 centimetres, when the capacity of the part CD of the tube is = 2 centimetres cubic. Then the greatest pressure being denoted by 78 centimetres, the least will be 70 centimetres, the difference of pressure being 8, and difference of the volumes two cubic centimetres.

Hence \( \frac{70}{8} \times 2 \) gives the bulk of the included air under the greatest pressure 17.5 cubic centimetres. Then \( 24 - 17.5 = 6.5 \) the volume of the body introduced. If the absolute weight of the body be multiplied by its bulk in centimetres, and divided by the absolute weight of one cubic centimetre of distilled water, the quotient will be = the specific gravity of the body in the common form of the tables, where distilled water is taken as unity, or the term of comparison.

Mr Nicholson supposes that the author of the invention had not finished his meditations on the subject. If he had, it is probable that he would have determined his pressures, as well as the measures of bulks, by weight. For if the whole instrument were set to its positions by suspending it from one arm of a balance at H (fig. 3.) the quantity of counterpoise, when in equilibrium, might be applied to determine the pressures to a degree of accuracy much greater than can be obtained by linear measurement.