an instrument lately invented in France for measuring the volume of a body, however irregular, without plunging it in any liquid. If the capacity of a vessel, or, which is the same thing, the volume of air contained in that vessel, be measured, when the vessel contains air only, and also when the vessel contains a body whose volume is required to be known, the volume of air ascertained by the first measurement, deducting the volume ascertained by the second, will be the volume of the body itself. Again, if it be admitted as a law, that the volume of any mass of air be inversely as the pressure to which it is subjected, the temperature being supposed constant, it will be easy to deduce, from the mathematical relations of quantity, the whole bulk, provided the difference between the two bulks under two known pressures be obtained by experiment.

Let it be supposed, for example, that the first pressure is double the second, or, which follows as a consequence, The instrument is a kind of funnel AB (fig. 1), composed of a capsule A, in which the body is placed, and a tube B as uniform in the bore as can be procured. The upper edge of the capsule is ground with emery, in order that it may be hermetically closed with a glass cover M slightly greased. A double scale is fitted on the tube, having two sets of graduations; one to indicate the length, and the other the capacities, as determined by experiment.

When this instrument is used, it must be plunged in a vessel of mercury with the tube very upright, until the mercury rises within and without to a point C of the scale. See fig. 2.

The capsule is then closed with the cover, which being greased will prevent all communication between the external air and that contained within the capsule and tube.

In this situation of the instrument, in which the mercury stands at the same height within and without the tube, the internal air is compressed by the weight of the atmosphere, which is known and expressed by the length of the mercury in the tube of the common barometer.

The instrument is then to be elevated, taking care to keep the tube constantly in the vertical position. It is represented in this situation, fig. 2, second position. The mercury descends in the tube, but not to the level of the external surface, and a column DE of mercury remains suspended in the tube, the height of which is known by the scale. The interior air is therefore less compressed than before, the increase of its volume being equal to the whole capacity of the tube from C to D, which is indicated by the second scale.

It is known therefore that the pressures are in proportion to the barometrical column, and to the same column diminished by the subtraction of DE. And the bulks of the air in these two states are inversely in the same proportion; and again the difference between these bulks is the absolute quantity left void in the tube by the fall of the mercury; from which data, by an easy analytical process, the following rule is deduced:

Multiply the number which expresses the least 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 will be the bulk of the air when subject to the greater pressure.

To render this more easy by an example, suppose the height of the mercury in the barometer to be 78 centimetres, and the instrument being empty to be plunged in the mercury to the point C. It is then covered, and raised until the small column of mercury DE is suspended, for example, at the height of six centimetres. The internal air, which was at first compressed by a force represented by 78 centimetres, is now compressed only by a force represented by 78—6, or 72 centimetres.

Suppose it to be observed, at the same time, by means of the graduations of the second scale, that the capacity of the part CD of the tube which the mercury has quitted is two cubic centimetres. Then by stereometry the rule \( \frac{78}{2} \times 2 \) give 24 cubic centimetres, which is 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. Suppose, in this case, the column of mercury suspended to be eight centimetres, when the capacity of the part CD of the tube is equal to two centimetres cube. Then the greatest pressure being denoted by 78 centimetres, as before, the least will be 70 centimetres, the difference of the pressures being 8, and the difference of the volumes two cubical centimetres. Hence \( \frac{78}{2} \times 2 \) gives the bulk of the included air under the greatest pressure 17.5 cubic centimetres. If therefore 17.5 centimetres be taken from 24 centimetres, or the capacity of the instrument when empty, the difference 6.5 cubic centimetres will express the volume of the body which was introduced. And 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 express 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.

After this description and explanation of the use of his instrument, the author proceeds with the candour and acuteness of a philosopher to ascertain the limits of error in the results; an object seldom sufficiently attended to in the investigation of natural phenomena. From his results it appears, that with the dimensions he has assumed, and the method preferred for operating, the errors may affect the second figure. He likewise gives the formulae by means of which the instrument itself may be made to supply the want of a barometer in ascertaining the greatest pressure. He likewise advertises to the errors which may be produced by change of temperature. To prevent these as much as possible, the actual form of the instrument and arrangements of its auxiliary parts are settled, as in fig. 3., by which means the approach of the hand near the vessel and its tube is avoided. In this figure the vertical position of the tube is secured by the suspension of the vessel, and a perforation in the table through which the tube passes. The table itself supports the capsule in its first position, namely, that at which the cover is required to be put on.

Mr Nicholson, from whose Journal this abstract is immediately taken, supposes, with great probability, that the author of the invention had not finished his meditations on the subject, when the memoir giving an account of it was published. If he had, says the ingenious journalist, it is likely that he would have determined his pressures, as well as the measures of bulks by weight. For it may be easily understood, that if the whole instrument were set to its positions by suspending it to 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.