of dilatation is not precisely, although very nearly, the same for all gases. The experiments of Regnault were conducted with very great care, and we shall now shortly describe, in the first place, his method of ascertaining the increase of elasticity of a constant volume of air between o°C and 100°, and, in the second place, his method of ascertaining the increment of volume between the same limits of air of which the elasticity remains constant.

63. Relation between elasticity and temperature of air whose volume remains the same. The following description of an apparatus, nearly the same as Regnault's, and used by the author of this work for the same purpose, will enable the reader to understand the method pursued

A bulb had its volume at 32°

and 212° Fahr.

accurately de

termined by being gauged by mercury at these temperatures, as described in Art.

39; and the contained air was also thoroughly dried by being

45 passed through

a desiccating

apparatus. The capillary termination of the bulb was then

attached to a tube T, connected with another tube T', which was open to the atmosphere.

The lower terminations of these tubes were fitted into a reservoir R containing mercury, and this reservoir might be enlarged or. contracted at pleasure by means of a screw S which moved a piston out or in.

The whole apparatus was made to rest firmly on a slab of slate. The experiment consisted of two parts: the bulb was first of all surrounded by melting ice, and by means of the screw S the mercury was forced to the heighth in the tube T, and the difference of level between the surface of mercury in the two tubes was read by means of a cathetometer, or instrument for measuring vertical heights. Adding this to the height of the barometer, which was observed at the same moment, the whole pressure under which the air in the bulb existed at the temperature of melting ice was thus ascertained. Let us call this P. The bulb b was next attached to a boiling-water apparatus, as in the figure, and by means of the screw S the mercury was forced up to the same height h in the tube T. Since the elasticity of air increases with the temperature, it is evident that the pressure will now be greater, and that in consequence the mercury will be pushed high up in the tube 7". Taking the difference of level as before, noting the barometer, and adding the two heights together, we get the whole pressure under which the air now exists at the temperature of boiling water. Let this pressure be called P'. It is now very easy to construct the formula which must be applied.

Let the temperature of the atmosphere around, including the mercury in the two tubes, be °C, and let 7° denote the temperature of boiling water at the present atmospheric pressure.

Further, let V denote the internal volume at o°C of the bulb and of that portion of the capillary tube which is

subjected to the heating and cooling agents, and let v denote the internal volume at o°C of that portion of the tube T above the mercury which is not subject to the influence of these agents, but which contains air having the tempe

rature t.

Also let κ denote the coefficient of expansion for 1°C of the glass, and let a denote the corresponding coefficient of increase of elastic force of dry air whose volume remains constant-this being what we wish to determine; and, finally, let us denote by D the mass of air which occupies unit volume under unit of pressure at the temperature o°C.

=

Then DPV (according to Boyle's law) will denote the mass of that portion of the enclosed air existing in the bulb (volume V) at the temperature o°C and under the pressure P when the bulb is surrounded by melting ice; also (Art. 62) DPV (1+xt) I + at enclosed air existing at the same time in the tube (volume = v(1+k/)) at the temperature of the atmosphere ( = 1) and pressure P. Hence the whole mass of enclosed air will be denoted by

will denote the mass of that portion of the

ข

DP{V+ 0 (1+x1) }

I at

(1)

Now let the bulb be subjected to the temperature of boiling water (= T'). The volume of the bulb then becomes V(1+KT), and hence the mass of air existing in the bulb at this temperature and under the pressure P' will be DPV (1+KT) while that existing in the tube (vol = v(1+kt))

I+aT

at the temperature of the atmosphere ( = 1) and pressure P

Hence the whole mass of enclosed air will be denoted by

But since the mass of air remains unchanged, being enclosed, we have (1) = (2); and hence, since D is a common factor,

= P' {V(1 + xT)

I a

I + at

where every thing is known but a, which may thus be easily determined. By a similar means Regnault found that if unity denote the elasticity of a given volume of dry air at o°C, its elasticity at 100°C if confined to the same volume will be 1.3665. The author of this work has obtained a somewhat larger increase, but we may probably assume the above number to represent the increase of elasticity of air of constant volume with great exactness.

64. Dilatation of air between o°C and 100°C under

constant pressure. A slight alteration in the apparatus of Fig. 15 enabled Regnault to make this experiment. Here the air will of course expand and occupy part of the tube T, and it will therefore be necessary to surround the two tubes T, T' with water of a constant temperature, since nearly a fourth part of the enclosed air will exist in 7, and its temperature must therefore be accurately known. By means of the screw S the mercury in the two tubes is brought as nearly as possible to the same level, both when the bulb is in melting ice and when it is in the boiling apparatus, so that in both these cases the pressure will be as nearly as possible equal to that of the atmosphere. Any small difference of level between the two tubes is read by means of a cathetometer, and the barometer is noted so that the whole pressure under which the air exists in the two cases is accurately known; but these pressures will in this experiment be very nearly the same in both. By calibrating the tube the additional volume occupied by the air at the high temperature may be determined, and thus the coefficient of expansion becomes known.

From these and other experiments Regnault has concluded

that while the dilatation of air between o°C and 100°C is equal to .3665 of its volume at o° when this dilatation is calculated by means of the law of Boyle from the change of elastic force of air of which the volume is constant; yet when the dilatation is deduced directly from the change of volume while the elasticity remains constant this coefficient is somewhat increased and becomes .3670.

Dividing these results by 180 we find the coefficient which denotes increase of elasticity for 1° Fahr. of air whose volume is constant = .002036.

Also, the coefficient which denotes increase of volume for 1° Fahr. of air whose elasticity is constant = .002039.

65. Dilatation of other gases at ordinary pressures. Regnault has investigated this subject minutely, and has found that different gases have notably different coefficients, and that the coefficient of the same gas differs according as it has been determined by the method of constant pressure or by that of constant volume. He gives the following results:

Dilatation between o°C and 100°C.

It will be noticed in this list that sulphurous acid and cyanogen, which have the greatest coefficients, are gases which may easily be liquefied; while, on the other hand, the three permanent gases which have never been liquefied have small coefficients.