tudes, the uncertainty of the values calculated by means of this formula will become still greater.

For atmospheric air we have to take for this ratio the value

this we obtain from Dulong's' and Masson's2 observations on the speed of sound, if we apply a correction that according to the newer measures is necessary; and this value is in harmony not only with Wüllner's experiments by the same method, but also with Röntgen's determinations by Desormes and Clément's' procedure, and with P. A. Müller's observations by Assmann's' method. From this value we obtain by the formula

:

the energy K therefore of the molecular motion in atmospheric air stands to the whole energy H contained in the gas in about the ratio 3 5. Thence it follows that the two parts into which we may break up the whole energy H, viz. the internal energy HK of the molecule (which we may distinguish as the atomic energy) and the energy K of its progressive motion, must bear to each other nearly the ratio 2: 3; or, more exactly, we have

The values of H and K have hitherto been referred to unit volume. If, however, we are concerned with only the ratio of their values, it is unnecessary to refer them to unit volume, and we may refer their values to any arbitrary

1 Ann. Chim. Phys. xli. 1829, p. 113; Pogg. Ann. xvi. p. 438.

2 Ibid. [3] liii. 1858, p. 257.

Compare § 36.

'Wüllner's Lehrbuch d. Experimentalphysik, 4. Aufl. 1885, iii. p. 522. Wied. Ann. iv. 1878, p. 321.

Pogg. Ann. cxlviii. 1873, p. 580.

Journ. de Phys. lxxxix. 1819, pp. 321, 428.

8 Inaug. Diss. Breslau 1882; Wied. Ann. xviii. 1883, p. 94.

• Pogg. Ann. lxxxv. 1852, p. 1.

volume, as, for instance, the molecular volume. Hence if, as in § 21* of the Mathematical Appendices, we denote the mean energy of forward motion of a single molecule by E, and the mean value of its internal atomic energy by E, the ratio of these two magnitudes is equal to that calculated above, viz.

This somewhat altered conception allows us to compare the mean amount of energy e possessed by a single atom with the molecular energy. For if the number of atoms in the molecule is n, then the desired mean value is

E ( = n

Since air is not a chemical compound of unchangeable composition it is not, strictly speaking, allowable to apply this formula to it. But since its components, nitrogen and oxygen, have the common property of possessing two atoms in a molecule, we may also for air put n = 2, and obtain

The energy of an atom is thus considerably smaller than the energy E of progressive motion of a molecule of air. This ratio is in agreement also with that for most other gases, as the following table shows.

The first column of figures contains the observed values of the ratio of the specific heats for a series of gases and vapours. The observations of Dulong (D) and Masson (Mn) are given according to Wüllner's corrected calculation; also in Wüllner's (W) determinations the corrections later applied by Strecker and Wüllner are taken into account. In addition to these I have taken the observations of Röntgen (R), P. A. Müller (Mr), Strecker (S),2 de Lucchi (L), Martini (Mi), Maneuvrier and Fournier Wüllner's Lehrbuch, 4. Aufl. 1885, iii. p. 522.

4

2 Inaug. Diss. Strassburg; Wied. Ann. xiii. 1881, p. 20; xvii. 1882, p. 85. 3 Nuovo Cimento [3] xi. 1882, p. 11; Exner's Rep. xix. 1883, p. 249. Atti del Ist. Ven. [5] vii. 1880-1, p. 491; Landolt and Börnstein's Tables, 2 ed. p. 340, tab. 137.

(MF), Lummer and Pringsheim (LP), Capstick (Ck), and also those of Cazin (C), though these may be less exact. From these observed values are then calculated the values of the ratios K: H, E: E, and e: E.

'Comptes rendus, cxxiv. 1898, p. 183.

Wied. Ann. lxiv. 1898, p. 555. Rep. Brit. Ass. 1894, p. 565.

3 Proc. Roy. Soc. lvii. 1895, p. 322.

'Ann. Chim. Phys. [3] lxvi. 1862, p. 206.

56. Approximate Calculation of the Atomic Energy in Polyatomic Molecules

A further series of approximately correct values of these ratios can be obtained by a theoretical method which has been used by Sadi Carnot' to calculate the values of the specific heat at constant volume from the observed values of the specific heat at constant pressure.

To explain this method we introduce the values of the specific heats г, y, which are referred to unit volume, instead of C, c, which refer to unit mass; these are given by

T=C, y= CP,

where p is the density of the gas referred to that of water as unity. Then for the ratio of the kinetic energy of the molecules to their whole energy we have the formula

This new form of the formula possesses an advantage when we take account of a law discovered by Carnot, which can be directly deduced from the formula

p=J(C― c) p✪

developed in § 53. If we write it in the form

p=J(T-7)

it contains only two constants, the mechanical equivalent J and the difference гy; of these only the latter can depend on the nature of the gas used in the experiment. But considering two different gases under equal pressures and at the same temperature, we see that the difference г-y of the two specific heats referred to unit volume has the same value for all gases.

It follows for our purpose, from this law, that the value of the ratio of K to H in different gases is inversely proportional to the specific heat y of unit volume of the gas at

1 Réflexions sur la Puissance Motrice du Feu, Paris 1824. Reprinted in Ann. Sci. de l'Ecole Norm. Supér. [2] i. 1872, p. 393. Translated into English by Professor Thurston, London 1890.