344 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
Table VII.—Values of f for Monatomic Gases. 
Gas. 
Absolute temperature. 
/• 
Authority. 
Helium 
° c - r 
273 \ 
2-51 
2-40 
Schwarze* 
Eucken! 
81 
2 • 23 
Eucken 
21 
2-02 
Eucken 
Argon . 
273 | 
2-50 
2-49 
Schwarze 
Eucken 
91 . 
2-57 
Eucken 
Neon . 
283 
2-50 
DornJ 
These results for argon and neon and, to a less extent, for helium at normal tempe¬ 
ratures agree very well with the theoretical value of /, especially since the combined 
experimental errors in their determination may easily exceed one per cent, at ordinary 
temperatures, and much more at low temperatures. 
The diminution in the value of f for helium at low temperatures, if confirmed by 
further experiment, is very interesting and important. Helium is peculiar at low 
temperatures also in the striking divergence of its viscosity from Sutherland’s law. 
Eucken suggests as the explanation of the former phenomenon a partial failure of 
interchange of molecular energy at collision, but (cf. Table VI. of his paper) down to 
81 C., at any rate, the value of C t , for helium remains constant and appropriate To a gas 
which possesses only translational energy. A failure in interchange of translational 
energy would contradict the ordinary dynamical laws, and it is certainly desirable to 
seek some other explanation, if this be at all possible. 
The alternatives are not numerous, and will be examined in turn. We may ride 
out a numerical error in the theory, of more than one per cent., as being quite 
improbable ; but though all the molecular models discussed in this paper lead to 
values of f equal to or slightly greater than 2'5, it is conceivable that for some 
peculiar model f may have rather different values and a wider temperature range. I 
think this is unlikely, and that it is probably possible to prove that f always 
exceeds 2‘5, but this is only a speculation ; helium agrees so well at high tempera¬ 
tures, however, with Sutherland’s law connecting ^ and T, that its molecules can 
hardly be supposed so different in behaviour from rigid elastic attracting spheres as 
to make,/theoretically equal to 2'0 at low temperatures. 
Again, molecular aggregation might seem to afford an explanation, since if part of 
the gas were polyatomic through clustering of the molecules, the value of /would 
* Schwarze, ‘Halle dissertation, Ann. d. Plq^s.,’ (4), 11, p. 303, 1903. 
f Eucken, ‘Phys. Zeit.,’ 14, p. 324, 1913, Tables 3, 6. Eucken (footnote 4 to p. 328) states that 
Schwarze’s value of / for helium is too large owing to a miscalculation in determining C„. 
\ This result was kindly communicated to me by Prof. Dorn, of Halle, as an extract from ‘ Mitt, d, 
Naturf, Ges. z. Plalle,’ 4, 1914. 
