THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 345 
probably lie between 2'5 and the lower values characteristic of polyatomic gases. In 
this case, however, the value of C„, the specific heat at constant volume, should rise 
to correspond with the internal energy of such molecules ; as the experiments indicate 
a constant value of C„, the suggestion must be abandoned. 
The only possible remaining hypothesis seems to be to attribute the fall in / to the 
neglect of multiple collisions between molecules, including also the effect of the 
attractive forces (in Sutherland’s case) in producing deflections without collisions; 
at low temperatures the molecules may be too close together for these postulates of 
our theory to continue valid. If we determine 3 for helium from the formula 2'5 p C v , 
using the value of p calculated from Sutherland’s formula (which is less than the 
observed value at low temperatures, as we have seen), the result is less than that 
observed at low temperatures. Hence both 3 and p diminish with temperature less than 
is predicted by Sutherland’s law, the divergence being greater for p than for 3, so that 
/ also diminishes. We cannot enter here into a test, by calculation, of this suggested 
hypothesis, but some confirmation might be sought experimentally by examining 
whether /is less than 2'5 for helium at normal temperatures but under considerably 
increased pressure. The latter would bring the molecules closer together in the same 
way as would a diminution of temperature, and this is all that our suggestion requires. 
It is known that over a large range of pressure p and 3 are constant, but that at 
high pressures p increases ; the independence of 3 on pressure has usually been tested 
by diminishing the normal pressures/ and experiments under increased pressure 
might throw valuable light on the present phenomenon. Gases other than helium 
may be expected to behave similarly, though perhaps only with lower temperatures 
or higher pressures. 
§ 12 (D) The case of mercury vapour may also be mentioned, as it was the first 
monatomic gas for which/ was determined. Koch! determined p for mercury vapour 
at 203° C., 273° C., and 380° C., while Schleiermacher| determined 3 at 203° C. 
These data, together witli the theoretically calculated value of C„, led to/ = 3'15. 
Meyer and others have raised objections to the determinations of p (a) because the 
three values show an improbable amount of variation with temperature, and 
( h ) because of the vitiating effect of condensed mercury on the walls of the capillary 
tube used in the experiments. Vogel§ has made are-calculation of ‘ p for mercury from 
an interesting formula which he gives, and finds that at 573' C. absolute|| p should 
equal 593'10 -7 ; this, combined with Schleiermacher’s result, reduces / to 2‘80. But 
*’it is desirable that more accurate experiments should be made in order that a 
thoroughly reliable value of / may be obtained. 
* Eucken, ‘Phys. Zeit.,’ 12, p. 1103, 1911, Table 2. 
t Koch, 1 Wied. Ann.,’ 19, p. 857 (1883). 
\ SCHLEIERMACHER, ‘Wied. Ann.,’ 36, p. 346 (1889). 
§ Vogel, ‘Berlin dissertation,’ p. 57, 1914. 
|| So given by Vogel; it may be a misprint for 473° C. 
3 A 2 
