24 DE. C4. PT. BEYAN OX THE KINETIC THEOEY OF PLAXETAEY ATMOSPHEEES. 
about thirty years ago. The special objections which at that time might have been 
raised against the law being applied to planetaiy atmospheres, and which arise from the 
necessity of taking account of the effects of gravitation, axial rotation, &c., appear to 
l)e met by the modified form of the Boltzmanx-Maxw'ell distribution used as the 
basis of the })resent Investigations (§ G. equation 9), and the arguments in § 7. There 
I’emains the more general objection ]iow raised by Dr. Stoxey that Maxwell’s Law 
does not correctly represent the distribution in any actual gas, in support of which 
he remarks that the distribution according to Maxwell’s Law is a function of one 
variable, while he thinks that the distribution in an actual gas may be represented 
by a far less simple law. 
Hitherto it has been generally supposed, however, that the deviations of an actual 
gas from Maxwell’s Law only l^ecome important in the ca.se of dense gases, where 
the ratio of the volume of the molecules themselves to the total volume of the o-as is 
o 
no longer so small as to be negligible, where the time during which a molecule is 
encountering otlier molecules is not infinitely small compared with the time during 
which it is describing free paths, and where multiple encounters are not so 
exceptional that their effects may he neglected. So far as I am aware, the most 
successful attempt at dealing theoretically with such dense gases is Mr. Buebery’s 
method, in which tlie view is advanced that the velocities of neighbouring molecules 
become correlated, and the distribution function involves two constants. It is 
precisely in the more rarefied poidions of a planet’s atmosphere that the conditions 
seem to me to approach most nearly to those assumed in the ordinary proofs of the 
permanency of Maxwell’s Law, and of the generalised Boltzmax^X'-Maxwell distri¬ 
bution. Dr. Stoxey’s objection appears to inquire either {a) that the gases in the 
upper atmosphere do conform much more nearly to Maxwell’s Law than the denser 
gases near the Earth, and that the deviations in the latter are so great that experi¬ 
ments made with them lead to the velocity of mean square in the upper regions of 
the atmosphere l)eing greatly under-estimated, or (J>) that the Kinetic Theory of 
Gases must be abandoned in just those cases in which we have been accustomed 
to regard it as being least open to objection. 
With regard to tlie contention that these deviations have been omitted from the 
present investigation, there do not as yet appear to be sufficient data available for 
including them in any calculation. The present methods may be utilised in tlie 
determination of such data. Bv calculations in wliich the unknown data are omitted, 
combined with experimental observations, it is possible to formulate an estimate of 
the extent to which the Boltzmaxx-Maxwell distribution may fail to account for any 
experimentally observed phenomenon. The present investigation Avould tlien hecome 
an a posteriori determination indicating the extent to which the omitted causes must 
be invoked, and it would thus afford an estimate of their magnitude.] 
