Properties of Matter in the Gaseous State. 339 



of s were obviously different in the different regions, the 

 assumptions on which the complete integral had been obtained 

 were clearly at fault. The further division into eight regions 

 was not only for the sake of symmetry, but that all the other 

 terms which enter into the partial integrals might be examined, 

 and as being necessary in particular cases — as, for instance, in 

 that of a round tube, which is also treated of in the paper. 



Having thus shown that, however elaborate and inelegant, 

 the division of space into regions is essential, it is unnecessary 

 to defend it on other grounds. But I may remark, by the 

 way, that such a division does tend greatly to simplify the 

 consideration of motion. This, I think, is proved by the uni- 

 versal adoption of north, east, south, west, zenith, and nadir. 



I have dwelt at considerable length on the foregoing point, 

 as the misconception of this point is fundamental to all Mr. 

 Fitzgerald's criticism. The rest I may answer shortly. 



With regard to Professor Maxwell's remarks on my paper, 

 and his own work on the same problem, of course the sad cir- 

 cumstance of his death occurring, so that this was about the 

 last work he did, renders it very difficult to approach the sub- 

 ject ; but with reference to what I have already said, and in 

 explanation of the apparently imperfect idea at which he 

 arrived as to the scope and purpose of my method, it may be 

 stated that, before writing his own paper, Professor Maxwell 

 had only seen my paper in manuscript in the condition in 

 which it was first sent in to the Royal Society, when the pre- 

 liminary part was very much compressed, and, as I fear, some- 

 what vaguely stated, besides being founded on different assump- 

 tions from the present. Without entering further upon this 

 now, I may refer to a letter which I addressed to Prof. Stokes 

 after seeing an early copy of Prof. Maxwell's paper, and before 

 I was aware of his illness, which letter was subsequently pub- 

 lished in the Proceedings of the Royal Society for April 1880, 

 p. 300. 



Mr. Fitzgerald has asked me for an explanation of the 

 system on which certain terms are retained and others neg- 

 lected. This is difficult to give in a few words ; but I was 

 under the impression that it is sufficiently explained in the 

 paper. It seems to me that the difficulty which Mr. Fitzgerald 

 has found must have arisen from his having adopted the 

 hitherto vague way of looking at the mean path of a particle 

 (or in this case the mean range) as a small quantity, without 

 strictly inquiring as compared with what it is small. In my 

 paper, s is nowhere to be regarded as small except in cases 

 where it comes into direct comparison with some definitely 



larger quantity. The small factors are — , - -£. and - -r-; 



oc a. ax ct ax 



