Properties of Matter in the Gaseous State. 337 



la ted equations (43) to (47) without rendering a difficult sub- 

 ject tenfold as elaborate as was necessary." And then he goes 

 on to show how I might have obtained equations for the ag- 

 gregate results at one integration. Clear Ij, then, he has seen 

 no object in my division of space into regions, and is at a loss 

 to account for it except as mere clumsiness in the integrations. 

 Had he, however, looked closer, or even been careful to be 

 accurate in his statement, he would have seen that the two 

 equations (44), which are among those to which he refers, 

 only apply to the partial groups for which u is respectively 

 positive and negative, and that they contain a term which 

 apparently disappears if the respective members of the two 

 equations be added ; and he would have seen that the same 

 thing is true of equations (45)*, which hold only for groups 

 for which v is respectively positive and negative, and from 

 which two terms disappear when the results are added. Now 

 these terms, which are the first and second, are sufficiently 

 obvious in the partial equations, whereas they do not appear at 

 all if the integration be extended to both groups ; and if Mr. 

 Fitzgerald had followed the next articles (83) and (84), he 

 would have seen why these terms are important. To ignore 

 these two articles is to ignore the method by which the results 

 for transpiration are obtained; and these results w r ere the main 

 purpose of the preliminary work in the paper. 



To obtain any results at all for transpiration, it is necessary 

 to divide space into two regions, or else to consider the mean 

 range s as function of the position of the point and disconti- 

 nuous at the solid boundaries ; and by the latter method the 

 determination of the form of the function requires that space 

 should be divided. The results depend entirely on the terms 

 which, when s is constant, disappear in the complete integra- 

 tion, but which, if different arbitrary values are assigned to s 

 for the different regions, do not cancel when the partial inte- 

 grals are added. No result whatever is obtained by complete 

 integration if s be constant ; and although Mr. Fitzgerald does 

 not seem to have noticed it, the late Professor Maxwell fol- 



* The partial equations (45) : — 





a v+ (^h()— P*^ - s dpxU _ s dpa? 

 9 2Vn 2Vtt fy 2 ?r dx 



s dpocY 

 2\/n dx ' 



tr°~CMz6)— potU S dpaXj s dpx 2 



s dpaV 



y 2v^ 2Vtt dy 2tt dx 



2Vt^ dx 



The equation obtained by complete integration 

 2Vtj- dy 2Vtt dx 



