106 Mr. Gr. F. Fitzgerald on certain Dimensional 



"O 



the anomaly I want him to explain. It is that, after neglect- 

 ing both s a and U 2 as small quantities, he nevertheless keeps in 

 sU all through his equations and carries it forward into his 

 results. I thought at first that this must have been owing to 

 the terms he omitted not being of the same order in the result 

 as those in sU; but I worked out some of them, and they 

 seem to me to lead to terms of exactly the same order as those 

 he has retained. Omitting these terms does not seem to alter 

 the form of the result; yet it would explain Maxwell's doubts 

 as to Prof. Reynolds's method being a good one for determi- 

 ning the amount of the result. I shall return to this presently, 

 as I think it may explain a difference between his results and 

 those of Clausius. 



Having arrived at his fundamental equations, the way in 

 which he treats them and takes into account the disconti- 

 nuity at the surface of a solid is admirable; and the com- 

 parison of his results with experiment justifies his funda- 

 mental assumptions as far as this order of approximation 

 is concerned. In this connexion, however, it is well to 

 bear in mind that an assumption sufficient to explain one 

 result may not explain another. For instance, a very great 

 change might be made in Clausius's hypothesis without 

 affecting the conduction of heat, but nevertheless very ma- 

 terially affecting the resultant stresses. I have already 

 pointed out this in a paper, " On the Mechanical Theory of 

 Crookes's Force " (Transactions of ihe Roval Dublin Society, 

 1878, p. 62, and Phil. Mag. Jan. 1879). In this paper I do 

 not profess to have done more than point out how, upon 

 particular assumptions as to the average motions of the mole- 

 cules of the gas, these stresses may be most conveniently cal- 

 culated. 



When Prof. Reynolds comes to the question of Thermal 

 Impulsion, I do not know whether to be more puzzled jjat 

 what he retains in his equations or what he omits to notice as 

 their result. Before considering the discontinuity near solids, 

 he depends wholly upon the term in sU that I have already 

 noticed as of the same order as several terms he has rejected. 

 This must, I am sure, be explicable; and in any case the phe- 

 nomena, as Maxwell asserts, may depend entirely upon the 

 want of continuity at the surface of solids ; and in thefpart of 

 the investigation where this is introduced he treats the whole 

 question ah initio and escapes this difficulty. I come next to the 

 point that puzzles me by his omitting to notice it. I am sure, 

 however, that he has done so from want of space and not from 

 any oversight. The point is, that the pressure on a plane 

 drawn in one direction in the gas is generally different from 



