340 Prof. 0. Reynolds on certain Dimensional 



the squares of such quantities being consistently neglected. 



2 Jl 



Such factors as r~5 and variations of higher order are zero 



a tl\- 



in the case of transpiration, but in the case of impulsion they 



are of the same order as the results. But the retention of such 



terms in equations (42) to (48), or in the fundamental theorem, 



would only give rise in the results to such terms as — -=-%; so 





cW 



that as long as s is small compared with r no error can have 

 arisen from the neglect of these terms. And this is the only 

 case to which these results have been applied, the extreme 

 case where s is large compared with r having been dealt with 

 by a special method which gives rigorous results. In the first 



r d 2 a 



instance, all terms of the second order such as — -=-* were 



retained ; and it was only after it was found that these did not 

 in any way affect the results as a first approximation that they 

 were neglected. The terms I have neglected are, as far as I 

 perceive, the same as those neglected by Professor Maxwell; 

 and such was the care taken in this matter (which is of funda- 

 mental importance) that I am very confident that there is no 

 mistake. On the other hand, it is difficult for me to see how 

 Mr, Fitzgerald can have failed to see that the residual term, 

 which he instances as showing that I am wrong in saying that 

 my equations show that there is no force in the case of parallel 

 flow, is distinctly of the second order of small quantities. But 

 even to this term he has no right ; for in order to obtain results 

 to such an order the variations of s would have to be considered. 

 It seems that Mr. Fitzgerald is of opinion that the parallel flow 

 of heat does cause stresses in the gas, and that he has been trying 

 to find that I have not disproved the possibility of such stresses. 

 If he confines his attention to stresses of the same order of 

 magnitude as those now shown to exist in the case of conver- 

 ging or diverging flow, he will find that both Professor Max- 

 well and I have proved the impossibility of their existence ; 

 but if he goes, as he appears unwittingly to have done, to a 

 higher order of small quantities, then I have nothing to say, 

 except that he has no inconsiderable task before him. 



Lastly, as regards the charge of having changed my views 

 and having adopted a theory which is practically the same as 

 that which I had been previously combating, I can only say 

 that against no theory have I said a word of which I do not 

 maintain the truth. I have never asserted that the variation 

 of pressure in the direction of the flow of heat, which I have 

 consistently maintained to be necessary to the production of 

 the phenomena of impulsion, may not be attended by a differ- 



