338 Prof. 0. Reynolds on certain Dimensional 



lowed me in dividing space into two regions at the bounding 

 surfaces, calling the two groups the absorbed and evaporated 

 pas. But without the use of arbitrary coefficients he had no 

 means of dealing with the variable condition of his gas, except 

 by assuming that the same distribution holds in both groups 

 at all points. To meet this assumption (which, he points out at 

 the top of page 253*, is improbable) he had further to assume 

 a highly complex and improbable condition of surface ; and the 

 result is that the equation he obtains (77) is short of the most 

 important term. This term is that which gives the result when 

 the tubes are small compared with s ; and as this is the only 

 case in which the results are appreciable, when Maxwell came 

 to apply his equation to an actual case there was no sensible 

 result. 



In the first instance, I also began by considering space as 

 divided only at the bounding surface, and, assuming the distri- 

 bution in the two groups the same, integrated for the complete 

 space ; and the result I then obtained was precisely the same in 

 form as that subsequently obtained by Maxwell. These results 

 correspond with the experimental results for a tube whose diame- 

 ter is large compared with s — called by Graham transpiration ; 

 but they do not at all correspond with the law which Graham 

 found to hold when he used a fine graphite plug, and which I 

 have shown to hold also with coarse stucco plugs when the 

 gas is sufficiently rare, viz. that the times of transpiration of 

 equal volumes of different gases are proportional to the square 

 roots of the atomic weights. Graham had considered this 

 law as depending on the fineness of the pores of the plug, and 

 had suggested that the action then resembled that of effusion 

 through a small aperture in a thin plate, rather than transpi- 

 ration through a tube of uniform bore ; and this is the assump- 

 tion which Maxwell falls back upon to account for the differ- 

 ence between his calculated results and those of experiment. 

 That I did not do the same was owing to my having, by rea- 

 soning ab initio, after the manner explained in the analogy of 

 the batteries, in the very first instance found that the law of 

 the square roots of the atomic weights must hold in a tube 

 whenever the gas was so rare that the molecules ranged from 

 side to side without encounter, and to my having proved by 

 experiment that both laws might be obtained with the same 

 plug by changing the density of the gas. It was thus clear 

 to me that some term had been omitted in my equation ; and 

 after a long search it was found that, though the term vanished 

 in the complete integral, it appeared in the partial integrals 

 when space was divided into regions, and that, as the values 



* " On Stresses in Rarefied Gases," Appendix, p. 249, Phil. Trans. 1879. 



