108 Mr. Gr. F. Fitzgerald on certain Dimensional 



trie hemispheres of radii c x and c 2 . If P x bo the pressure on 

 the inner one of radius e u and P 2 on the other, and if p be the 

 mean pressure on the circular annulus of thickness c 2 — <?i be- 

 tween them, and be consequently the pressure at right angles 

 to I 3 ! or P 2 , then for the equilibrium of the shell we have 



PiC* + p(cl-c*) = F 2 cl 



Hence 



Pi-P»=(P.-iO 



C2- C l 



Now P x — P 2 is Prof. Reynolds's measure of the stress, while 

 P 2 — p would be Maxwell's at the outer surface, while Pi— p 

 would be his measure for the stress at the inner surface; and 

 this latter is the same as Prof. Reynolds's when c 2 = x> , which 

 is the case he compares. Where the discontinuity at the sur- 

 face of the solid is taken into account, the equation Prof, 

 Reynolds gives is 



P*-Pl„l ^-C? «,-«' 



2 



How this result is obtained is not very easy to see; for it does 

 not seem to follow without additional assumptions to those he 

 mentions; but, being derived ab initio, it is free from the 

 doubts arising from his omitting any terms he ought to retain. 

 This measure of the stress, of course, vanishes when the sur- 

 faces become parallel planes. But that does not prove that all 

 stress vanishes; for if we calculate Maxwell's measure for the 

 stress, we find that 



F 2 -p_ o\ * e - u < 



|P 2cJ 



and w T hen the surfaces now become parallel planes, this, so far 

 from vanishing, attains its maximum value, 



I cannot believe that Prof. Reynolds overlooked the fact 

 that the pressures on planes turned in different directions are 

 unequal; but he does seem to have overlooked the fact that 

 his measure of the stress is inadequate, and that the gas may 

 be subject to stress, even though his measure for it vanishes ; 

 and he certainly cannot have been aware that his equations 

 lead to the conclusion that there is a state of stress in the gas 

 between two infinite parallel plane surfaces, one of which is 

 hotter than the other, such that the pressure on each of them 

 is different from that out sideways between them. 



