1266 



When we again put M, =z — 6 jr C /i -\- s with .sA = 0, we find 



ci( once : 



L^ fdLy RT 



^ t \dtj N 



We can, however, also follow ilie course indicated in the text 



p. J258, and show, or make it at least highly plausible, that: 



(/,) I ir {O) {t — O)dO<^0 (5a) 





For this pui'pose we remember that the movement is I'eversible. 

 I shall suppose the reversed movement (in which of course all the 

 velocities, both those of the particles and those of the molecules of 

 the medium must be reversed) to take place between the limes /, and 

 t^. Of course then (^ — t^ =z t, — /,.' We have further ?r(^J = ?(;(^,) 

 and /_r{tf) = ip{t,), for the forces that iji the direct movement occur 

 at the beginning of the interval, in the reversed movement occur at 

 the end and vice versa. Finallv the |)ath A' = — A is travelled over 

 in the reversed movement. For the reversed movement the expression 

 analogous to (5a) becomes : 



■4 



U' (f J j U' 



(t,) . A' = .- (t,) u- (0) . {t^ - O) do <(}.... (56) 



This becomes for the direct movement: 



•a 



'■■ƒ 



- »- (t^) A = >r (^) I n- (0) {6 — t,) dO<:i), . . . (5c) 



for what for the reversed movement is expressed by t^ — 0, for the 

 direct movement becomes — t^. 



If therefore we have proved the validity of (5c), we have proved 

 (5*^) for the reversed movement. On account of the equivalence of 

 the direct and the reversed movement, we may also consider {5a) 

 proved for the direct movement. This appeal to the reversed move- 

 ment is not necessary. The validity of (5a) might have been demon- 

 strated in the same way as has been done with (5c). The represen- 

 tation and the mode of expression seemed somewhat simpler when 

 I started from (5c). 



Superficially considered the sign of this expression would be 

 expected exactly the contrary. When we namely choose a group of 



