526 Prof. R. Clausius on the Transmission of 



equal to null, and solving the resultant equations in respect 

 of v 2 . 



But from the frequent and multifarious occurrence of v 2 

 this calculation is tedious, even when the members contain- 

 ing the small values cr and \ are simplified by introducing 

 approximate values, as is undoubtedly allowable. We shall 

 therefore content ourselves with making the calculation for a 

 special case and with certain omissions, in order to get at any 

 rate an approximate idea of the magnitude of the value v 2 

 in question. The constant c, which is equal to (e — a)p } may, 

 according to the values of e and a, be either positive or nega- 

 tive, and thus may also be null in a particular case ; we will 

 assume that this constant has the last-named special value null. 

 The expression for i acquires then the following simple form: — 



i=pu r — b. 

 We will further disregard, in the calculation, all members 

 containing the factors p, a, and A, ; we have then to put v! 

 equal to (v,— v 2 )/R, and make y and 8 equal to null. The 

 equation which holds for T 2 passes then into 



,2 



T 9 =R^- 



,(**!? -*)' ' ' ' < 22 > 



«1 — tV 

 By differentiating this equation in respect of v 2 we get 



H 2 = T^k^ -^)(2^-3 W2+K -R^). (28 



If now this differential equation is equal to null, one of the 

 three factors of which the expression on the right hand con- 

 sists is thus null. The first factor cannot of course be null* 

 The second factor .. ,, 



P-Ti b 



represents the current-strength i, and for our purpose cannot 

 be made equal to null. We must hence make the third factor 

 null, and thus obtain for the determination of v 2 the equation 

 2pe*-3pv 1 v $ +pv 2 l -'Blv 1 = 0. . . . (24) 

 From this follows 



*-*•.* V^w+^- 



The upper sign before the root gives a value for v 2 which is 

 greater than v u and which therefore is inadmissible in our 

 case; hence we must use the lower sign, and then by a slight 

 transformation we get the equation 



t*«*(|-i^+8||). . . . (25) 



