SURFACES OF DISCONTINUITY 653 



Thus the figure representing the configuration would shrink so 

 that the lengths of the lines in the figure would be proportional 

 to the changing values of the tensions; therefore 



(Tad • o'xo = {Sad "T CISad) • Sad 



or 



((Tad + da-Ao) : (Tad = (Sad + dsAo) : Sad, 



and so 



Sad d(TAD ^= (Tad uSad- 



Hence 



d{cFAD Sad) = 2sad ddAD, 



etc. 

 Thus it appears that 



d{Ws — Wy) = i d{(TAD SaD+ . . . -(TbC SbC— . . ■) 



= h dWs. 



Since Ws = when Wv = 0, it follows that 



Ws -Wy = l Ws 



or 



Wa = 2Wy. 



This disposes of the details in the first step. Turning to the 

 second we again consider a variation of the type just considered 

 from the equilibrium configuration, i.e., such that the new 

 figure a'h'c'd remains similar to abed. This varied configura- 

 tion is of course not one of equilibrium for the actual tensions 

 and pressures, but this is of no importance as regards the 

 conditions of equilibrium and stability of the unvaried con- 

 figuration; Ws and Wy' can be reckoned for this varied con- 

 figuration, but of course Ws is not equal to 2Wy since this 



