654 RICE 



ART. L 



configuration is not one of equilibrium; actually Ws' in- 

 volves the same <xad, etc., as does Ws, but a different Sad] in fact 



Hence on account of the similarity of the figures 



Wv' Ws" 



Wv W, 



2 



(As mentioned earlier there is no contradiction here with [633] 

 since Ws 9^ 2Wv'-) Expressed in another way 



Wv + AWv _ (Ws + AWsy 



Wv ~ Ws"" 



or 



AWv AWs 



= 2 4- 



Wv Ws ^ 



Since Ws = 2Wv, it follows that 



/AWsV 

 \Ws) 



/AWsV 



Neglecting quantities of the second order b{Ws — Wv) is zero, 

 as it should be for equilibrium ; but if we retain higher quantities, 

 A{Ws - TFy) < if T^y is positive, and A{Ws - Wv) > Q if Wv 

 is negative, since {AWs/Ws)"^ is positive for any sign of AWs- 

 For stable equilibrium A{Ws — Wv) must be positive for all 

 variations; thus a necessary condition of stability is that Wv 

 should have a negative value in the equilibrium configuration. 

 This is the result obtained in the second step. The reader can 

 now probably manage the remaining points on pages 294, 295. 

 Note that on page 294 a well known theorem in the mensuration 



