652 RICE ART. L 



so that 



(W/ - Ws) - {Wy' - Wy) = {cad' - <rAD)SAD + CAD'dSAD + • . . 



— ((Tflc — (TbcjSbc — Cbc CISbc — • • • 



— Pd dvo -{■ PAdvA-{- ... 

 or, at the Hmit, 



dWs — dWy = (Tad dSAD + Sad d(TAD + . • . 



— (Tbc dSBc — Sbc d(TBc — • • • 



- Pd dvo + PAdvA + ... 



But since [629] is true for any small change in the configuration 

 it is true for the change indicated by dsac etc., so that 



(TAD'dSAD I • • • (TBcdSBC • • • 



- Pd dvo + PAdvA -\- . . . =0, 

 and from this it follows that 



d{Ws — Wy) = SADdcAD + . . . — SBcd(TBC — . . . 



which is equation [630]. Now this change in Ws — Wy 

 accompanies small changes in the functional forms which express 

 aBc, etc. in terms of t, jjli, H2, • • • but not in the forms for Pa, 

 etc. Suppose these changes to be of such a nature that the 

 tensions all diminish in the same ratio, the pressures of course 

 not altering. Since 



etc. 



