THE EQUILIBEIUM OF ELASTIC SOLIDS. 



By solving these equations, the values of the pressures P,, P,, P 3 , and the 



s\ o 5? 

 compressions --, -J-, - may be found. 



8/3 



Sa 



Sy 



(6). 



a 



From these values of the pressures in the axes a, /3, y, may be obtained 

 the equations for the axes x, y, z, by resolutions of pressures and compressions""". 



For 



and 



q = aaP, + lbP 3 + ccP 3 ; 



dSz\ dSx 



d8z 



dS 



d8x 



dSx 



dSz 



_ m id8y dSz 

 = ~"'~ 



m idSz dSx 

 ^ \~dx~ ~ 



_ in idSx dSy\ 

 = ~ 



(8). 



.(9). 



* See the Memoir of Lame and Clapeyron, and note A. 



