Maiicliesicr Mcnioiis, Vol. Iviii. (1914), No. 5. ]/ 

 with two otlier equations, aiul 



^/ = ;/ + ) . . . . (30). 



I [. I now prcKcetl as before to equate S and .S"', 

 7' and 7', 6'^ and U\ but in tliis case it is with the object 

 of finding whether and under what conditions a form of 

 displacement can be discovered, such as will conform 

 with the requirement. 



Assuming, for convenience, 



2 dz 

 we deduce i d . 



«;, = li'.(o,-(L-o,) + ^i:ii^-^ . . . (31), 



2 " r 



from the equality of 5 and .S", T and T' . 



The equality of U and U' requires the condition that 

 ;-(0, -e,) = (32), 



and, with this system of coordinates, it is possible for the 

 relations to subsist together onl}- if this conditicMi is 

 satisfied. This condition is therefore a consequence 

 following on Hooke's Law. 



1 2. The notation, which it has been found convenient to 

 employ while dealing with the connection of the shearing 

 stresses and the discovery of the form of displacement 

 may now be replaced more conveniently by the assump- 

 tions 



ej-e,,-e,= 2(/'>/<0> 



