AND DEFORMATION OP A THIN ELASTIC SHELL. 



a m 3 



50'J 



. r /, 3u> u\. 3 /i\ 



= * L- (*' - s) * * U) 



The relation X' = K' reduces to 



(16) 



and each of these expressions vanishes (L.AM6, p. 80) ; thus, this condition is fulfilled 

 identically.* Using these relations, we find 



m. 9/9 3/9 9a p 4 9 pi 9/9 



X _;. j.* 

 AI H AI 



3/3 3/3 i 



. 

 AZ 3/8* H ^ 2 3/9 3/9 



/i\ * ? 



\hj ~ Pi 8/9 



(18) 



7. The quantities defined by equations (5) have been calculated directly ; we wish 

 to obtain an interpretation in terms of quantities defining the curvature of the 

 middle-surface after strain. 



This may be taken as a verification in some degree of the preceding work. In endeavonring to 

 form equations referred to the above set of moving axes, ARON neglects the f-0^ fO^ I0 t and deduces 

 values of X'g, t\ (my notation), which do not satisfy the relation V a + ', = (see the memoir above 

 qnoted, pp. 169 et .-/.). In consequence, he is obliged to make an assumption that 3 (t'/ij" 1 ) / cU is a small 

 quantity of the second order. 



If the relations (17) had not been known, the theory of deformation would prove them. 



