AND DEFORMATION OF A THIN ELASTIC SIIKI.I, 



501 



du'/dtt . . ., and afterwards neglects them as small. So that the equations (6) and (7) 

 to be obtained below are unaffected by the modification of the theory here proposed. 

 Equating the differential coefficients of (1) with respect to a and p, we get 



a 



i . a 



a/i, 



a /i 



i a 



at/ a/ 



and, similarly, by differentiating with respect to ft and q. 



3. Now, taking the set of three equations above written, multiply them by l l} m u n l 

 and add, then by 1 2 , m it n 8 and add, then by l z , m^, n^ and add, and repeat the process 

 on the second set ; the six resulting equations may be written 



A, 



r > 



(2) 



and 





*i 



. . (3) 



In these cr lf o-., are the extensions of the line-elements (1), (2), and m is the sine of 

 the angle the axis y makes with the line-element (2) after strain, so that, if (L 2 , M s , N g ) 

 be the direction cosines of the line-element (2) after strain referred to the fixed axes 

 of (6 >?, 0, 



