MR. R V. SOUTHWELL ON THE GENERAL THEORY OF ELASTIC STABILITY. 197 

 and since the co-ordinates of the point which ultimately goes to (x + Sx, y, z) were 





we 



have 



1 8 9a: a aa; _8 &( , 



' 



It follows that (13) may be written (to our approximation) as follows : 



20 \av, av av 



, 



i+e a 2 



Substituting for m',, n\, we have finally 



m-iav av av m /av av 



(- 1 h I ^ :r~ T ^ ^~ 



m 2 fa 3 dw 1 cz m2\cxcy czcx 



+ 



/ay av \ x I+ z 7 /av av\_ 

 8 ^ *w 4ci + ^^^ 82! 



(15) 



X 



and two similar equations. In any ordinary problem we may neglect e^... in 



comparison with -j=f ... . 



The equations thus obtained may also be written (with LAMP'S notation for the 

 elastic constants) as follows : 



= 0,..,&c. ( . (16) 



2 



where 



., aw' dv' , du/ 



A = ^ + - + - 



T7.=- 4..+ 



= fa* + w*dz>' 



a/ a' , a' 

 == -~'' ~"' 



