200 Mi: i: V. SOUTHWKl.L ON THE IJKNKKAL THEORY OF ELASTIC STABILITY. 



(licin must vanish. Hut, as we have already seen, the line which becomes a direction 

 < )//' of principal stress has initially the direction-cosines 



m,, 1, n, : 



it follows that at the surfaces of the plate the expression for m t and n a must vanish 

 identically ; moreover, at these surfaces, Y'y must vanish. These conditions may be 

 written in the form 



identically, when y = t. . . (24) 



i i\ v , i . 

 (m-l) + + = 0, 



cy tiz dx 



The first condition is already satisfied. The other two give (if we neglect terms of 



and 



or 



rf// 



- when y = +t, 



(25) 



2m- 



G 



; E 



m+ 



m-2 40 



.GL\ 



/. _ 



shaj/ 



and 



(m-2) ay sinh ay-2 (m- 1 ) 



4G 



cosh ay 



when 



___ G_ 

 m-2 40 



(m-2) ay cosh ay-2 (m-\) ^ sinh ay 



m G 



m-2 40 



y = t . . > 



+ Q(m 2) a sinh ay 



+ S (m 2) a cosh ay = 



(27) 



