112 Dr. J. Prescott on the Equations of Equilibrium 

 Equation (27) gives 



d ( dyjr\ _ dw d 2 w 

 dr \ dr / dr dr 2 ' 



whence, by integration, 



dtyr _ l/dw\ 2 

 r ^rtr~ ~~2\dr~) 



the constant of integration being clearly zero. 

 Integrating again 



^ 7= _8H 2 (i&V-^V+ ^A +B, 

 that is, 



efore 



Therefore 



Thus the radial tension is 



P = A# 



1 r dr 



To make Px zero at the rim we must have 



(43) 



^B=^HV(6J 1 -4tV + a 1 ). . . . (44) 



L o 



Again, by equation (28), 



2 Wi 3 _ 2EA d /dwdd>\ 



V— ol 5 V w j-\^~ j 



1 6 1 — cH r a?'\ar ar/ 



_ _ 2EA d /dw dcj>\ 

 " l r dr\dr ' dr/ 



=p 1 + 8KBEh(b 2 -2r 2 ) 



- 1 H 3 E/^ 2 (126 6 -20^V 2 + 20/>V 4 -5r6) . (45) 



Denoting the difference of the deflexions at the middle 

 and the rim of the plate by w , and denoting the pressure at 



