116 Dr. J. Prescott on the Equations of Equilibrium 



zero for C, provided we find finally that this leaves the xy 

 plane somewhere very near the tangent plane mentioned.' 

 Then 



r/ 2 c/>_ 1 

 df a 

 and, substituting this in equation (61), we get 



(63) 



2 EA 3 dSo x 2Eh ,,,., 



Now let ^ = 0. Then 



^^-4».S, (65) 



where 4m 4 =- , t 7" o ' ^ . ..... (66) 



/ra 2 



The complete solution for it 1 ! is 



Wi = H cosh 77?y cos 772!/ + K sinh 7723/ sin my 



+ H : cosh 7773/ sin m?/ + K x sinh 7713/ cos my ; . (67) 



but since wi is an even function of y we know that Hi and 

 K x are zero. Therefore 



w 1 = H cosh my cos my + K. sinh my sm my. . (68) 



Now let the width of the plate, that is, the dimension 

 parallel to the y-axis, be 21. Then, in order to make the 

 stresses zero at the circular edges of the bent plate, we must 

 make 



F;io} where ^ = * (69) 



But 



= C < 2m 2 (H sinh my sin my — K cosh my cos my) -\ — £ 



. . . (70) 

 and 



_ Cm 3 J H (cosh my sin my 4- sinh my cos my) ) 



h ( - K (sinh my cos my — cosh 7?iy sin my) J 



Writing 6 for 777/, the conditions that M 2 and F 2 should be 

 zero where y = l are 



— H sinh 6 sin 6 + K cosh # cos # = _ — „- , 



27?i 2 a 



H(cosh sin 6 + sinh # cos 6) = K(sinh 6 cos 6 — cosh 6 sin 0). 



