Becord. xxxv 



while the surface conditions for z — dz h become 



cIwq ,, dw^ . 

 (9) o=k-^^ + h^^^ + 



. . + 2u,, + 4.h\, + . . . . 



+ (2ft + \) 2^0 + 3(2/^ + ^)'^^^i + • • • • 



For very thin discs we may neglect the powers of z and h 



higher than the first. Then, to determine u^q and Wq, we 



have the first of the equations (7) together with the surface 



conditions 



dwa . ^ 

 (9 bis) 0=^-^2u,,, 



from which we can eliminate «„. The problem now is very 

 simple and we give below only the results. 



I. Full disc* 



[2(1 + <r)^ '^J 



rz 









66 = 



2E 



7z=o 



r7' = 



4E 



(i?2-r2); 



/oa)2(l + o-)(3 + o-) 

 4E 



i?2_ 



5—60- 

 7 — 2o- 



* In these fonnulas Young's modules (^) and Poisson's ratio ('J') 

 have been introduced. The results (for full discs) are identical with those 

 obtained by Mr. Chree (Camb. Phil. Soc. Proc. 1890) if in his formulas we 

 discard the terms of the order of h^ and higher. However, the general 

 solution as obtained above, is entirely different from Mr. Chree's and can 

 be made to satisfy all surface conditions, which Mr. Chree's solution does 

 not do. 



