PuRSEK — AppHcdtioHS of BchucVh Fnnrtio)is (o Pluj^ic^i. 50 

 Also f .. . . . , 



Wu have then 



Also 



r-Ji (mr) dr = «/, (ma). 



Jo 



J 



r-d) (r) = — - + . - Jo' (jna)y 

 4 



from which two equations, c;„, are determined, and thence 

 A„^, Aq as before. 



M. — Suppose, now, that the curved surface is acted on by 

 tangential forces, while the terminals are free. 



We now assume 



y 



u = sin nzK^ {nr) ~ , 



V = - "ZB,, sin nzKi {tir) - , 

 w= 0, 



where the origin is taken as before, the values of n being given by 



«7r 



"= -21' 



s having all odd values, I denoting semi-height of cylinder. 



The typical terms in the strains at the curved surface are then 

 given by 



du dv ^ xy . dw 

 — = - — = — O sin wz, -r = 0, 

 dx dy a dz 



dv dw ^ X ^. . . 



-7" + -7- = - nB„ - A, ina) cos W2, 



dz dy a 



dw du -r, y / X 



-7- + — = nB,, - ina) cos W2, 

 dx dz a ^ ^ 



du dv 7/ - x^ 



J- + -7- = n sin nz. 



dy dx a 



Where a is radius of cylinder, 



E2 



