CYLINDRICAL AND SPHERICAL THIN ELASTIC SHELJ.S. 
419 
We are now in a position to test the correctness of some of our work, for picking 
out the terms involving dSiv/d(f) — Sv, dSwIdz in the line integrals in (36) and (39), 
and equating them to the corresponding terms in the value of SH winch is given by 
(28), we see that we have reproduced the values of the couples, which we have 
already obtained in equation (14). We may therefore leave the couple terms out 
henceforth. 
Collecting all our results from (26), (28), (29), and (39) the variational equation 
becomes 
8W, + 8W, + m,' + 8W; + "P “r + ("p - so ^ cm 
nld" f f dSw I dm fdZio 
dz dz la dz \ d0 
-j- 2/3^ J J [uhu + vSy + ivhiv) dS 
+ - S^) + E(EK-yc,)SK}rfS 
+ t II j-l s„ + 8„ _ (X + ■^) s™ IJS 
= 2MII (X S« + Y 8. + Z 8») cZS - If II{ X + I (If - 8.) + ZE 8K } dS 
+ I (T^ hu -f Mg Sy + Ng 8u;)« d<^ + j (Mj Su + Stc) dz . . (40) 
where the values of SW^, SWg are given by (30) and (36), and the values of SWg', 
SW^ are obtained from (30) by changing certain letters as we have explained above. 
We have now got rid of all the terms involving the second differential coefficients 
of hu, hv, Sw, and all that now remains to be done is to integrate by parts the terms 
which involve the first differential coefficients. Putting 
we have 
_ 2n ^ I dv; X 
pa dz dz a a ’ 
^ n dm , 1 (dio . Y 
Q=. - - r ffi-hr - 2u > 
pa dz a \d(p / a 
y = E (EK — iv/a + Z/(() . 
3 M 
(-H), 
MDCCCex.—A. 
