446 
MR. A. B. BASSET ON THE EXTENSION AND FLEXURE OE 
Substituting the values of ctj, o-g, ttt from the first, second, and sixth of ( 6 ), and 
integrating by parts we shall obtain 
8W] = 4:7ih +• -g a cl(f> + ^nh j(-|- rshu + 9l38v) dz 
(30). 
Now 8 W 3 , 8 W 3 , 8 W 4 depend upon Id ; if therefore we substitute in (25) the value 
of 8 W]^ from (30), and the portions of 8 ®^, 8 U, and 8 ?!., which depend upon h, we shall 
obtain the approximate equations 
and 
= Anh T 3 = 4n/i ^ 
= M 3 = 27^^sT 
pu = ‘In 
pv = 2n 
piv = — 2n 33/ct + pZ 
1 
I 
j 
(31). 
(32). 
These equations are the same as those obtained by Mr, Love,*' and which are 
employed by him in discussing the vibrations of a cylindrical shell. The complete 
equations giving pu, pv, pw in terms of the displacements and their space variations 
contain certain additional terms involving Id (since the common factor li disappears) 
which it is our object to determine ; but, since we do not retain terms higher than Id, 
we may, if convenient, substitute the above approximate values in all terms of (25) 
which are multiplied by Id. 
Again 
SW 3 = f nJd ||(i£ 8 X -f ^1? V + \P ^P) ^ 
Substituting the values of X, p, p from (15), (16), and (17), we obtain 
jjic S\dzd(f) = — dz d(f) 
= ((“f -dz) . 
also 
* ‘ Pliil. Trans.,’ A., 1888, pp. 538 and 540. Equations (32) correspond to Love’s equations (86), 
(87), and (88) ; and (31) to (101). 
