192 T. H. Havelock 
We use the notation 
© p—2va ae ( me 1)” e—2ub 
oi = 1+e-2d 
ondv, 
(73) 
. 2 e—2vd 
s =|. Tags 
By comparison with the expressions for the flat plate between two rigid 
boundaries, it is easily seen that we may write down the corresponding 
results by replacing the coefficients r,, by —s, and rj, by —s/. 
Thus we obtain, making these changes in (45), 
L/[Lo = 1+6, p +b. p? +b, p?+byptt..., 
b, = — 2s) sin 0, 
b, = 3s? sin? 0 —s, + 28} cos 20, 
b, = — 4s? sin? 0 + 2sys,(2 sin 6 — sin? @) + s, sin @ cos 20 — 8s) 8; sin 8 cos 20, 
b, = 5s$sin* 0 — 3s2s,(3 sin? 6 — 2 sin*@) + $5? + 3s, cos 20 
— 4598_(7 sin? 0 — 12 sin? @) + 1882s; sin? @ cos 20 — 3s, 5; cos 20 
+ 38}? cos? 20 — 385 cos 40. 
(74) 
Similarly, for the moment, 
M/My = 1+e,p+Cyp?+C3 p> +e pi +..., 
¢, = — 2s)sin 0, 
Cy = 3sésin? 6 —4s,(1+ 4sin?0) +5), 
Cs = —4s§ sin? 0+ sys,(3 sin 6 + 2 sin?) 
+ ts,(sin @— 8 sin? @) — 2s)5;(3 sind — 4 sin? 6), (75) 
C, = 5s4sin* 0 —43s?.s, sin? 0 — 2s)s,(sin? 0 — 3 sin’ 6) 
+4s7(1+14sin?6—12sin*@) + 4s,(1—8 sin‘ 0) 
+ 3s2.s{(5sin?6 — 8 sin*@) —s,s}(1+ 10 sin?0— 20 sin’ 6) 
+81?(1+ 6 sin? 6— 16 sin4 @) — 4s3(1—4sin?6). 
453 
