200 
MR. L. N. FILON ON THE. ELASTIC EQUILIBRIUM OF 
n. 
r = 0. 
■/• = 9/3. 
- r =—29-/3. - 
■ 
r = 
1 
•000000 
- - .382470 
--615993 
-000000 
2 
•000000 
- -200638 
- -645084 
•000000 
3 
• 000000 
- -540924 X lO-i 
- -426702 
•000000 
4 
• 000000 
- -111882 X 10 ' 
- -230912 
•000000 
5 
•000000 
- -204756 X 10-- 
- -112874 
•000000 
6 
1 
•000000 
- -349986 X 10-3 
- -518839 X 10-1 
•000000 
The above, when siilxstituted in the formulae, give quite fi^irly rapid convergence 
when r<o, the convergency ratio l)eing’ in this case less than unity by a finite 
amount. But when r =: a, the series liecomes comparable with the series 
s' cos““u where i is a positive integer, and, as in the first problem, a special 
procedure has to lie adopted. 
19. Methods of Evaluation at the Curved Boundary. 
When r — a, rr and rz are of course zero; hut tlie stresses and (fxif) require 
separate evalution. 
Now, if we use the series for I,, and I, in descending powers of the argument, the 
first few terms of these give a very good representation of the function when a is at 
all large, and will lie quite sufficient for a >18, at whicli point the tables of the 
last paragraph stop. 
Tieplacing I,„ I| by tliese series, we find 
h (a) 
> ('^) = 
fB («) -- 
^ + 9 “i' o ■-> T o> + 
o 
_ 7 _ ^ ^ 
^ ~r • 
. _ 14 31 2^ _ , 
^ a or 4 > 
. 49 157 503 
2 I n « ■■ --’o s ”1 ■ • ' 
oa ol'x 
■ . (107), 
li lyf — , "Pji {yf .— 1 , — 0, 
and 
