98 
MESSES. G. F. C. SEAKLE AXD T. G. BEDFOED 
Expanding in powers of z and comparing the coefficients of z and of z^, we find 
TT^/S = X (2m + l)-2, 7rV'96 = :S { 2 m + 1)“^ 
1 
Hence 
^ — tanh ^ 
(2m + 1)2 {(2m + 1)2 + ^2} ’ 
Now put z = {2n fi- 1) ajh, and then 
fl'X _ 1 { ir-h- vrS'^ tanh (2?i + 1) 7ra/25 
It ~~ ^ {2n + 1)2[8(2« + l)2a2 4(27i + l)3fr 
_ ah /dBy r b ^ tanh (2??. + l)7ral2b 1 
cr \dt) I l2a ir'^cr (2n + 1)® J 
Writing this in the foiin d^jdt = QA(r/B/(:/?)Ycr, we have 
„ _ & 16&2 ^ tanh (2?i + 1) 7ra/2& 
(2?i + ly • • • 
As ajh increases, the expression (9) very rapidly tends to the limit 
W 1 
TT'Yr ^ { 2)1 1)“ 
b^ 
I2d 
•05255 
¥ 
( 9 )- 
( 10 ) 
[since %{2n + l)~^ = 1'0045], the error not exceeding 1 in 4000 when ajh is as small 
as 2. We give a table of the values of Q for small values of a/6 ; it will be seen that 
Q is rather smaller for a square than for a circular rod. 
ajh. 
1. 
1 -5. 
2. 
2-5. 
3. 
4. 
8. 
16. 
32. 
64. 
Q 
•03512 
•03260 
•02853 
•02492 
•02194 
•01755 
•00960 
•00500 
•00255 
•00129 
Mr. L. N. G. Filon has kindly verified our results, emplo 3 dng the mathematical 
method used by de St. Venaxt in finding the torsional rigidity of a rectangular 
prism. [ Cf . Thomson and Tait, ‘ Nat. Phil.,’ Part II., p. 248,)'^ 
Appendix II. 
On the Demagnetising Force due to Rods of Finite Length. 
§ 74. In order to find how the demagnetising force at the centre of a long 
cylindrical rod depends upon the induction at the centre of the rod, the following 
experiments were made. The magnetising solenoid was placed at right angles to the 
* [For an elliptic cylinder, axes 2a, 2b, 4> = hq{x-ja- + y^jh-) a-b-j{(d + b-) satisfies (6) as well as the 
condition that no current crosses the boiinding surface. 
We hence find Q = abi{4:- {a- + ^<2^}.— Decembei' 26, 1901.] 
