138 Mr. G. F. 0. Searle on the 



off by the pulse is given by 



p _ fiunQ 2 C (1 — s^)x chv 



+ i 

 ^ J -i ( 1 - nxf y^« + (a*- &*j ^ 2 



= ^J 2 {_2Ji+ (3-n*)J 1 -(l-nijJ i -nJ 4 J J 



where i _ I ^'^ _n 



Tims, using yaKr 2 = l, we find 



By § 15 we obtain the results 



x- Q 2 f »*<* 2 + 2£ 2 — n 2 Z 2 , a 4- / aw 2 ") 



L = 4K 1 — ir ~ log s=i — f ) ' 



r =4K?i.-2?-V»8 a --/-^- 



By (27), M=2T/«. 



These values of U and T agree with those I obtained by 

 integration throughout the whole field of the moving 

 ellipsoid*. 



§ 26. When a<b, the quantity c is imaginary, and when a 



becomes still smaller, so that a<b s/l — ri 2 , the quantity I is 



imaginary also. The last case corresponds to an ellipsoid 



more oblate than Heaviside's. The expressions for U , TV, 



and P can be adapted to the case where &(1— n a )i<a<6, and 



where c is imaginary but I is real, by putting fr 2 — a 2 =C 2 and 



writing 



2 , t C „ 1, a 4- c 



— tan - - tor log- 



L « c ° a — c ' 



When a<b(l— n 2 )%, both c and I are imaginary and we must, 

 in addition, put"S 2 (l — ra 2 )^ r a 2 =L 9 ~aTid~Write 



2 . .L . 1, a + Z 



T - tan" 1 — tor =- Jog , 



L a / & a — Z 



For a disk of radius &, we put a==0 and hence C=6 and 

 Jj = h[l — ?i 2 )i. We thus obtain 



ttQ 2 / 2-h 2 \ 



4K6iA(l— rc 2 )i )' 

 * Phil. Mag. Oct. 1897, p. 340. 



