r 425 ] y 



XLII. Radiation and Electromagnetic Tlieory. 

 II. ^Eolotropic Potential. Bij R. HarGREAVBS *. 



§ k 20--o. Solution of the equations of Laplace and Poisson in general 

 ssolotropic form for an ellipsoid. The asolian quadrics which 

 replace confocals. 

 § 20. A theorem akin to Maclaurin's. 



§ 27-29. Special motional form, the derivation of momentum, simpler 

 cas 

 '. 31. Solution for density a linear function of coordinates. Application 

 to rotation. 

 § 82. Case where the translation exceeds the velocity of light. 



-36, A theorem of reciprocation and a new form of the solution with 

 geometrical interpretation. Direct verification of new form. 

 Indications of differences in forms and constants required for n 

 dimensions. 

 § 38. General validity of new form for isotropic or aeolotropic potential. 



v hit ion for Ellipsoid* of the JEolotropic form of the 



Equations of Laplace and Poisson. 



§ 20. In the following analysis for ellipsoids a general 

 aeolotropic notation is used. The ellipsoid is first treated as a 

 conductor, and then as having a uniform distribution through 

 its volume ; and the equations are taken to be 



dx ' d.v </// 1 dz da 



so that \ (71) 



%p^ - 2V ^_ + k P =0, say V;> + *P = 0. j 

 dar dydz 



The passage to the motional case is made by writing 



for / ,' , g : , r .: p' > «' ' '•' ). . (72) 



1— p\ 1— o z , 1-/'-, — gr, —rp, —pgj 



In the motional case k is 1— "2/r 2 , and in the general case 

 we may put 



1: = 



p v' 



i 

 7 



= \- 



r' q 



V' 





9' J/ 



r 





Tho successive rows of this determinant are the coefficients 

 appearing in X Y Z. 



ssociated with this is the problem presented by the 



* Communicated by the Author. 



Phil. Mag. 8. 6. Vol. ( J. No. 52. April 1905. 2 F 



