PROCEEDINGS 



OF 



THE ROYAL SOCIETY 



December 11, 1890. 

 Sir WILLIAM THOMSON, D.C.L., LL.D., President, in the Chair. 



The President announced that he had appointed as Vice-Presi- 

 dents 



The Treasurer. 

 The Astronomer Royal. 

 Professor Alfred Newton. 

 Sir G. Gabriel Stokes. 

 Lieut.- General Strachey. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : 



I. " On Ellipsoidal Harmonics." By W. D. NIVEN, F.R.S. 

 Received October 23, 1890. 



(Abstract.) 



In the paper, of which the following is an abstract containing 

 statements of the principal results arrived at, an attempt has been 

 made to develop the subject of ellipsoidal harmonics from their 

 expressions in Cartesian coordinates. 



The harmonics of the ellipsoid of three unequal axes are first 

 investigated, as being the most readily dealt with on account of 

 symmetry and, afterwards, those of the prolate and oblate spheroids 

 are deduced as particular cases. 



1. It has been found convenient to discuss separately the forms 

 which are respectively suitable to the inside and outside of the 

 ellipsoid, the former being taken first 



VOL. XLIX. B 



