On the Potential of a Symmetrical System. 237 



In taking my experiments one by one, it is passible to point 

 out in each some defect which might account for the negative 

 result of that one experiment. But the general conclusions 

 which I have stated* are based on the ensemble of four widely 

 different experiments, and are confirmed by a fifth, a very 

 conclusive one, regarding the existence of open currents. 



Each of these experiments has, besides, been subjected to 

 numerous criticisms. Up to the present I have always met a 

 criticism by an experiment, and this latter has always con- 

 firmed my conclusions. 



While thanking Mr. Wilson for drawing my attention to a 

 point in connexion with my first experiment which might 

 have been unnoticed by me, I think myself justified in replying 

 to him that : — 



(1) Electric convection produces no magnetic effect. 



(2) There is no electrostatic effect on a charged conductor 

 due to a variable magnetic field. 



I cannot conclude without tendering to Professor H. 

 Toincarc my best thanks for the suggestions received from 

 him in the preparation of this brief note. 



XX. JSote on the Potential of a Symmetrical System. 

 By T. J. PA. Bromwich f. 



IT was proved by Legendre that if the potential of a 

 system (symmetrical about Qz) is known at all points of 

 the axis of z, then the value of the potential can be expressed 

 at any point of space in terms of zonal harmonics. But it 

 does not seem to have been remarked that this method may 

 lead in some cases to an apparent discontinuity in the 

 potential functions when so expressed. 



To illustrate the point, let us examine the potential of a 

 circular disk for all poiuts of space ; this is, of course, a 

 stock example of Legendre's method, given in all the 

 ordinary text-books. From Thomson and Tait's 'Natural 

 Philosophy ' (1890 edition), Art. o±6, we find 



V «2^( Ci ^+c 2 ^P 2 + C3 Jp 4 + .,.) (r>a) 



v 1 -t^(.-rp;+^p i+ ^p 4+ . v ) ( ;^ i?r ) 



or 2 7 r,(« + ,P 1 + o/- 2 P 2+ c 8 5p 4+ ...) (^<* <w ) 



* V. Cremieu, These de Paris, Gautkier- Villain, 1901. 

 f Communicated by the Author. 



