2'2& Dr. S. P. Thompson and Mr. Miles Walker on 



due to m 1 in dealing with the potential of points in the field 

 we are considering, and so that we may take the surface of 

 the sphere as an equipotential surface of practically zero 

 value*. The distribution of the field outside the sphere will 

 be the same as if no sphere w;ere thexc, but instead a pole of 



oc 



strength ~"» l iXn were pl ace( i a ^ B. We may say that the 



sphere acting like a convex mirror has given a diminished 

 image at B. 



We can find the position of B by the following construc- 

 tion : — Describe the arc 00 (fig. 14) with A as a centre, and 



Fig. 14. 

 ■ C 



* [Note added after readiny of Paper. — At this point our original paper 

 contained the following remark as a footnote : — " If the magnetic object 

 is large, or is far removed, then besides the image as above defined it is 

 necessary to take into account the raising of the potential of the whole 

 sphere, which would be represented by another image at the centre." As 

 some discussion took place on this point after the reading of this paper, it 

 may be well to deal further with the matter. The case is then analogous 

 to the case of an electric charge q brought up to an insulated conduct- 

 ing sphere having no previous charge. Lord Kelvin, in a paper dated 

 July 7th, 1848, has shown that the effect on external points of the 

 charge residing on the surface of such a sphere is the same as the effect 



f acharo-p. — ~A at ^ (%• 14), and a further charge of -4- _ q at the centre 

 o- a d 



O. His reasoning being applicable to the magnetic case, we see that the 

 image of a North pole at A consists of a doublet having a South pole 



situated at B of strength m l — and a North pole also of the strength m x - 



d d 



situated at the centre 0. Now any magnetic object such as a solenoid 

 will have a South pole as well as a North pole, and if the object is 

 small compared with the size of the sphere, both North and South may 

 be taken as equidistant from the centre, and their images at the centre 

 will therefore neutralize each other, and we have left the image that is 

 considered in the text. If the object is large as compared with the 

 size of the sphere, then in both the magnetic case and the optical case 

 there is a confusion of images.] 



