Mirrors of Magnetism. 



223 



then describe the arc OB with C as a centre, B being on the 



r-\ 

 line AO. The condition that — shall be constant for all 



points- on the circumference is that -^= shall be equal to y^, 



-dU \J\j 



and this is seen to be true from the similarity of the triangles 



ACQ-. and- COB. : 



If we had any number of magnetic points outside the sphere 

 each would have its virtual image inside the sphere ; thus any 

 form of magnet, such as a solenoid carrying a current, would 

 also have its image. 



It is easy to see that the experiments above mentioned with 

 a large iron plate can be explained in this way. For if we 

 may consider the plate as part of an infinite sphere : 









Fig. 15. 







7^"^ 



C 









^^-<2 





A^^ 







: 



\B 













toO 



toO 



at infinity 



in this case r^ =1 ; therefore — =1 ; therefore w?i=m 2 : 

 (JC m 2 



and further — =1 ; therefore r x = r 2 . 



To assimilate to optical formulae let us now express the 

 relations in terms of the distance of object and image re- 

 spectively from the pole E of the mirror, and write AQ = d ; 



BO = b ; u=AE=d— r ; v=zBE=r- b (fig. 14). Now 



d r 



- = - , by similar triangles. 



This may be written 



u + r 



r—v 



