434 On the new Action of Magnetism, 



The direction of rotation is the same in diamagnetic and 

 ferromagnetic bodies as we find by experiment, being different 

 in the two ; for it is well known that the rotation of the plane 

 of polarization is opposite in the two media, and Mr. Hall 

 now finds his effect to be opposite in the two media. This 

 result I anticipated from this theory of the magnetic rotation 

 of light. 



But the formula makes the rotation inversely proportional 

 to the wave-length, whereas we find it more nearly as the 

 square or cube. This I consider to be a defect due to the im- 

 perfect theory; and it would possibly disappear from the com- 

 plete dynamical theory. But the formula at least makes the 

 rotation increase as the wave-length decreases, which is accord- 

 ing to experiment. Should an exact formula be finally obtained, 

 it seems to me that it would constitute a very important link in 

 the proof of Maxwell's theory of light, and, together with a 

 very exact measure of the ratio of the electromagnetic to the 

 electrostatic units of electricity which we made here last year, 

 will raise the theory almost to a demonstrated fact. The de- 

 termination of the ratio will be published shortly ; but I may 

 say here that the final result will not vary much, when all the 

 corrections have been applied, from 299,700,000 metres per 

 second ; and this is almost exactly the velocity of light. We 

 cannot but lament that the great author of this modern theory 

 of light is not now here to work up this new confirmation of 

 his theory, and that it is left for so much weaker hands. 



But before we can say definitely that this action explains 

 the rotation of the plane of polarization of light, the action 

 must be extended to dielectrics, and it must be proved that 

 the lines of electrostatic action are rotated around the lines of 

 force as well as the electric currents. Mr. Hall is about to 

 try an experiment of this nature. 



I am now writing the full mathematical theory of the new 

 action, and hope to there consider the full consequences of the 

 new discovery. 



Addition, — I have now worked out the complete theory of 

 the rotation of the plane of polarization of light, on the assump- 

 tion that the displacement currents are rotated as well as the 

 conducted currents. The result is very satisfactory, and 



i 5 

 makes the rotation proportional to p, which agrees very per- 

 fectly with observation. The amount of rotation calculated 

 for gold is also very nearly what is found in some of the sub- 

 stances which rotate the light the least. Hence it seems to 

 me that we have very strong ground for supposing the two 

 phenomena to be the same. 



