Electrodynamics and Cremieus Experiment. Z%1 



the wave, which is in contradiction to IV. The equation is 

 therefore 



/F(?)+/(2)=0- 



The velocity of the wave is v=p/q, and by IV. is constant. 

 This requires f(q) = —v 2 q 2 F(q), and F(y) can be cancelled 

 out. Since only powers of V enter into the differential 

 equation, the same must be true of it, and the equation can 

 be reduced to 



(£+**)»-o CD 



5. We must now consider the magnetic fcrce. 



VII. Experimental Fact. The magnetic force in a plane 

 icave is perpendicular to the electric force, and the ratio of the 

 amplitudes of the tivo is independent of the wave-length. 



VIII. Assumption. The magnetic force is connected with 

 the electric force by a differential equation. 



IX. Assumption. The component in any direction of the 

 electric force produced by a changing magnetic field is equal to 

 the induced electromotive force in an element of a wire lying in 

 that direction. 



X. Definition. The unit electromotive force is that which 

 is produced in a circuit by unit rate of cha?ige in the surface- 

 integral of the magnetic force. — This definition implies that the 

 electromotive force depends only on the rate of change of the 

 surface-integral. This is proved below ; the definition of the 

 unit is all that is required from X. 



6. Let the magnetic force be t. Then since S . V^ and 

 V . V = V? the differential equation can contain only powers 

 o£ V> and its solution will be 



5 O". 



'fr ') 



By using u 2 V 2 = —d 2 /dt 2 this can be reduced to the form 



where f, f 2 may be of fractional form. From VII. we see 

 that /i = const., f 2 = c<mst./(d/dt) 9 and hence 



-('+&} 



