Maxwell's Electro-magnetic Theory of Light. 383 



For a medium whose permeability is unity, we shall finally obtain, 

 -eliminating a, /3, 7 between (9) and (7), 



8. Consider the propagation, parallel to the axis of z, of a train of 

 plane waves, the electrical disturbances being parallel to the x axis. 

 (10) reduces to 



<f-P d'P d 



It only remains to express the last term on the right-hand side in 

 terms of P. 



Consider a molecule whose axis, as previously defined, makes an 

 -angle with the axis of ST. For simplicity, suppose both atoms com- 

 prised in the molecule to have equal masses. It has been shown by 

 Mr. Heaviside and Professor J. J. Thomson,* that a charged sphere 

 moving with a velocity small in comparison with the velocity of 



light, has an apparent mass greater than its true mass by , 



3 a 



where q is the charge, and a is the radius of the sphere. When 

 other charged spheres are moving in the neighbourhood, a further 

 correction might be necessary. Let, then, m represent the apparent 

 mass of either atom in the molecule. The differential equation for 

 the rotational displacement of the molecule will be of the form 



Here 7 is the molecular viscosity, the other letters having the 

 same meaning as in 4. 



If 7 is so small that the time of free rotational vibration is not 

 appreciably affected thereby, this equation may be written 



fZ 2 7 (70 , 4?r 2 , 2gP 



-J&+ --- + ^ -- 7 sm0 = 0, 

 dt 2 m at TI ml 



where r^ = 27rv / (Kim) = time occupied by a complete rotational 

 vibration. 



* O. Heaviside, ' Phil. Mag.,' April, 1889 ; ' Electrical Papers,' p. 505 ; J. J. 

 Thomson, ' Recent Researches,' p. 21. 



