288 Maxwell. 



The memoir of 1864 contained an extension of the equations 

 to the case of bodies in motion ; the consideration of which 

 naturally revives the question as to whether the aether is in 

 any degree carried along with a body which moves through it. 

 Maxwell did not formulate any express doctrine on this subject ; 

 but his custom was to treat matter as if it were merely a 

 modification of the aether, distinguished only by altered 

 values of such constants as the magnetic permeability and 

 the specific inductive capacity ; so that his theory may be 

 said to involve the assumption that matter and aether move 

 together. In deriving the equations which are applicable to 

 moving bodies, he made use of Faraday's principle that the 

 electromotive force induced in a body depends only on the 

 relative motion of the body and the lines of magnetic force, 

 whether one or the other is in motion absolutely. From this 

 principle it may be inferred that the equation which determines 

 the electric force* in terms of the potentials, in the case of a 

 body which is moving with velocity w, is 



E = [w . /zH] - A + grad ^. 



Maxwell thought that the scalar quantity -fy in this equation 

 represented the electrostatic potential; but the researches of 

 other investigators-)- have indicated that it represents the sum 

 of the electrostatic potential and the quantity (A . w). 



The electromagnetic theory of light was moreover extended 

 in this memoir so as to account for the optical properties of 

 crystals. For this purpose Maxwell assumed that in crystals 

 the values of the coefficients of electric and magnetic induction 

 depend on direction, so that the equation 



fjbK = curl A 

 is replaced by 



= curl A ; 



* It may be here remarked that later writers have distinguished between the 

 electric force in a moving body and the electric force in the aether through which 

 the body is moving, and that E in the present equation corresponds to the former 

 of these vectors. 



t Helmholtz, Journ. fiir Math., Ixxviii (1874), p. 309; H. W. Watson, Phil. 

 Mag. (5), xxv (1888), p. 271. 



