272 Mr. Gr. H. Livens : Influence of Density on Position 



know from elementary theory, not circuital, and this leads 

 to a distinction between magnetic force and magnetic in- 

 auction. The two are, however, practically the same, 

 except in iron, and we shall not further distinguish between 

 them. 



The quantities involved in these two statements are : 



1. Magnetic force (magnetic induction) H; (H iT , H y , H r ). 



2. Electric force E; (E*, E„ E«). 



3. Total current U; (U*,U y ,U*). 



There are three (vector) quantities and only two relations 



between them. We want one more ! The two relations 

 given are independent of what the body is, and they might 

 be called the fundamental dynamical equations. In addition 

 to these there must be a constitutive relation of some kind 

 connecting the quantities : it will depend essentially on the 

 constitution of the body, and we must discuss this before we 

 can form any idea as to what it is likely to be. 



§ 2. The physical conceptions of the body : constitution oj 

 the atom] introduction of the electron hypothesis. — We imagine 

 a body composed of innumerable molecules or atoms, of 

 "particles," as Lorentz calls them, each molecule containing 

 a certain number of " electrons/' These electrons are now 

 fairly well known elements of electrical and optical theories, 

 and I shall not now enter into any discussion of their properties. 

 As is now generally done in optical work, I shall regard 

 them as "particles" (in an electrical interpretation of the 

 Newtonian word) with a definite electromagnetic mass. 

 This is, as we know, an assumption which is not really 

 justified except in very special cases. It is only a very 

 good approximation to the truth when the dimensions with 

 which we deal are large compared with the dimensions of 

 the nucleus comprising the electron ; and also (and this is 

 very important) when its velocity is small compared with 

 that of radiation. These two assumptions are still very 

 generally made in dealing with optical theories of matter, 

 although some notable authorities disbelieve the justifi- 

 cation of the step made in doing so. A very powerful 

 argument in favour of making these assumptions is, however, 

 that it enables us to go very deeply into the phenomena 

 under discussion. It is not pretended that this is the last 

 word on the subject, and our theory may have to be very 

 considerably modified as our knowledge of facts broadens ; 

 but in the present state of science they are reasonable hypo- 

 theses, besides being the only ones with which we can to 

 any extent work. 



