CHAPTER XVI. 



DYNAMICAL THEORY OF CURRENTS. 

 GENERAL THEORY OF DYNAMICAL SYSTEMS. 



541. WE have so far developed the theory of electromagnetism by 

 starting from a number of simple data which are furnished or confirmed by 

 experiment, and examining the mathematical and physical consequences 

 which can be deduced from these data. 



There are always two directions in which it is possible for a theoretical 

 science to proceed. It is possible to start from the simple experimental data 

 and from these to deduce the theory of more complex phenomena. And it 

 may also be possible to start from the experimental data and to analyse these 

 into something still more simple and fundamental. We may, in fact, either 

 advance from simple phenomena to complex, or we may pass backwards from 

 simple phenomena to phenomena which are still simpler, in the sense of 

 being more fundamental. 



As an example of a theoretical science of which the development is almost 

 entirely of the second kind may be mentioned the Dynamical Theory of 

 Gases. The theory starts with certain simple experimental data, such as 

 the existence of pressure in a gas, and the relation of this pressure to the 

 temperature and density of a gas. And the theory is developed by shewing 

 that these phenomena may be regarded as consequences of still more funda- 

 mental phenomena, namely the motion of the molecules of the gas. 



In our development of electromagnetic theory there has so far been but 

 little progress in this second direction. It is true that we have seen that the 

 phenomena from which we started such as the attractions and repulsions 

 of electric charges, or the induction of electric currents may be interpreted 

 as the consequences of other and more fundamental phenomena taking place 

 in the ether by which the material systems are surrounded. We have even 

 obtained formulae for the stresses and the energy in the ether. But it has 

 not been possible to proceed any further and to explain the existence of these 

 stresses and energy in terms of the ultimate mechanism of the ether. 



