JAMES CLERK MAXWELL 341 



everywhere in space be given; the equations then allow these 

 forces to be calculated, by means of the rules of mathemat- 

 ics, for all future time; and therefore likewise every conse- 

 quence of the given initial condition according to the laws 

 summarised. We notice the similarity in structure and 

 applicability between Maxwell's equations, and, for example, 

 the fundamental equations of hydrodynamics. The latter 

 also are differential equations, that is they relate also only to 

 volume elements of space and their immediate neighbour- 

 hood, and they allow - as far as the powers of mathematics 

 go - the prediction of the future state of the liquid from 

 its initial state. What, therefore, hydrodynamic equa- 

 tions do for a liquid. Maxwell's equations do for the ether. 

 Both sets of equations only depend upon experience; but 

 while the hydrodynamic equations contain in the main 

 nothing but Galileo's and Newton's laws of motion, the 

 content of Maxwell's equations is, as we have explained, 

 very complex; curiously enough, without their being unduly 

 complicated. This fact, as well as the simplicity of the fun- 

 damental concept of the unity of the ether, already tells in 

 favour of their agreement with reality, that is to say, for the 

 correctness of the added hypothetical matter. It was only 

 the inaccessibility of the ether which, in this case, made it 

 necessary for many separate and partial discoveries to be 

 made, which could then be simply combined; while in the 

 case of liquids, which are more tangible, it was possible 

 immediately to arrive at the final goal. The agreement 

 with reality was proved fifteen years later by Hertz's dis- 

 covery and exact investigation of the hypothetical electric 

 waves. 



It is noteworthy that Maxwell did not arrive at his equa- 

 tions directly by mathematical summarisation, but - starting 

 from Faraday's experimental investigations - by a thorough 

 consideration of possible mechanical ethers, which might give 

 the observed effects which were to be summarised. He later 



