140 The State of the Medium in the Electrostatic Field [OH. vi 



velocity does not justify us in concluding that it has a real physical existence, for, as we 

 shall see, the potential appears to be propagated in the same way, and the potential can 

 only be regarded as a convenient mathematical fiction. 



155. We accordingly make the tentative hypothesis that all electric 

 action can be referred to the action of an intervening medium, and we have 

 to examine what properties must be ascribed to the medium. If it is found 

 that contradictory properties would have to be ascribed to the medium, then 

 the hypothesis of action through an intervening medium will have to be 

 abandoned. If the properties are found to be consistent, then the hypotheses 

 of action at a distance and action through a medium are still both in the 

 field, but the latter becomes more or less probable just in proportion as the 

 properties of the hypothetical medium seem probable or improbable. 



Later, we shall have to conduct a similar enquiry with respect to the system of forces 

 which two currents of electricity are found to exert on one another. It will then be found 

 that the law of force required for action at a distance is an extremely improbable law, 

 while the properties of a medium required to explain the action appear to be very natural, 

 and therefore, in our sense, probable. 



156. Since electric action takes place even across the most complete 

 vacuum obtainable, we conclude that if this action is transmitted by a 

 medium, this medium must be the ether. Assuming that the action is 

 transmitted by the ether, we must suppose that at any point in the electro- 

 static field there will be an action and reaction between the two parts of the 

 ether at opposite sides of the point. The ether, in other words, is in a state 

 of stress at every point in the electrostatic field. Before discussing the 

 particular system of stresses appropriate to an electrostatic field, we shall 

 investigate the general theory of stresses in a medium at rest. 



General Theory of Stresses in a medium at rest. 



157. Let us take a small area dS in the medium perpendicular to the 

 axis of x. Let us speak of that part of the medium near to dS for which x 

 is greater than its value over dS as x+, and that for which x is less than this 

 value as #_, so that the area dS separates the two regions x + and a?_. 

 Those parts of the medium by which these two regions are occupied exert 

 forces upon one another across dS, and this system of forces is spoken of as 

 the stress across dS. Obviously this stress will consist of an action and 

 reaction, the two being equal and opposite. Also it is clear that the amount 

 of this stress will be proportional to dS. 



Let us assume that the force exerted by x+ on x_ has components 



P^dS, P xy dS, P xz dS, 



then the force exerted by x_ on x + will have components 

 -P^dS, -P xy dS, -P xz dS. 



