of Electrons in an Elastic Solid ^Ether. 149 



Its bodily equation of motion is 



'r)n/A=—S7 2 7} (55) 



An isolated finite portion of the medium tends to shrink to 

 evanescence, but if the medium extend through all space, 

 and n and A be constant everywhere [this means merely 

 that the standard, not the actual density is the same for all 

 points], (55) shows that it will be stable, because it shows 

 that rj will be propagated according to the familiar laws of 

 ordinary wave motion. This linear differential equation, and 

 these deductions therefrom, are in the present case true for 

 finite displacements of any magnitude. 



In surmounting the older statical optical difficulty con- 

 nected with reflexion, the term efy (e, /, g, being now small) 

 in io had appeared as of fundamental significance. 



I had for several years entertained the idea that an elastic 

 solid with two possible states was the medium by which to 

 explain the properties of sether and matter. It occurred to 

 me to unite these contributing items into the one hypothesis 

 that to consisted of three terms, multiples of 



%&, EVQ, efy. 



The results were essentially the same as have already been 

 arrived at by another constitution, and seemed so encouraging 

 that that other constitution was tried, because it involved the 

 simplest (in degree) expression of w as a function of r) and 

 its -pace derivatives. The fact that both constitutions led, 

 for our purposes, to essentially the same result, came as a 

 surprise *, for they by no means agree in general mathe- 



* At the moment of despatching the paper I see why the results of 

 the two hypotheses are for our purposes identical, lu the first we 

 assume, to make progress, Sv? = or e+/-f-/y = 0. Now when this con- 

 dition holds the cubic term (— «+/+#)()( ) of the first hypothesis 

 becomes a multiple of eft/, as in the second hypothesis. This indicates 

 the essential reason, though for a complete account we ought to mention 

 the second order terms also. The case of iv equal to the general sym- 

 metrical rational function of degrees two and three in e+3 ga i/-bi/ ?a > 

 ff+jiff* seems worthy of study. For stationary values other than 

 c\=f l =f/ l =0 we must have two of e v f v , y x equal unless e x +/, +/7i is a 

 factor of the cubic term; if it is a factor there are an infinite number of 

 values for which w is stationary; in the last case iv is a function of the 

 two expressions %c x , 2/v/,, and the infinite number of values belong to 

 5<? a = one constant, '2,f l g l = a second constant. Putting this case aside? 

 and taking the quadratic terms as £§(/! — $\) 2 +c(2|ei) a , assuming c/b 

 large, and therefore ^ small, or say zero, \ve see that this constitution 

 also gives us the same results as the two hypotheses of the text. In a 

 word, those results now from taking the cubic terms into account and 

 assuming the aether almost incompressible, and that one of the stationary 

 values occurs with a small strain ; no more detailed assumption is 

 required. But note that the second hypothesis stands out peculiar in 

 that we do not with it require to postulate approximate incompressibility. 



