WEBSTER. — PROPERTIES OF THE ETHER. 523 



tions exactly at tlie times /i ami t,, wluTca.s, in equation (i J j tliey must 



+ - 



be such as to f,nvc the actual vectors E and E. Hence, from analogy, 

 we may say that these vectors are pr()l)ahly suiiicient to specify the 

 configuration of the ether completely. 



And if this last statement is true, their time derivatives must be 



+ - 



sufficient to specify completely, not only the (juantities P and P, but 



all the motions of the ether; and it seems probable that the.se motions 



-i- - + ^- - - 



at any point are speciiied by the values of E, E, p P, and p P at that 



+ - 



point, and not by the values of the vectors H and H, which depend on 



the values of the other vectors at distant points. This hypothesis 



is further strengthened by the fact that the whole theory of the ether 



+ 

 might be developed without any use of these vectors, replacing H 



where\er it occurs by 



-^ VxPot (E + p p), and H by — VxPot (E + p P), 



and therefore without any use of equations (3) and (4), except as 

 they express the indestructibility of the charges. 



Therefore we may consider equations (3) and (4) as merely equations 

 of continuity and partial definitions of two convenient mathematical 

 functions fully defined by equations (3) and (4) and (11) all together, 

 and whose values at any point depend on the motions of the ether at 

 all points, but not in any way on the motions or configurations at the 

 point in cjuestion only. And thus, although they contain time deri\a- 

 tives and quantities dependent entirely on motion and existing only 

 when there is motion, they tell us nothing al)out what is going to 

 happen at some future time from what is happening now, and there- 

 fore cannot be considered as laws of motion, but only as mathematical 

 definitions of convenient functions. 



Equation (11), however, in form and substance, is essentially an 

 equation of motion, from which no information about the geometrical 

 configurations of the ether can be derived at any time, unless the 

 configuration and motion at some other time, or the configurations at 

 two other times, are specified; but without which no information 

 about the configuration or motion at any time can be derived even 

 if they ar(> gi\'en at any number of other times. 



Properties of the Ether. — The first question that arises about 

 the properties of the ether is, Is its structure continuous or granular? 



