172 L. Page — Relativity and the Ether. 



the emission of strains does not necessarily involve an emission 



of energy. In fact, in the simple case under discussion, it is 



obvious that the energy density at any point in space, if it 



varies with the square of the strain, would remain constant, and 



that the total energy of the iield would be finite. 



In the following mathematical treatment Gibb's vector 



notation will be used. If i, J, k are three unit vectors 



parallel respectively to the XI Z axes, the vector operator 



.9 9 9 



I '*-+!*- +k^ will be denoted by v. PQ denotes the 



9x J 9y 9z 



scalar product of the two vectors P and Q, P X Q the vector 

 product of these two vectors, v • P is the divergence of P, 

 V XP the curl or rotation of P, Q* vP the derivative of P in 

 the direction of Q multiplied by the magnitude of Q, etc. To 

 distinguish vectors from scalars, Gothic type will be used for 

 the former. Thus c is the vector whose magnitude is c. 



Fig. 1 



The Effects of Matter on Ether. 



(a) Effect of a Charged Particle. 



A charge at O (fig. 1) has a velocity V in the direction OQ 

 and an acceleration f (not shown in the figure) in any direction. 

 This charge may represent an electron, if the electron is con- 

 sidered to be a point-charge, or an element of an electron if the 

 electron is supposed to occupy a finite portion of space. In the 

 time dt the charge will have moved to Q. Let r = OA, 

 r, = QD, p - DA, where DA and CB are the bounding elements 



