1 86 Mr. A. M c Aulay on a Modification 



15. However this be, our ideas would be greatly simplified 

 if Maxwell's ignoratiou of the equilibrium equation could be 

 justified by some suitable modification of the fundamental 

 assumptions. 



Let us now assume that the aether has a material density 

 sufficiently large to render cr' small compared with the velocity 

 of light. This is case II. of § 6 above. In this case Maxwell's 

 ignoration will be justified. 



To fix the ideas let us suppose that a plane-polarized wave 

 with the energy of strong sun-light causes the maximum aether 

 velocity to be b times that of light where b is small, a 1 may then 

 be regarded as a small quantity in equations (15) and (17), so 

 that equations (15) reduce to Maxwell's. 



Since we now suppose the velocity to be small and oscilla- 

 tory, the present and standard positions may be assumed to 

 coincide, and we have 



E vK = Ai cos { 2-7T (z — vt) /a } = Ki cos 6, 

 B.v , fi=Aj cos 0, 



for the w T ave we contemplate. The energy X per unit volume 

 is given by 



\ = - (KE 2 + yuH 2 ) /8?r = A 2 cos 2 0/4tt. 



Hence the average value X of \ is 



^=A78tt=4-225x10- 5 



in ergs per cub. centim., according to the data given in § 793 

 of Maxwell's ' Electricity and Magnetism/ 



The velocity of the aether may be calculated from Maxwell's 

 stress, or written down at once from equation (12) above. 

 For in the present case W, P, and P e are zero, and a-' 2 may 

 be neglected. Thus 



T>a=dYDB/dt= (4*rv)- l k*kd (cos 2 0)/dt 



= v^Xkd (I + cos 26) /dt. 



Since <r is to vary about a mean value 



D(T=v- 1 Xkcos20. 

 Thus 



where <r M is the maximum value of a-. Thus approximately 



6D = 5xlO- 26 . 

 The lower limit obtained by Lord Kelvin for the density of 

 aether (< Math, and Phys. Papers/ ii. 32) is 



D = 10- 22 



approximately. In this case b = 1/2000. There seems then 



