Motion of the Earth and the JEthev. 813 



velocity of the matter resolved along ds. If the aether is in 

 motion, this becomes 



r ds r c ds 



J c/p+(v m -v,)(i-i/p*) + v. 01 jc/r+v m {i-i/p*y+v 9 /p*' 



where v e denotes the velocity of the aether resolved along ds. 

 If we neglect the squares of v m and v e in comparison with c 2 , 

 the change in the time due to the aetherial motion is 



-tf 



\ds. 



If </> denotes the velocity potential of the aether, then 

 r e =—d<f)/ds, 



so that the difference is - 2 \ d<p. Now according to the theory 



described above <p is due to sources and sinks, and so is a 

 single-valued function. Consequently J d<f> has the same value 

 for any path between two points. It follows that the aetherial 

 motion due to the supposed aether doublets can never have 

 any first order optical effect either inside or outside matter. 

 Jt is assumed here that the return streams from the sinks to 

 the sources inside the atoms can be ignored for optical 

 purposes. This seems justifiable since the atoms are very 

 small compared with light-waves. We may imagine that 

 the constitution of the atoms is such that light does not travel 

 along the return streams. 



The influence of the motion of matter relatively to the 

 aether on the velocity of light expressed by FresneFs co- 

 efficient 1 — 1/fM 2 is to be explained on the present theory in 

 in the usual way, that is by the presence of systems in the 

 atoms having definite periods of free vibration, which also 

 serve to explain refraction and dispersion. 



It is of course possible that only certain substances have 

 a high aetherial permeability; but .in order to explain the 

 negative results of the second order experiments like Michelson 

 and Morley's it is necessary to suppose that the bulk of the 

 earth is composed of such substances, or else that the aetherial 

 stream was screened off by surrounding buildings. If all 

 substances have a high permeability, it will probably be very 

 difficult to detect aetherial motion, even by experiments 

 capable of detecting second order effects, because of such 



screening actions. 



Although it has been shown that the supposed aetherial 

 motion can only produce second order optical effects, it is 

 perhaps worth while to show specially that the irrotational 



