Fizeau's Experiment and the ALtlier. 2.17 



is small. Then 



^K'O-.HS)] 



a / 1 A djj\ 

 = - + t>(l 5 ~ — n)> 



on making the permissible assumption that V — c//jl in the 

 coefficient of v. 



Thus the formula is proved. The proof can easily be 

 extended to take in the case of several " virtual " sethers each 

 with its own free period. If the medium is not moving in 

 the direction of the light-wave, v is to be understood as the 

 component of its velocity in that direction. 



§ 3. Any theory which is to explain the phenomena of 

 light must involve two vectors vibrating at right angles 

 to one another in the same way as the electric and magnetic 

 intensities do in the electromagnetic theory, i. e. it must have 

 equations formally the same as the equations of the electro- 

 magnetic theory, and it must also have boundary conditions 

 formally the same as the boundary conditions of the electro- 

 magnetic theory. The two vectors may, for example, re- 

 present displacement and rotation of an aether. There are 

 various theories of this type, e. g. the elastic theory of 

 W. Voigt. The above discussion shows, that if such a system 

 of equations is coupled with a theory of dispersion of the type 

 given by Maxwell or Sellmeier, it will apparently do all that 

 the original theory of Lorentz does for moving media, and 

 more simply than the latter, for it is simpler to suppose par- 

 ticles reacting on an elastic aether than to connect electrons 

 with the light-wave by means of the displacement current. 

 It is a case of phenomena being represented well from two 

 different standpoints, which shows that each has only one 

 aspect of the truth. 



Now Lorentz's original theory explained astronomical 

 aberration and the null effect of the earth's motion through 

 space on all optical experiments to the order v/c, but did not 

 explain the null effect of the earth's motion through space 

 on the Michelson-Morley experiment in the order (v/cjK It 

 is exactly the same with this theory. To explain the 

 Michelson-Morley experiment on the Lorentz theory it is 

 necessary to make the FitzGerald-Lorentz assumption, that 

 the earth contracts in the direction of its motion. But if we 

 assume an elastic aether we have another loophole of escape; 

 we may suppose that the aether is moving with the earth in 

 space, that it is participating in the earth's motion of trans- 



