114 PHYSICS OF ETHER 



tion, merely suggests a compensation to meet an apparent residual 

 effect, and would be of no significance if it were impossible to incor- 

 porate such a condition into a consistent theory of ethereal action. 

 This has been done by Lorentz and by Larmor in their theories of 

 moving systems. Lorentz, who was the first to develop a satisfactory 

 theory of a quiescent ether, assumes that, in all electrical and optical 

 phenomena taking place in ponderable matter, we have to deal with 

 charged particles, free to move in conductors, but confined in dielec- 

 trics to definite positions of equilibrium. These particles are perfectly 

 permeable to the ether, so that they can move while the ether remains 

 at rest. 



If now we apply the ordinary electromagnetic equations of a system 

 of bodies at rest to a system having a constant velocity of transla- 

 tion in addition to the velocities of its elements, the ether remaining 

 at rest, the displacements of the electrons arising from the electric 

 vibrations in the ether and the electric and magnetic forces are the 

 same functions of the new system of parameters as for the case of 

 rest, if we neglect quantities of the second order of the aberration. 

 This theorem assumes that the distance of molecular action is con- 

 fined to such excessively small distances that the difference in their 

 local times would have no effect. An exception to this may be found 

 in a rotary substance like quartz which, as mentioned above, has 

 been examined by Mascart and Rayleigh to the first order with 

 negative results, which seems to warrant the conclusion that the 

 molecular forces are themselves altered by translation. This theory 

 of Lorentz seems capable, then, of explaining the uniformly negative 

 results of all the first order tests which have been described previously, 

 without, however, necessarily establishing it finally, since we have 

 not yet studied its adaptability to second and higher orders of the 

 aberration. 



The suggestion of a contraction, as stated above, lends itself in 

 a similar manner and under like restrictions to that for the first order 

 transformation. This requires the introduction of a second coefficient 

 differing from unity by a quantity of the second order as did the 

 coefficient used in the first transformation, but differing from the 

 latter in that it is left indeterminate from the fact that there are no 

 means as yet for giving it a definite value. Introducing these new 

 parameters we again obtain a set of equations in which the velocity 

 of translation does not explicitly appear. Such a moving system 

 has therefore its correlate in a system at rest, the former having 

 changed into the latter through the assumed contraction the moment 

 motion begins. The occurrence of these coefficients as factors in the 

 electric forces and the accelerations arising from the electric vibra- 

 tions in the ether in the expression for the corresponding system at 

 rest, necessitates that if the degree of similarity required is to exist 



