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114 merely suggests a compensation to meet an apparent residual effect, and would be of no significance if it were impossible to incorporate 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 dielectrics 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 translation 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 confined 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 vibrations in the ether in the expression for the corresponding system at rest, necessitates that if the degree of similarity required is to exist