MATTER, A MODE OF MOTION 355 



linear terms to Maxwell's equations. While this also makes the electro- 

 magnetic equations more like those of the ether, an important difference 

 still remains. An equation obtained in this way is not necessarily invariant 

 under either a Newtonian or a Lorentz transformation. If, then, the axes 

 with respect to which it is expressed are not to be unique, it must be shown 

 that some transformation exists under which it is invariant. Not only is 

 the form of the equation important here but also the interpretation of the 

 dependent variables. For example, since the complete equations of the 

 ether contain q-V, if the mechanical variables be replaced by the analogous 

 electromagnetic ones, the equations will be Newtonian invariant only if 

 E, which replaces q, is interpreted as a velocity. It is evident, therefore, 

 that the fact that we are dealing with a mechanical model is an important 

 point in the argument. Also, unless the added terms make the effective 

 constants depend on the time as well as the dependent variables, there will 

 be no reflection of the energy in a finite disturbance and the medium will 

 not have the energy trapping property which is essential to the present 

 argument. 



Stationary Wave Patterns 



The first question to be considered is the possibility of setting up a sus- 

 tained wave pattern suitable to represent a particle at rest with respect to 

 the ether. The simplest procedure might seem to be to look for it as a solu- 

 tion of the approximate linear equations in the form of a pair of spherical 

 waves propagating radially, one outward and one inward, so as to form 

 together a standing wave pattern. However, certain difficulties are en- 

 countered. There is nothing in the free linear ether which can serve as 

 boundary conditions to fix the position or size of the pattern. Even if these 

 were determined, there would be nothing to fix the amplitude, and so the 

 energy. Most patterns, particularly those which involve a single frequency, 

 have one or more of the following features. Some of the variables become 

 infinite at the center; the total energy is infinite, energy is propagated away 

 radially. 



These difficulties disappear, however, when we take account of the prop- 

 erties of the ether for disturbances of finite amplitude. Let us suppose that 

 the energy which is to constitute the pattern is supplied by a central gener- 

 ator, the impedance of which is mainly reactive, so that reflected waves 

 which reach it are reflected outward again. Once a standing wave pattern 

 has been established as described above, let the force of the generator be 

 reduced to zero without changing its impedance. The pattern will then 

 persist except for a small and decreasing damping due to the outward radia- 

 tion at its periphery. However, in the region near the center the displace- 

 ments will be very large, and the incoming reflected waves will suffer reflec- 



