354 BELL SYSTEM TECHNICAL JOURNAL 



function of the magnitude of the disturbance and of the curvature of the 

 wave-front, the attenuation constant approaches zero as r increases in- 

 definitely. 



Whether or not the total energy stored in the wave pattern will approach 

 a finite or infinite value depends on how fast the attenuation decreases with 

 distance, and a more complete solution is needed to give an exact answer. 

 If it does approach infinity it will do so much more slowly than for a medium 

 which does not reflect. 



The disagreement between classical electromagnetics and mechanics, re- 

 ferred to above, may now be stated more explicitly. The former says that 

 electromagnetic waves are represented exactly by Maxwell's equations, 

 regardless of the magnitudes of the electromagnetic variables. When these 

 waves are interpreted as existing in a mechanical ether, classical mechanics 

 says that Maxwell's relationship is approached as a limit as the mganitudes 

 approach zero. Waves of finite amplitude are to be represented by the more 

 complicated relations. 



The two systems differ in three important respects; their relation to 

 uniform linear motion, the linearity of their equations and the nature of 

 the elasticity involved. Because the classical electromagnetic equations are 

 not invariant under a Newtonian transformation, the set of axes to which 

 the equations refer are uniquely related to other sets which are moving 

 uniformly with respect to them. In special relativity, this condition is 

 avoided by modifying the classical concepts of space and time to conform 

 to the fact that the equations are invariant under the Lorentz transforma- 

 tion. The Newtonian invariance of the ether equations, however, insures 

 that a set of axes at rest with respect to the undisturbed ether is not unique. 

 Hence in the modified model, in which Ihe motions which constitule matter 

 conform to the laws of the ether, a uniform linear velocity of the entire 

 system cannot be detected. This is consistent with the accepted principle 

 that absolute velocity is meaningless. 



We are, however, still faced with the question of the detection of uniform 

 motion of matter relative to the ether. This is discussed at length below, 

 where it is shown that the properties of the ether lead directly to an auxili- 

 ary space-time, which applies very closely under the experimental condi- 

 tions and accounts for the failure to detect the motion. This "experimental" 

 space-time is formally identical with that of special relativity. Thus the 

 modification of the space-time of classical electromagnetics which appears in 

 special relativity might be said to bring it into closer formal agreement 

 with the classical mechanics of ether wave patterns. At any rate the es- 

 tablishing of this theoretical connection between the space-time of special 

 relativity and a classical mechanical model is a step toward unification. 



On the matter of linearity, proposals have been made to add arbitrary non- 



