240 ftEPoftfs o& The state op science. 



All we can say therefore is : if we had a complete scheme of equations for 

 a theory embracing moving electrons, and if this completed scheme were 

 invariant under the above transformations, then in the domain of phe- 

 nomena included in this scheme it would be impossible to say that (x y zt) 

 rather than (&' y' z' t') were true space-time co-ordinates. 



Supposing the indicated gaps in the chain of argument to be filled, it 

 follows that the co-ordinates winch we should use in anv given case de- 

 pend upon what velocity we choose to assign to any given moving point 

 at any instant, just as they do in Newtonian dynamics. Thus, the length 

 of a given material body as far as our description of optical phenomena 

 ?.re concerned will depend upon what velocity we assign to the body. 

 This is the theory of the FitzGerald-Lorentz contraction hypothesis. 

 The measure of the time between two events at the same point will like- 

 wise be dependent upon the velocity which is assigned to the point. Thus, 

 apart from the ordinary first order Doppler effect owing to the motion 

 of a source of light in the line of sight, there is a second order change, 

 which should be apparent even for bodies moving entirely at right angles 

 to the line of sight. Laub has suggested that this transverse effect 

 might be apparent in the Kanalstrahlen, but the experiment has not yet 

 been carried out. 



5. 



Let us now turn to another aspect of the principle. Let us assume 

 that experimental evidence is sufficiently strong to warrant our using it 

 as a general working hypothesis — that is, we make it a test of the validity 

 of any theory that no phenomena shall enable us to determine uniquely the 

 velocity of a point relative to the so-called aether. We have already seen 

 that the Lorentz fundamental equations satisfy this requirement. 



The question arises as to the electrodynamic equations of ponderable 

 matter in motion. The late Hermann Minkowski, in an already classical 

 paper 4 which has done perhaps more than any other work to make clear 

 the position above outlined, sought to find equations satisfying the same 

 criterion and reducing for matter at rest to the commonly agreed upon 

 equations of the Maxwell-Hertz theory. He obtained differential equations 

 which differ only in notation from those of Lorentz. Translated into the 

 notation of Lorentz the polarisation and magnetisation of bodies must be 

 subject to the following transformations, not quite similar in form to 

 those for E and B, 



P.y = ?>,> P Y = p (p„ + rm./c), P =ft{f t —vm t lc), 

 M. v = m : „ M y = ro„//3, M z = mji], ^ v) 



and in addition we must have these equations for current and density 

 R = /?(p — vjjc), J x = jjfi, J Y = j v , J z = h- • (v) 

 Minkowski cmplovs no theory as to the constitutive nature of P, M, J, R. 

 If now we assume any equations we please connecting E, B, P, M, J, R for 

 a body at rest as characteristic of the matter in question, these may by 

 means of (ii), (iv), and (v) be translated into equations connecting c, b, 

 f, in, j, p. These relations according to the theory of relativity are the 

 constitutive equations for moving bodies. 



The P, M transformations have been obtained without any view to 

 electron or anv other theory ; but if the Lorentz theory is mathematically 



* Oott. Nachr., 1908, pp. 1-59. 



