652 SCIENCE PROGRESS 



THE GENERAL THEORY OF RELATIVITY AND EINSTEIN'S 

 THEORY OP GRAVITATION (G. W. de Tunzelman, B.Sc.) 



THE amount of the Fitzgerald- Lorentz contraction, dealt with in my preliminary 

 article, is defined by the condition Zo = L v v\ — # 2 , where Zo is a length measured 

 in a body at rest in the ether, Lv the contracted length of Zo when the body moves 

 with a uniform velocity v in the direction in which the length is measured, c is the 

 velocity of light relative to the ether, and |3 is written for the ratio vjc. For v=c, 

 L v = o, so that the body will be spread out into a flat sheet of vanishing thickness 

 in a plane transverse to the direction of motion ; therefore no material substance 

 can actually attain a velocity as great as c. This agrees with observations on 

 electrons moving at velocities up to about 96 per cent, of c, the inertia of which 

 increases at a rapidly increasing rate as v approaches c, and with electrical 

 theory, which makes the inertia infinite for v — c. Now Maxwell's electromagnetic 

 equations for stationary media, which are in complete agreement with observation, 

 are the basis of accepted electrical theory. Lorentz, therefore, taking these 

 equations, expressed in terms of the rectangular space coordinates x,y, z, relative 

 to axes fixed in the ether, and of the time /, sought for a transformation which 

 should reproduce them, unchanged in form, in terms of new coordinates moving 

 uniformly through the ether. He succeeded with respect to the equations for the 

 free ether, but with a slight deviation in the presence of electric charges. Taking 

 the jr-axis as the line of motion, the new coordinates x', y\ z', t' were determined 

 by the equations 



x' = y{x-vt\ y'=y, z' = z, t'=y(\-vxjc*), 



where y= i/v 1 -/3 2 . The time /' is here introduced as a mere auxiliary mathe- 

 matical quantity bearing as yet no physical meaning. 



This was presently assigned by Einstein, who pointed out that our observations 

 can determine only coincidences, i.e. simultaneities in time and space of material 

 particles with each other and with light rays. On a material system S, such as 

 the earth, the simultaneity of coincidences observed at different stations could be 

 determined if all observing stations were supplied with synchronous clocks. 

 Assuming the principle of constant light velocity, clocks at stations A and B were 

 defined by Einstein as synchronous only if, when a light flash at A at the time t± 

 by the A clock reached B at the time /a by the B clock, and was instantly reflected 

 back to A, reaching it at the time t 'a by the A clock, the relation t'j,-tB = tB-tA, 

 or £s = (V.4 + //)/ 2 holds good. Thus a universal time /, say *S"-time, can be 

 established for all S observers. Similarly, an 5'-time, /', may be supposed 

 established on a system S' in uniform rectilinear motion relatively to S. 



Then, always assuming the principle of constant light velocity, c, Einstein 

 enunciates as the General Principle of Relativity : The laws according to which 

 the states of physical systems are changing are the same, whether these phenomena 

 are referred to the system S or to any other system moving uniformly with respect 

 to it. Since such laws are the results of observations of coincidences only, the 

 condition that laws expressed in terms of 5-time and 5"-space coordinates should 

 be similarly expressed in terms of .S"-time and S' space coordinates, will be that 

 events locally simultaneous for S' observers should also be simultaneous for 

 5 observers. Einstein then found that this condition would be fulfilled if x',/, 

 *', /', the 5'-coordinates and S'-time, were derived from the ^-coordinates and 

 5*-time by the Lorentz transformation. Further, the transformation from 5 to S' 

 differs from that from S' to 5 only in that v, the velocity of S' relative to S, is 



