4 PRESIDENT S ADDRESS — SECTION A. 



This is the transformation obtained by Larmor and Lorentz in 

 their correlations of moving and stationary electrodynamic systems. 

 It is more general than theirs in this respect : from their standpoint 

 one system was stationary in a stagnant aether ; from the standpoint 

 of the Theory of Relativity no account is taken of absolute motion, 

 and the transformation connects any system with any other moving 

 relatively to it with uniform velocity. 



The transformation C is derived, as we have seen, by purely logical 

 deduction from reasonable assumptions. This fact is a strong justi- 

 fication for adopting it as giving the true correlation between the two 

 systems. Subsequent developments of the older Restricted Theory 

 of Relativity which are based on this transformation strengthen 

 its claim to be so regarded. On the electrodynamic side it is found 

 to include various ad hoc hypotheses, such as the Fitzgerald-Lorentz 

 contraction and the Fresnel convection co-efficient, which have been 

 put forward to explain experimental results in terms of the older 

 electrodynamic theory. On the dynamical side it foretells a variation 

 of mass with velocity, which has been experimentally verified in the 

 Kaufmann experiments. There is thus every reason to accept the 

 Principle of Relativity in its earlier restricted form. Three of the most 

 important implications of the principle are the following :■ — 



(1) Length is not an absolute property of an object but a relation 



between object and observer. 



(2) Measurements of time and space are not independent, but are 



interwoven in a manner depending on the motion of the 

 observer relative to the system observed. 



(3) Mass (inertia) is not an absolute dynamical constant, but 



depends on velocity and cannot be sharply differentiated 

 • from energy. 



The transition from the Restricted Theory to the General Theory 

 of Relativity is effected by means of the work of Minkowski, who showed 

 that the substitutions ti =: tct, jS = cos 6, tv^/c = sin 6 reduced the 

 Einstein transformation to the form : — 



x' = X cos d -{- usin 6 



y' = y 



z' ^ z 



u' = — x&ind -\-u cos 6 J 

 and that consequently the transformation was equivalent to the rotation 

 of the system through an angle 6 in the {x, u) plane of a four-dimensional 

 continuum specified by the rectangular Cartesian co-ordinates 

 {x, y, z, u). 



Minkowski calls this four-dimensional continuum a world, and the 

 point {x, y, z, ?<) a world point. He records the history of any physical 

 entity by plotting its world points corresponding to different instants. 

 The resulting one-dimensional continuum he calls its world line. 



