128 Woolard — Generalised Relativity and Gravitation. 



aether, it is aeoessary to postulate that a body, when set 

 in motion, automatically contracts in the direction of 



i 



motion in the ratio 1 : (1 j I ; this masks all effects of 



relative motion. From this, the transformation equa- 

 tions connecting the coordinates of two systems moving- 

 relative to one another can be deduced, and they are the 

 same as (2) ; this transformation should replace (1) ; 

 the physical phenomena really being the same in the two 

 systems, our mathematical equations for the operations 

 of nature should be invariant for the Lorentz-trans- 

 formation, as (2) is called. 5 Lorentz showed that the 

 above contraction would take place if the intermolecular 

 forces were of electrical origin ; such considerations gave 

 rise to the electron theory of matter of to-day, before 

 electrons themselves were dissembled and experimented 

 upon. 6 



The Newtonian equations are not invariant for the 

 Lorentz-transformation, and a new system of dynamics 

 and mechanics was built up. 



II. ' ' Generalized ' ' Relativity. 



5. Evidently, the Principle of Relativity in its purest 

 and most general form w x ould be: The mathematical 

 equations expressing the laws of nature must be inva- 

 riant for all arbitrary transformations of coordinates. 7 

 The new theory of general relativity satisfies this postu- 

 late. In this new theory, gravitation plays an important 

 part. Gravitation is certainly different from everything 

 else because of its absolute independence of distance, 

 physical and chemical conditions, etc. Furthermore, all 

 bodies fall with the same acceleration, and all inertial 

 masses are gravitating masses. From these facts, Albert 

 Einstein deduced his "Equivalence-Hypothesis": 8 



6. ''Consider an observer situated in a closed lift, 

 observer and lift being free from the attraction of gravi- 

 tating matter. If the lift were in uniform motion there 



5 Campbell, Modern Electrical Theory, 2d erl., pp. 357-9, 376-7, 1913. Cun- 

 ningham, Relativity and the Electron Theory, pp. 21-2, 31-34. Carmichael, 

 Theory of Relativity, pp. 44-48. 



6 Bumstead, Science, N. S. 47, pp. 57-58, 1918. 

 'Fokker, Phil. Mag. (6), 29, art. 10, sec, 16, 1915. 



8 Einstein, Annalen der Physik, 35, pp. 898 et seq., 1911. 



