PRESIDENT S ADDRESS — SECTION A. 3 



Professor Eddiugton, in his Report on Eelativity to the Physical 

 Society of London, suggests that the correlation between the two scales 

 should he obtained by making and 0' agree in their measures of some 

 natural physical length. Eddington uses the dimensions of the 

 hydrogen atom, but we might take some simpler length, say the wave 

 length of the light from some definite source. I am of opinion that 

 there is a fallacy in this line of argument, due to a failure to dis- 

 discriminate between a relationship and the measure of that relation- 

 ship. Suppose observes the light from a source S in his own system 

 and 0' observes that from a similar source *S' in his. Each will measure 

 a certain relationship between the light and himself, which he calls 

 the wave length of the light. It follows from Einstein's first assumption 

 that each will obtain the same numerical value for the wave length. 

 This conclusion is based on the assumption that each observer has 

 developed his system of physics in the same way and so has a similar 

 system of fundamental units ; but it tells us nothing about the relative 

 scales of the two systems. To complete Eddington's correlation it is 

 necessary to assume that the relationship between the light and 

 observer, as distinct from its measure, is also independent of the motion 

 of the system. 



Another attempt to obtain the correlation is based on the considera- 

 tion of the motion of relative to 0'. If equations A are solved for 

 X, y, z, t, it is found that 



X^: Jc-i^ix' -\-Vt') 



y=k-iy' 



z = k~h' 



B 



From these it is clear that the velocity of relative to 0' is — v. 



The second and third equations of A and B show that a length 

 perpendicular to the direction of motion appears to be changed in the 

 ratio k^- : 1 or k~^ : 1 according. as the observer is moving away with 

 velocity -\-v or ~v. To infer from this that k is equal to unity we must 

 assume that k is independent of v. Otherwise it is possible for k to 

 equal e'" where iv is any odd function of v. 



It appears, then, that the passage from the equations A to the well- 

 known Lorentz transformations involves the assumption k = 1 ot some 

 equivalent assumption. Any one of these assumptions is reasonable 

 and obvious, and can be justified on the ground of making the simplest 

 assumption that will cover the known facts. 



If such an assumption is made the transformation A takes the 

 form 



x' = /3(x — vt) "i 



•", = " l-c 



" ' J 



t' ^ I3{t — vx/c^ 



