2 PRESIDENT S ADDRESS — SECTION A. 



The first of tliese two principles asserts the impossibility of detecting 

 absolute velocity by means of physical experiments ; and finds its 

 justification in the failure of the Michelson-Morley experiment and 

 subsequent experiments undertaken with that object in view. 



The second was enunciated by Fresnel for a system fixed in the aether, 

 and has been generally accepted by physicists since his time. Einstein's 

 generalization is an immediate inference from the application of his 

 first principle to that of Fresnel. 



The principle has recently received strong support from the results 

 of Majorana's experiments on reflection from moving mirrors, and 

 Jeans goes so far as to say that it is now a proved experimental fact. 



To investigate the implications of the two assmiiptions of Einstein,, 

 consider two observers 0, 0' , moving with uniform velocity relatively 

 to one another. Suppose that they coincide at time f = 0, and suppose 

 further that at that instant a light; pulse starts from their common 

 position. At a subsequent time t each observer will imagine that the 

 wave front is the sphere x^ -\- y'^ -\- z^ — cH^ = 0, referred to axes 

 with his own position as origin. It is evident then that the observers' 

 co-ordinate systems are different. 



If follows from Einstein's first principle that the beams of light 

 which appear straight to will also appear straight to 0' . Consequently 

 the relations connecting the co-ordinate system (x', y' , z' , t') adopted 

 by 0' with the system {x, y, z, t) adopted by must be linear in the 

 co-ordinates. 



Under this restriction and the condition that x^ -\- y^ -\- z^ — cH^ = 

 when x'^ + tj'^ + ^'^ — c^t'^ = 0, it is clear that 



k{x^ + ?/^^+ 2- - c'e) = x" + y" + z" - cH'^ 



where ^ is a quantity depending on the transformation, independent 

 of the co-ordinates but not necessarily independent of v. 



If both observers take their x axes in the direction of motion of 0' 

 relative to 0, and if further the y and z axes of one are parallel respec- 

 tively to the y and z axes of the other, it is easy to show that the equations 

 of transformation are 



x' = B^lx — vt) 



y' = ^^y 



z' — k^z 



t' 



H'-7) 



where jS = (1 -v^/c')-^ 



The quantity k indicates the scale of the measurements of 0' in terms 

 of those of 0. It is customary to take this quantity as unity, but it 

 appears that this involves a further assumption. As some presentations 

 of the subject conceal this assumption, it is advisable to discuss it in 

 detail. 



