﻿508 Prof. E. V. Huntington on a New 



Theorem 7. The transformation equations which give x", y" ', t" at 

 any point of S" in terms of the x', y', t' at the opposite point on S' are 



y"=¥, 





x"=lk(x'—vt'), 





f' = lk(t'-^ 2 x'), 



where 



V=V"-V, 



and 



*$■ 



As was to be expected, these equations are of precisely the same form 

 as those in Theorem 1. 



All these equations are somewhat simplified if the clocks at 0' and 

 0" are so regulated that 



r'= v/l — ( v '/ c ) 2 an d r" = \/l — {y" fc) 2 , 



in which case all the Vs become unity. It is in this simplified form that 

 the equations are given by Einstein. 



We have thus shown that as far as experiments of the 

 first type (§ 20) are concerned, the Principle of Relativity is 

 satisfied by our system S'. 



Experiments with a portable measuring-rod : first physical 

 assumption involved in the Theory of Relativity. 



25. We now suppose that the observers on S' are provided 

 with & portable measuring -rod, with which they can "measure/ 5 

 for example, the adjacent sides A'B' and B'C of one of the 

 townships A'B'C'D' into which the platform S' is divided by 

 its coordinate network ; and ive inquire whether this process 

 of measurement will enable the observers to detect the motion of 

 their platform S' through the cether. (It must be remembered 

 that the coordinate network has been laid out, not by ordinary 

 measurements, but by the method of light- signals explained 

 above.) 



26. Definition. The observed length o£ a rod MN with 

 respect to a platform S' is the distance (§8) between the 

 points M' and N', where M' and N' are the "images " (§ 15) 

 of M and N in S'. The absolute length of the rod is its 

 " observed length " taken with respect to a platform S which 

 is at rest in the sether. 



Now there are two assumptions which we can make in 

 regard to the behaviour o£ the rod when moving through the 

 sether. 



If we assume that the absolute length o£ the rod is the 

 same whether the rod be moving lengthwise or sideways 

 through the sether, then by Theorem 2, a rod which just fits 

 the side A'B' of our " township " would not fit the side B'G" 

 unless the platform were at rest, in the sether, and the 



