236 REPORTS ON THE STATE OF SCIENCE. 



The Principle of Relativity. By E. Cunningham. 



[Ordered by the General Committee to be printed in extenso.] 



Bibliographical Note. 



The memoirs bearing most directly on the lines of thought developed in this paper 

 are as follows :— 



(1) Einstein : ' Zur Elektrodynamik der bewegten Korpern,' Ann. d. Phy*., 17 



1905. 



(2) Minkowski : ' Die Grundgleichungen fiir die elektrbmagnetische Vorgange in 



bewegten Korpern,' Qiitt. Nachr., 1908, and Math. Ann., 68, 1910; ' Raum 

 und Zeit.,' Phyz. Zeitschr., 10, 1909. 



(3) Planck: 'Zur Elektrodynamik bewegter Systeme,' Ann. d. Phys., 26, 1908. 



(4) Einstein : ' Uber das Relativitatsprinzip und die aus demselben gezogenen 



Folgerungen,' Jahrb. d. Rod. v. Elektr., 4, 1907. 



(5) Born : ' Die Ableitung der Grundgleichungen fiir die elektrom. Vorgange in 



bewegten Korpern,' Math. Ann., 68, 1910. 



(6) Cunningham : ' The Principle of Relativity,' Proc. Lond. Math. Soc, 8, 1910 ; 



' The Application of the Principle of Relativity in Electron Theory,' Proc. 

 Lond. Math. Soc, 9, 1911. 



The experimental side of the subject is very fully discussed by Laub — ' Uber die 

 experimentellen Grundlagen des Relativitatsprinzip ' in the Jahrb. d. Pad. u. Elektr., 

 7, 1910, where a complete bibliography of the whole subject is given. 



The principle of relativity carried to its furthest extent would declare 

 that the phenomena of physical science do not lead us to any knowledge 

 of a permanent and unique frame of reference relative to which the 

 motions of bodies may be determined. The principle is intimately bound 

 up with the theory of the electromagnetic constitution of matter, but 

 there was, in a sense, a principle of relativity before the days of Lorentz, 

 of Maxwell, or even of Faraday. Newton, when he enunciated his laws of 

 motion, postulated an absolute frame of reference for the. position of a 

 point. A priori there seems to be small ground for such a postulate, but 

 the hypotheses of natural science have all to be justified a posteriori, and 

 it does appear true that it is possible to choose such a frame of reference 

 for the motion of material systems, that Newton's laws accurately describe 

 the changes in the motion from time to time. But inasmuch as those laws 

 involve not the velocities but the accelerations of the various elements of 

 the system, it appears that the frame of reference so defined is not 

 unique, but that any one of an infinite number of such frames, each of 

 which has relative to any other a uniform velocity of translation, will 

 equally satisfy the requirements ; and among this infinite number there 

 is no particular one which has an advantage over the rest in giving any 

 additional simplicity to the general laws of motion. The frame of refer- 

 ence may be, however, fixed once for all by assigning to any one point at 

 any one instant an arbitrary velocity ; but the arbitrariness thus allowed 

 to the velocity of any one point of the system does not apply to the 

 angular velocity of any part of the system. In the light of Newtonian 

 dynamics this vector has a unique value at each instant. 



