﻿Approach to the Theory of Relativity. 495 



often led beyond the safe ground of mathematical deduction 

 into the realms of" metaphysical speculation. 



The purpose of this article is to show that the famous 

 " transformation equations " which stand at the centre of 

 the theory can be easily deduced from simple conventions 

 in regard to the setting of clocks and the laying out of 

 coordinate systems, without any conflict with our ordinary 

 conception of the aether, or with our ordinary notions of 

 space and time, thereby freeing the theory from the least 

 appearance of paradox. 



The method pursued is in some sense a return to the point 

 of view of Lorentz *, who retained the concept of the aether 

 as his starting point, and never abandoned our ordinary 

 notions of time and space ; and the " transformation equa- 

 tions ,J here obtained resemble the equations of Lorentz 

 in being slightly more general than those of Einstein. 

 Lorentz's method of deducing these equations, however, 

 involves a large and difficult part of the modern electro- 

 magnetic theory, while the method here adopted depends 

 only on the most elementary considerations. 



The present article is purely expository, and does not 

 attempt any critical or historical discussion f . 



I. System at Rest in the ^Ether. 



1. We assume an aether in which light-waves are propa- 

 gated uniformly in all directions, and we consider first a 

 rigid platform, S, at rest in the aether. 



This platform is supposed to be inhabited by intelligent 

 beings, who are able'to communicate with one another, but 

 are not supposed to be capable of locomotion ; that is, no 

 observer is to leave his own station. Each station is provided 

 with a clock, that is, any mechanical contrivance which 

 "clicks^ at regular intervals. These clocks are not portable, 

 and they must be "regulated" and "set" before they can 

 be used. 



We proceed to define methods by which such beings may 

 regulate and set their clocks, lay out a system of coordinates, 

 and develop the entire theory of analytical geometry and 



* H. A. Lorentz, ' Versucli einer Theorie der elektrischen mid 

 optischen Erscheiuungeii in bewegten Kbrpern,' Leiden, 1895. Neudruck, 

 Leipzig, 1906. Also, " The Theory of Electrons " (Columbia University 

 Lectures, 1906), Leipzig, 1909. 



f For an extensive bibliography of the " Theory of Relativity," the 

 reader is referred to an article by J. Laub, in the Jahrbuch der JRadio- 

 aktiviUit und Elektronik, vol. vii. p. 405, December 1910. 



