230 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 3 



meaning can be given to invariance of direction ; this can be accom- 

 plished with the aid of a gyro-compass. I can now repeat my obser- 

 vations as often as I please and as close together as I please, either 

 by using a Morse-code method of signaling or signaling with differ- 

 ently colored lights. I must simply be able to recognize and identify 

 return signals. I can then graph X against T. I can in particular 

 find the slope of this graph at any time T. If this slope happens to 

 be constant, I shall say that the object B is in uniform motion with 

 respect to myself, and call the slope the velocity V, all in terms of 

 my arbitrary clock. The value of V is unaltered by multiplication of 

 the clock readings by an arbitrary factor. 



Suppose B, also provided with a clock, performs similar observa- 

 tions on myself, A. He can send me signals and receive them back ; 

 choosing the same number c, he can assign epochs T' and distances 

 X' to the events which are the arrivals of the signals at myself. He 

 can thus determine my velocity with respect to himself. 



Now suppose that B stands in precisely the same relation to A as 

 A stands in relation to B. Then when A finds B to be moving with 

 a uniform velocity by his clock, there must exist a set of clock 

 graduations for B such that B finds A to be moving with a uniform 

 velocity and, moreover, with the same uniform velocity, for other- 

 wise they would not be equivalent. A and B are then said to possess 

 similar clocks. The possession of similar clocks by the two observers 

 is thus capable of experimental test. 



We are thus able to say what we mean by A and B possessing 

 similar clocks without its being required to bring these clocks side 

 by side. The latter test would indeed violate the conditions of the 

 situation, the essence of which is that the two clocks are in relative 

 motion. If we reduced one clock to relative rest, we should have 

 no means of testing whether we had altered the clock in the process. 

 As it is, we have effected a comparison of the clocks whilst they are 

 in motion: what A finds B is doing by his (A's) clock, is described 

 in the same way by A as what B finds is happening to A (by B's 

 clock) is described by B ; A describes his experience of B in the same 

 way as B describes his experience of A. 



A and B can, however, make one further type of observation. 

 They can read one another's clocks. Or, what is the same thing, B 

 can inform A of the time recorded by his (B's) clock at the epoch 

 of arrival of a signal from A. A can then compare B's reading of 

 B's clock with the reading of his own clock which he has assigned as 

 simultaneous with this event. In ordinary words, A reads B's clock 

 through a telescope, at a certain time by his own clock, corrects this 

 latter time for the time of travel of the signal, and compares his 

 own (corrected) clock reading with his telescopic observation of 



