WILSON AND LEWIS. — KELATIVITY. 415 



The units of distance and time, namely the centimeter and second, 

 were chosen without reference to each other. Retaining the centi- 

 meter as the unit of distance, we may take as the unit of time one 

 which had been frequently suggested as the rational unit long before 

 the principle of relativity was enunciated, namely, the second di\ided 

 by 3 X 10^*^, or the time required by light in free space to travel one 

 centimeter. The velocity of light then becomes unity. 



Let us consider in our geometry two perpendicular lines, and meas- 

 ure along the (7)-line extension in space, along the (5)-line extension 

 in time. Then any point in the plane will represent a given position 

 at a gi\en time. We are considering the motion of a particle along a 

 specified straight line in space. If x denotes distance along the line 

 from a chosen origin, then in terms of our previous nomenclature, 

 we shall take .r = Xi and / = .r4. The k,- or f-axis, or any line in the 

 a-^-plane parallel to this axis, represents the locus in time of a particle 

 which does not change its position in space, in other words, of a sta- 

 tionary particle. Any straight line of the (5)-class making a non- 

 Euclidean angle 4^ with k4, represents the locus in space and time of a 

 particle moving with a constant velocity 



u = -7~ = tanhvi' 

 at 



A singular line in our plane represents a velocity u = 1, and is the 

 locus of a particle moving with the velocity of light. 



We have seen that in our plane no pair of perpendicular lines is 

 better suited to serve as coordinate 

 axes than any other pair. If then 

 we consider (Figure 14) two (5)-lines, ^^^ 

 marked t and t', and the respectively ^ 



perpendicular (7)-lines, marked x 

 and x', and if we regard the first 

 (5)-Iine as the locus of a stationary 

 particle and the second as the locus ^^'^ 

 of a moving particle, we might ^^ 



expect to find that we could equally Figure 14. 



well regard the second (5)-line as the 



locus of a particle at rest and the first as the locus of a moving particle. 

 And this is, in fact, the first postulate of the principle of relativity. 

 The one relation between the two lines, which is independent of any 

 assumption as to which line is the locus of a stationary point, is 



