L. Page — Fundamental Relations of Electrodynamics. 59 



Let K (o) denote the earth's system at any instant. Then 

 K(w) denotes a system with velocity v relative to the earth. 



Let XYZ be a set of orthogonal right-handed axes fixed in 

 the earth's system, and so oriented that K(v) has a velocity v 

 in the positive z direction. 



Let X'Y'Z' be a set of orthogonal right-handed axes fixed in 

 system I\.(v) and mutually parallel to XYZ. 



Unprimed letters denote quantities as measured in the earth's 

 system, and primed letters denote the same quantities as meas- 

 ured in the system K(v). 



Then the space time transformations between K(o) and K(V) 

 take the form : 



.1 



t — 



V 



c' 



- z 



I 













/'- 



V* 





x' 



= X 







y' 



= y 







?! 



z 



— 



vt 





/' 



— 



v 2 





t' 











_ v 7 



0* 



X 



= x' 





y 



= y' 





z 



z' 



+ vt' 





/! 



V* 



where c denotes the velocity of light, and where the time 

 epochs are so chosen that the times at the respective origins of 

 the two systems are zero when these origins coincide. 



Let a particle have the velocity Y relative to K(o), and V 

 relative to K(V). Let Y x , Y y , V z , be the components of Y, 

 and Y x ', Y y ', Y/ the components of V. Then the following 

 kinematical transformations follow at once by taking the time 

 derivatives of the space time transformations, with consider- 

 ation of the relation 





dt+/i - J£ = 



-- d H /, _ V" 





y; 



/ Y' a 



v,' V ' - — 



-^ /l- 



« 2 



c 2 



v x 



Y, - v 



Y/ = — rr 



bv, 



1 - — 7T- 



z - l+« v .' 



c a 



