39° Leigh Page, 



where v^ is the component of v perpendicular to rfr^ Giving dr-^^ 

 the vakies d.%\, dy^ and dz^, and choosing axes in S' parallel 

 respectively to those in S, it follows that 



9x' _ C'dt^ 



9y__C'9j^J _v^ 

 9y " C 9t^ ^ C" 

 9s^_C9^ V _ v' 

 '9z ~ C 9t ^ ^ a' 



all the remaining partial derivatives with respect to x, y and z 



vanishing. Moreover 



9x' 9x' 



Therefore the space intervals dx' , dy' and dz' between two 

 points as measured in 6"', are given in terms of space and time 

 intervals in 5" by the expressions 



, , C 9t' ./ v' , . . 



C 9t' v^ 



Hence, from (5), (6), (7) and (8) 



,r'^-C-^ ^r= [(§' ^Q« (.-^)] i^r^-a ./n, (9) 



and conversely 



„■' - c- ,//■'= [(^^; ID' (.-;;.:)] (,r"-c' ,.■% (.c) 



where 



z/ _ / ldx\ 

 'C'~ C\di']x 



_ '^' 

 ~ ~ C 



