﻿748 Prof. Hackett on Relativity- Contraction in a Rotating 

 We have 



z'=qZ. 



The co-ordinates y, z and axes Y, Z introduced here have 

 no reference to the co-ordinates and axes used to deduce 

 equations (6), (7), (8). 



Returning to 97, f axes, we have 



7}' = y' cos 8 — z' sin 8, 



f'= ?/' sin 8 -f^'cos S, 



Y = 7j cos a + f sin a, 



Z = — 77 sin a-f f COS a, 

 which give 



7]' — r/(p cos a cos 8 + 9 sin a sin S) 



+ £(jt? sin a cos 8 — ^ cos a sin 8), 



J ' = 7) (p cos a sin 8 — 5 sin a. cos S) 



-f f (p sin a sin S + q cos a cos 8). 



Comparing with (9) and (10), we get 



e - p cos a cos 8 +■ q sin a sin 8, . . . (13) 



5 = jt9 sin a cos 8 — q cos a sin 8, . . . (14) 



f = p sin a sin 8-\-q cos a cos 8,. . . . (15) 



= p cos a sin S — ^ sin a cos S. . . . (16) 



We get from (14), (15) 



/sin 8 + s cos 8 = p sin a, 



/ cos 8 — s sin S = 9 cos a, 



p = (f+scotS)^, .... (17) 

 r yj y sina 



giving 



from (16) 



S = (/- S tan8)^- 8 ; .... (18) 

 2 w y cos a 



^_tana qqx 



<7 tan 8 " 



