16 

 where 



BELL SYSTEM TECHNICAL JOURNAL 



I COS IJ\ sin JJ\ 0^ 

 y = I — sin Z7i cos IJ\ 

 V L 



or 



1 Q 6 



cos 1^2 sin Vi 

 ^0 — sin Vi cos [72/ 



cos £/i sin Vz 



cos ?73 sin Vz 0^ 

 — sin Z73 cos Vz 

 1; 



cos V\ cos C/3 



sin Vx cos ^2 sin t/3 +sin V\ cos 1/2 cos Vz 



sin f/i sin t/2 



— sin l]\ cos C/3 —sin V\ sin f/3 cos t/i sin Vi 



— cos t/i cos Vi sin ^73 +cos t/i cos V^ cos Z/a 



sin JJ-i sin 1/3 



— sin Z72 cos Vz 



cos Z72 



(5.9) 



P2^. ^ ^- 



P2-« 



P,-* 



Fig. 37 Fig. 38 



Fig. 37 — The (0, 0, 0) position of a shop system of direction angles. 

 Fig. 3i8 — The second position of a shop system. 



From (5.8) we see that P = rx and hence, if this is to be the same plate 

 the designer specified by P = Rx we must have R — r whence we may 

 equate the terms of (5.6) and (5.9) to get the relations 



