Poats — Isogonio Transformation. 



49 



we have 



b 2 x 2 + 2b 2 x 1 z 1 tan a + b 2 z 2 tan 2 a 



+ b 2 z 2 sec 2 a + a 2 y 2 = a 2 6 2 . 



Again transforming by means of 



cCj = z sin + x cos 



& => y 



z 1 — z cos — x sin # 



(10) 



equation (10) becomes 



b 2 x 2 



+ cos 2 



— 2 tan a sin cos 



+ sin 2 



+ 2 tan 2 a sin 2 



+ a 2 ?/ 2 4- b 2 z 2 



+ sin 2 



+ 2 tan a sin cos 



+ cos 2 



+ 2 tan 2 a cos 2 



+ 26 2 #2 



4- sin cos 

 + tan a cos 2 



— tan a sin 2 



— sin cos 



— 2 tan 2 a sin cos 



= a 2 6 2 . 



(11) 



From the coefficient of xz in ( 11) it is seen that 



and 



1 — sin a 

 Equation (11) now becomes 



b x 2 b 2 z 2 



=— : : h d 2 V 2 4" z, : = Cl 2 b 2 



1 4- sin a J 1 — sin a 



or 



x l 



+ y - + 



1.2 I 



a 2 ( 1 4- sin a ) b 2 a 2 (1 — sin a 



= 1 



(12) 



