Poats — Isogonic Transformation, 



49 



we have 



b\^ + 26 Vi tan a + 6 V ta°^ « 



(10) 



Again transforming by means of 



aSj = z sin + X cos ^ 



z^ = z COS ^ — 03 sin ^ 

 equation (10) becomes 



6V 



+ cos2 e 



— 2 tan a sin ^ cos ^ 



4- sin2 d 



+ 2 tan'-* a sin2 (9 



-hay + 5V 



+ sin2 d 



+ 2 tan a sin ^ cos & 



+ cos2 (9 



+ 2 tan2 a cos^ ^ 



+ 2^2 «;;» 



+ sin cos ^ 

 + tan a cos^ ^ 



— tan a sin'^ ^ 



— sin 6 cos ^ 



— 2 tan^ a sin ^ cos 



= a262. 



(11) 



From the coefficient of cc;^ in (11) it is seen that 



2^ = 90° — a 



a 

 6> = 45° - ^ 



and 



A = 



b^ 



1 + sin a 



62 



C = 



1 — sin a 

 Equation (11) now becomes 



_^!^ + aY + -JX— = a262 

 1+ sm a ^ 1 — sm a 



or 



+ ^ + 



a*(l-|-sina) ' 6^ a^^i^gjn^ 



= 1 



(12) 



