emch: theory of compound curves. 105 



tivit}' of one of the pencils with the normal pencil of the other, i. 

 e., consists of two circles which both pass through M and O. 



Kig. :i. 

 The equation of the line V is 



xk ; V — ak — b=;0, 



xk 



V 



ak-t-b 



— =0, 



1 i-^k" 1 I— k2 1 i4-k2 

 and of the v- -axis 



The equations of the inner and outer bi-sector are, thefefore, 

 ;iven by the expressions 



and 



x(k — 1 i+k^)— y — ak — b— o, 



(13) 



