13 DR. J. BOTTOMLEY ON COMPOUND 



parameter. Differentiating with regard to m, we obtain 

 the following equation : — 



{y — ml{w—a)}< iy—(oc — a)j f- =o. 



The condition 



y—ml{oc—a) = o, 



along with equation (6), gives the condition 



the two lines represented by this equation touch all the 

 ellipses generated by varying m. 



The condition 



. . m 

 2y-{x-a)-j-=o, 



gives for m and / the values 



2y 



m = 



1 = 



00— a 



These values introduced into equation (6) give the follow- 

 ing equation : — 



1 6«/* + 8?/" (^ - a) " + (a? - a) * = 1 62/ V, 

 an equation which is resolvable into the two following : — 



(.-0V 



4 ~4 



{y-'i) 



{x—aY _ c^ 

 4 ~ 4 



each of these equations represents an ellipse^ of which the 

 major axis is equal to the diameter of the circle, and the 

 minor axis to the radius ; both ellipses touch the axis of 



