10 DR. J. BOTTOMLEY ON COMPOUND 



the projectrix will be 



J( 





Froni the relation between the coordinates, we may infer 

 that the equation to the projectrix will be of the same 



degree as that of the primitive. Also since -^ vanishes 



when -j~ vanishes, if the primitive has any singularities, 



the projectrix will have some singularity at the corre- 

 sponding points. 



That portion of the primitive area lying below the line 

 ED will on projection be situated below the axis of x. 



The relation between the areas of the primitive curve 

 and its projectrix may readily be obtained by means of 

 equations (3) and (4) : — 



Ar — 



: 1 1 <^»? c?^ or I »; f/^ ; 



by substitution this becomes 



A.x=^ rn{l{x — a) + {y—b)m}dx, 



= m* 1 1 dec dy. 



*J*J h--lx-a) 



(5) 



■ — (x-a) 

 m 



In equation (4) make »7 = o, then we obtain 



{x — a)l -\- {y — l))m-=o. 



This is the equation to the complementary axis, and the 

 limits in (5) show that the integration is to extend from 



