100 



JAMES CLERK MAXWELL. 



[CHAP. iv. 



Let TLO, PXS be the circles : at any point C, BC : CO : : m : n 

 and PC : CA : : m : n. 



For m CA ~ n CB = constant difference, but m OA = constant 

 difference . . m CO = n CB and BC : CO : : m : n. QED. 



And nEP = constant difference . . wiCA = nCP and PC : CA : : m : n. 

 Cor. 1. If the constant difference = the curve is a circle. Cor. 2. 

 If an oval be described with a thread = constant difference, with 

 the same foci and the same powers as the meloid, and any line be 

 drawn from A, and CB, OB, VB be joined, the angle CBO = VBO. 



For BC:CO::m:7i and BV : VO : :m : rc . . BC : CO : : BV : VO 

 . . BC : BV : : CO : VO and CBO = VBO (6.3). 



PROPOSITION 4 THEOREM. 



When the less focus is in the curve, an angle will be formed = that 

 in the Oval (Prop. 4). 



For take an indefinitely small arc DB 

 in the circle, CBD = DBE (3. Cor. 2), 

 and LBT = TBP .-. CBL = EBP. 



Or it may be proved as in the oval. 

 If the greater focus A is at an infinite 

 distance the figure will appear thus : 



PROPOSITION 5 THEOREM. 



If the distance between the greater focus and the point where the 

 axis cuts the meloid, be to the distance between that point and the less 



