92 



JAMES CLERK MAXWELL. 



[CHAP. iv. 



For take any point C. There are m plies of thread between A 

 and C, and n plies between B and C, which taken together make up 

 the thread or the constant quantity, therefore m AC + n BC = EF. 



The focus A, which has the greatest number of plies is called the 

 greater focus, and B is called the less focus. 



PROPOSITION 2 THEOREM. 



The greater focus is always within the oval, but the less is within, 

 on, or without the curve, according as the distance between the foci, 

 multiplied by the power of the greater focus, is less equal or greater 

 than, the constant quantity. 



The greater focus is always within the Oval, for suppose it to be at 

 A, Fig. 1, then m AG + n BC = constant quantity = m AD + ra DC + 

 n BO, and m AD + n DB = constant quantity = m AD + n DC + 

 n BC = ?ft AD + m DC + n BC, and n DC = m DC, and m = w, but 

 m > n. 



The less focus B is within the oval when m AB < EJ? the con- 

 stant quantity. 



EF - mAB 

 For it is evident that BC (Fig. 2) = m + n 



It is in the curve when m AB = EF, this is evident. 



EF - n AB 

 It is without the curve when m AB > EF, for AC = - 



PROPOSITION 3 THEOREM. 



If a circle be described with a focus for a center, and the constant 

 quantity divided by the power of that focus for a radius, the distance 

 of any point of the oval from the other focus is to the distance from 

 the circle as the power of the central focus is to the power of the other. 



The circle EHP is described with the centre B and radius = con- 

 stant quantity, divided by the power of B. At any point C, AC : CH : : 

 power of B : power of A. 



