Of GREATEST ATTRACTION. 207 



Again, from the equation *x (2* — x l ) =z$m 3 , we have 



2 x zz + z* x — 3 x 1 x s= 0, and ? — ™ , and by fubfli- 



.y> '2d X Xj 



tuting this value of J in the former equation, we have 



x 



5f J x z -f- -2 . — = o. 



2 2 Z 



* 



As this equation is homogeneous, if we make - = u, we will 



% 



obtain an equation involving u only, and therefore deter- 

 mining the ratio of z to x, or of AB to AD. Subftitu- 

 ting, accordingly, u z for x in the laft equation, we have 



%t — 5. u z* -f- 3 #3 z * — o and 1 — £ u 4- v »3 = Q . 

 22 22 



This equation is obvioufly divifible by u — 1, and when fo 



divided, gives ^ u -J- * u — 1 = 0, or u 1 4- » = -> whence 

 22 3 



1 +, /i£ 



2 V 12* 



This is the value of -, and as - muft be lefs than unity, 



z z 



becaufe AB is greater than AD, the negative value of ?/, or 



— - — \/— , is excluded; fo that u r= — - -f- V — — '457^1 

 212 212 



nearly .. 



AD 



Now u = -^— - = the cofme of the angle BAD, or half the 



angle of the cone > therefore that angle = 62 °. 46' nearly. 



As 



