AND ENVELOPES OF HOMOLOGY. 603 



will envelope the tri-tangent conic 



±G0'± (£)'*(*)'=» • • • ™- 



XXVI. (4.) Required the envelope of afaisceau of circumscribing conies, when 

 the centre of homology moves in a given bi- tangent conic, &V = 0? . 

 Here we have 



f 9 s h s A 1 



— + %• + — = = tt 



" P 7 



and (79). 



f - h?gh = / 



Hence, differentiating, and merging the factor (s — 1) in the indeterminate coeffi- 

 cient, which we may suppress, as it divides out in the final substitution, we have 



/ s - 2 = 2« .... . ( L) 



9 s - 1 = - & 2 A/3 ...... (2') 



h *~ l = -k 2 g 7 . .... (3') 



(20 x (3') (y*)-" = fc^y (40 



< 2 ') - <*> (f J = f (50 



s — 2 . s — 2 



(40 gives W=t'-(fir) 



(60 



(5') x (60 







g 6 = k "'(/3y) S ' x y (7') 



45 5 



5 — 2 /o \ 5—2 



g^ k s - 2 {f$y) 



P 2 ~ ' pY 



4s 2 



Ji 2 



By (10 /l = 2 s - 2 a s - 2 (100 



a 



s 2 2s 1 



By (79), (90, (100 2 s " 2 « ^ = ± 2k °~ 2 ~ (/3y)^ 



* 2 = (jP)fy ■ ' ... (80); 



the required envelope, which is another bi-tangent conic, very neatly related to 

 the former. 



XXVII. Required the locus of the fourth point of intersection of the direct 



VOL XXIV. PART III. g A 



