AND ENVELOPES OF HOMOLOGY. 



609 



will envelope the circumscribing conic 



*+?£ + 5-=0 (103). 



* p y 



XL VIII. If the centre of homology move in a straight line, the faisceau of tri- 

 tangent conies 



±£±£±£ = o 



/* V h * 

 will envelope the self-conjugate conic 



t + S + S=« (104) ' 



XLIX. In general ; in order that the envelope may be of the form 



Xa + /jbj3' + vy = 



we must evidently have 1 _ 1-2* 



And the jftmcmw 



1 — I t 1 — 21 1 — 2< 



±f 2t ^±9 n fi±h 2t y* = 



gives the envelope 



± l 1 ' 2 ' ■ «' ± m 1-2 ' . j8* ± n 1_2i 7 = 0. . (105). 



L. (2.) Required the envelope of a faisceau of tri-tangent conies when the 

 centre of homology moves in a conic circumscribing the triangle. 



Here, by the same consideration as we have already employed in like cases, 

 the envelope required is got from (101') by reading — s for s, namely, 



fP\ 55=5) ± fnP\ 21^1) ± frP\ Tfr=§ = 



(106). 



Hence, giving s the appropriate values ^ ; f ; f : we find as follows : — 



LI. If the centre of homology move in a circumscribing conic, the faisceau of 

 tri-tangent conies 



± J fa ± JgJ ± Jhy = 

 will envelope the straight line 



± « ± ^ ± 7 =0 (1Q 



LII. If the centre of homology move in a circumscribing conic, the faisceau 

 of tri-tangent conies 



± slf* ± V<pj8 ± Jh?y = 



will envelope the circumscribing conic 



I s m 3 n s n 



