610 REV. HUGH MARTIN ON CENTRES, FAISCEAUX, 



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

 of tri-tangent conies 



will envelope the self-conjugate conic 



a 2 B 2 v 2 



73 + ^T + ^ = ° (109). 



LIV. (3.) Required the envelope of a faisceau of tri-tangent conies when the 

 centre of homology moves also in a given tri-tangent conic, say, 



± la- ± ni(3- ± Wy* = 0. 



Here we have ± /»o# ± g^p ± fry = ° ) 



and Z_ m n _ ft > ( no > 



p r h> ) 



Now, /% g h , h h are involved in equations (110) precisely as/, #, h are involved 

 in equations (101), provided in equations 101 we substitute 2s for s. Making, 

 therefore, this substitution in (101'), we have the envelope now required, namely, 



± (!*„)»«•+» -j- ( W 4»/S)2(2» + D ± ( n 4f y )«» + l) _ o . . . (HI). 



Hence, giving 5 the appropriate values, ■— £ ; — f ; — f : we find as follows : — 



LV. If the centre of homology move in a tri-tangent conic, the faisceau of tri- 

 tangent conies 



will envelope the straight line 



± " ± ^-± 7 = (112). 



I m n 



LVI. If the centre of homology move in a tri-tangent conic, the faisceau of 

 tri-tangent conies 



will envelope the circumscribing conic 



P 7 



± >r ± %. ± ■?. = o (H3). 



LVII. If the centre of homology move in a tri-tangent conic, the faisceau of 

 tri-tangent conies 



