<)08 REV. HUGH MARTIN ON CENTRES, FAISCEAUX, 



XLIV. It is evident that if the centre move in this last bi-tangent, the 

 envelope will be 



'1 £_+_? 



JPa 2 = 2 2 jSy. 



If, again, in this, the envelope will be 



»« ** + 2s + 4 



&V = 2 4 £7. 



And so on en suite; the law being obvious, namely, that the t h envelope will be 



( — 1 t—i ( — 3 (—4 



> +2» + 4s + 8s + &c.~ 



k 2 ' \ 2 = (2 . J/3 7 (100). 



or k —- - . « 2 = jS 7 (100'). 



1 (si) 



—a somewhat curious result. 



Section IV. — T/iC Faisceau of Homology being Tri-tangent Conies. 



XLV. (1.) Required the envelope of a. faisceau of tri-tangent conies when the 

 centre of homology moves in a straight line. 

 Here we have 



±/« . a* ± g«/3j ± fc'7 4 = 



and ' + - + - =o^ ' • • (101) ' 



/ g * 



and the envelope, found as before, is 



±(^.«) 2& + 1) ±(m*./S) 8 * + 1) ±(n 2 »7) 8(,+1) = . . . (101'). 



Hence, giving to s the appropriate values, namely, — %; — f ; — f : we find as 

 follows : — 



XLVL If the centre of homology move in a straight line, the faisceau of 

 tri-tangent conies 



will envelope the straight line 



±7±-±? = . . . . (102). 

 I m n v ' 



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

 tangent conies 



± /- ± /?4- /F- 



