AND ENVELOPES OF HOMOLOGY. 607 



XLI. If the centre of homology move in a self-conjugate conic, the faisceau 

 of self-conjugate conies 



/" ' 9" 

 will envelope the circumscribing conic 



3 3 



(98). 



«2 , fp y2 



f + if + h 6 - 



■j 3 3 3 



£ + % + n l= o 



a /3 7 



XLII. If the centre of homology move in a self- conjugate conic, the faisceau 



of self-conjugate conies 



pa 2 + g 6 (3 2 + h 6 7 2 = 



will envelope the tri-tangent conic 



iffaYifm^Ydr (nyX = .... (99). 



XLIII. (4.) Required the envelope of a faisceau of self-conjugate conies when 

 the centre moves in the bi-tangent conic 



k 2 a 2 = /3y. 



Here we have /« 2 + g s P 2 + h s y 2 = = u. 



and f*' - Wgh = 0. 



Differentiating as before, suppressing the factor (s — 1) as merged in the indeter- 

 minate coefficient which is suppressed because it divides out in the final substi- 

 tution, we have 



s — 2 



[1] 



g s-lp2 



V 



- k 2 h 



and 

 and 



[2] x [3] 



Substituting in u 



If s is even 



VOL. XXIV. PART III. 



= - k 2 g 



(ff =-H 



g s l3 2 = h s 7 2 



m^(g 



[2] 

 [3] 



if 



= (Py-2.(/?y) -<| 



2 

 s — 2 



gf/3» = (P)*" 2 . (/3y) 



± as s is even or odd. 

 2/3/ : - the envelope required. 



a 



a 4 



& 5 a 2 



*r-®'.: 



8b 



