602 EEV. HUGH MARTIN ON CENTRES, FAISCEAUX, 



will envelope the self- conjugate conic 



ZV + m 3 /3' + n 3 / 3 = .... (73). 



XXL Cor. From the preceding we see, that since the inverse centre of homo- 

 logy describes a circumscribing conic, when the direct centre describes a straight 

 line, and vice versa, it follows that the direct and inverse faisceaux of circum- 

 scribing conies have the same envelope. Compare (66) and (71) ; (67) and (72) ; 

 (68) and (73). 



XXII. (3.) Required the envelope of & faisceau of circumscribing conies, when 

 the centre of homology moves in a given self-conjugate conic. 



In this case, instead of (64), we have 



f + f + W = ° (74 > 



If, therefore, instead of/, g, h, we take as variables their squares, and consider i 

 as having half its former value, our new variables will again be involved precisely 

 as in (62) and (64), and (65) will represent the envelope we now seek, provided 

 for s we read ^s, which gives 



ill 



(ir+(?r + (?r=° ^ 



Hence giving s the appropriate values, — 4 ; — 3 ; — 6 : we have as follows : — 



XXIII. If the centre of homology move in the self-conjugate conic, 



W + mj3 2 + ny* = , 



the faisceau of circumscribing conies 



J~a + <PJS + Vy = ° 



will envelope the straight line 



Pa. + m 2 /3 + n'- 7 = (76). 



XXIV. If the centre of homology move in the same self-conjugate conic, the 

 faisceau of circumscribing conies 



_L A _! 



f a + g*P + AV> 7 ~ 

 will envelope another self-conjugate conic, namely, 



Fa 2 + m s P 2 + ny = .... (77). 



XXV. If the centre of homology move in the same self-conjugate conic, the 

 faisceau of circumscribing conies 



fa + g e l3 + h 6 7 



