50 Frederick C. Ferry, 



?S=? + 2b=.U;_.) + Xv . (2a . V;^, + (aX' + b,.'). ^^ ) + ,=. 

 (2W' _,) + H-v . ( 2bV' + (aX' + b|.') .^ZL^ ) = o , 



^ ' 0[JL / 



a (2,2); and if P' lie on the generator aX -j- b[i. = 0, the 

 tangent quartic (2,2) is 



i\ a'u;_, + 2X[x . abu;_, + J.2. b'u;_2 + 



Xv.aV ., + av.bV' o + vlW .=0. 



p— 2 11' p— 2 I p— 2 



If q = l, we would have a tangent cubic (2,1), whose 

 equation is given by putting W'^ ,, = in the equation of 

 the tangent quartic and is 



(aX + b[x)l U;_2 + V . (aX + b[x) . V;_, = ; 



this tangent cubic is consequently made up of the conic 



(ax + b}.).u;_, + v.v;_3=o 



and the generator aX -|- b|x = ; hence one branch of the 

 curve cp = has the direction of the generator at the point 

 P', when q=l. 



If V 2 be wanting in the equation or Y' ,, = 0, the 

 tangent quartic (2,2) consists of the two conies 



aX + b[x + v. )/ ^^P=? = and aX + b|i. — v. V ^^^£ = 



üi-,_o Ui-,_5 



If both W_,_o and V _., are wanting or = at P', the 

 tangent curve consists of the generator aX-j-b(i. = occur- 



