212 
ME. A. CAYLEY ON THE DOUBLE TANOENTS OE A PLANE CLEYE. 
which is the general identical equation referred to in the introduction to the present 
memoir. 
34 It is to be noticed that for w=3, the equation is 
(® - 2»,)U +iB» • DU -iDH. JBT- (H- 2H.)T = 0. 
But we have H.=H, and in like manner 1.=®, and the equation thus becomes 
-®U+iBl.DT-lDH.BT+HT=0. 
And so also for w=4, the equation is 
(ia®-3B®,)U+WB16-3B'*.)DU-i(D’H-3D’H,)i3T-(DH-3DH,)T 
= 0. 
But we have in general r)H.=^|DH, and therefore in the present case DH.-iDH 
and consequently and the equation thus becomes 
-B®.U+i(B'‘®-3BW)DU-i(D*H-3D“H,)BT+DH.T_0, 
which agree with the results previously obtained for the two particular cases. 
