MINDING’S SYSTEM OF FORCES. 525 
or (D?— BC) 7? + (E’ — CA) m’ +(F’— AB) n’ 
—2(AD + EF) mn — 2(BE+ FD) ni — 2(CF + DE) m=0 
If we consider the conics corresponding to all the planes that pass through Meridian 
L a pee surface. 
a given line, we get a surface which PLicker calls the meridian surface of the 
conic. 
It is obvious that this surface is the envelope of the complex-cones whose 
vertices lie on the given line. 
Let the equations to the given line be 
la+ny+nze+p=0 
let+my+nzt+p'=0. 
It is easily seen that the equation to the envelope will be (15), with 
P7—Pl’, P’n—Pim’, P’x—Pn’ written in place of ln, 
where P-= le + my + nz—p 
P=la+my+n'c—p' . 
So that, putting a=mn'—mn, w=p'l—pl’, and so on; 
U=yy— Bz V=az—yx W=62-ay, 
and noticing that 
D?— BO= 7 (974+) —-Vy-9P2—-Ph?—-r'v=S—1°2" say, 
and AD +EF=—(f?2-72)yz, 
we get for the equation to the meridian surface 
(S—ar?)(o+U)?+ &e. +2(f2—22)y2(o + V)(o+W)+ &. =0 . (16) 
this equation is apparently of the sixth degree; but the terms of the sixth 
degree are equal to 
r(2U +yV +2W)?, 
and those of the fifth to 
27°(wx+py+oz)(aU +yV+2W), 
which vanish identically, so that the degree is really the fourth. 
EKaploration of the Complex by central radii. 
From what we have already proved it follows that through any point of a ae 
intersect a 
given line there pass in general two rays parallel to a given plane. given line. 
