130 KANSAS UNIVERSITY QUARTERLY. 
The abscissa or the point C, is given by 
hence 
bas Or a,)(b,—b+am) | 
a y,—b,—m(x,—a,) ek 
kath b,)—y,(a—a,)-+ab,—a,b 
a apes y,—b,—m(x,—a,) 
Xx 
In like manner we find the abscissa of C and thence X—a, 
x(b—b,)—y(a—a,)-++-ab,—a,b 
y—b,—m(x—a, ) 
xX 
a= 
From Fi fiery ae) ie 
rom Lo 2 Wwe See Neve = —— 
8 AC AC 
Hence 
a by their values we have 
Replacing X,—a and X 
> en | ea 1 
a, b, LO bal eee aun 
Eee 0] Aral eanay 20) 
= + (5a) 
cosé 5 
b, I| 
Dp ih osaies e/a} 
These two equations (5) and (5a) constitute the normal form of 
a transformation of type II. They may also be expressed in homo- 
geneous coordinates. 
