139 
2 2 
v3= [x—@+x/ dr px” + eo} : Jx—x(4x/dtpx7S + eat 
dr rs rd x Ne (pi tees aN 2 x44 
Te wa (S) +aede | (G7) —4}+ Pe tepad : 
These functions show 
x’ y’ y yy yx’ 
a I, = yi, 1,= a (x2 = Jo x’, and 
fe yi’ a y/ CG ot yx” ‘y/ (x//\? y; (x’) ; yx” 
3 83x’ 2x’)? 3 (x’)? 9 (x4)8 3 = UE 9 
to be invariant. Eliminating the parameters x’, x’’, we have 
2 ti cer ets a 
}is-+1,— 35} -I,= CA 
SECTION Il. DIFFERENTIAL INVARIANTS DETERMINED BY THREE OR MORE POINTS. 
In the case of the more complex groups it is necessary to bring into consid- 
eration three, four, five, .......... points, and consequently employ additional 
Paramevers, Ty So... « 
5. For three points, the group 
|p a xp + eyq | 
| 
possesses the point-invariants 
y — y(2) x — x(3) Se 
ST EEO) ae ean en Or 
Expressing u, in series expansion for x(2), y(2), we have 
y—(y-ty/dt-iy” 22 +.) 
LS = 7 77 At2 c 
13 (x+x’dt +x a+ ate 
eon pi SES Ry , x7 
~ lyst (vB) + 
