OF A SURFACE, AND THEIR GEOMETRIC SIGNIFICANCE. 303 
magn tildes of the second, the tliird, and the fourth orders, can he exjiressed 
til^ebi aicall\ in terms of an algebraically complete aggregate of 20 members. 
Ibis aggregate is composed of 20 quantities, each divided by an appropriate power 
of A ; the sections quoted give the significance of the respective invariants. These 
quantities are as follows ; 
[§ 34] 
[§35] 
[§ 34] 
[§3(i] 
[§38] 
[§36] 
= (E, F, GX</>oi, - 
iv\. = (L, M, — ^in)'^ 
-1 (ir.,, = 
EM 
EN 
FN 1 
- FL 
-GL 
-GM ! 
i 
I ich) = EN - 2FM + GL, 
a’", = («, 5, eX<^on 
J (vt^, = 
E6 
Ec 
Fc 
- Fo 
— Go 
-G6 
1 (a^, w'h) = Ec — 2Fh + Go, 
- (P, Q, R, 
[§37] j{ir.,w.^) = 
eq 
1 
2ER 
ES 
-FP 
-fq 
+ FR 
- GP 
- 2GQ 
a,= 
EPt 
E8 
-2FQ 
- 2FR 
H-GP 
+ gq 
FS 
-GPv 
i‘l,. 
E^S 
EFS 
- 3EFR 
- (EG + 2F') R 
+ (EG + 2F‘) Q 
+ 3FGQ 
- FGP 
-G^P 
X'^on - 
U’ 
'3 = /, 
3 E 
a’ol. ccr.—A. 
