688 
(Vi,)! i, containing but i; and i, on account of (38), we find in 
connection with (67): 
ij inv? VI sn =O, j AE, heals kl, hill pean — 5) (D,) 
This equation (D,) can be decomposed into: 
ieu Wend, . Eu NCD) 
iS Wv) wreede en (C8) 
or: 
and: 
PW WIED ete Sos a (©) 
4 
When K is the Riemann-Caristorret-affincr of Vn, (99) can 
be written: °) 
4 
AVEN IES Der aten Sa 3 5 (OO) 
or 
a 
B SOHN Ker ot keneden (UD!) 
The equations (C,), (D,), (D';) and (100) are deduced by Riccr.®) 
(n—1) (n—2) (n—8) 
Loe) 
The number of the equations (D',) is ‚the number 
: n—1 —2) (n—3 
of the equations (D") is Cae 5 eer 8) 
mutate not only j and &, but also & and 7‘). (D,') contains third, 
(D,") only first differential quotients of y”. 
The conditions (D,") vanish identically, when the characteristic 
, because we may per- 
4 
numbers /4£j7n of K vanish. Since in a space of constant RifmMann- 
curvature K,: 
4 
K=2K,(a~b)(a—b) 5). . . . . . (101) 
the equation holds: 
4 
ND EG too pe oa) (LOE) 
so that the condition (D,") is an identity in such a space, and hence also 
in a euclidean space. Thus (D,) reduces in this ease to (D',). For 
1) (Cs) can also be deduced from (84) in an analogous: way as (Dj). 
2) Comp. A. R. page 59. 
5) G. Rreer, Dei sistemi etc, p. 314. Here the equations (C3) and (Dj) are lettered 
(Aj) and (Bj). G. Rreer, Sui sistemi, p. 151. 
*) Compare the observations of Riccr on occasion of a paper of Dracu, Comptes 
Rendus 125 (97) 598—601 and 810—811. 
5) Compare Cf. Brancur-Lukar, Ist. german edition, p. 574. 
