r 
DIFFERENTIAL INVARIANTS DF SPACE. 
remark may be made. Out of the aggregate of sixteen, six already have l)eeu 
identified; thev are invariants of order less than three, so that there remains the 
identification of the ten invariants winch actually involve quantities of the tliird 
order. Let H and K denote the mean curvature and the specific curvature 
respectively of the surface (f) — constant, so that 
H - p + ^ 
L, 
K. ’ 
K = 
_1 
TL R, ■ 
Then the o-eometrical magnitudes available for the identification of the invariants are 
dR 
r/H 
dR 
dll 
’ ds. 
ds, ’ 
dK 
r/K 
dK 
dn 
ds, ’ 
d^ 
d (d^\ 
d /d^\ 
dn^ 
dS] \drd) 
ds, w~r 
d~ /d(f)\ 
1 , 
(1" 1 dff) \ 
ds^\dnl 
dsydsAdn/ 
ds^Unl ' 
being twelve in number. 
Accordingly, it is to be 
ex])ected that 
quantities and the ({uantities 
already used, which are 
-rr clcf) iP(j) cl I d(^ \ cl fd(ji\ 
’ ’ rhi ’ dn- ’ [dnj ’ di^ [dn.l ’ 
two algebraical relations exist. 
so ms 
