DIFFERENTIAL INVARIANTS OF SPACE. 
287 
from the coefficients of I'qh, '>7oin ^oii respectively; the three equations 
Scr 
0cr , 7 0cr , ^ 0cr , , 
a -h h -h 2g — - \- (pioo -5 
^'9ooi 
0(T 
^9 
001 
^/ooi 
0 ( 
^/ooi 
0 c 
001 
+ h —h 2/ ^ -h (/>oio 
9 
0 
cr 
2^/1 
+ / 
jCT 
001 
9/( 
+ 
001 
0cr 
001 
0c 
+ 
'001 
001 
^4*002 
ccr 
2^003 
0cr 
3</>003 
0 
= 0 ^ . 
= 0 
(He), 
from the coefficients of ^ 002 . ^ 002 . ^002 respectively; the six equations 
0cr 
Ai (cr) = ‘2h^ h ^ ^^110 p JL 
^ ^ ^ 0C^ 0/1 C(J C(j).20o 
^ _L 2/; 
^'‘010 „ 
'010 
+ </> 
'020 
+ (^^010 ffi 2/lioo) 
da 
100 
0 a, 
+ 2/i 
0cr , I 0cr 
VT-r roil 
<^9i]0 
0cr 
3^101 
0cr 
+ ^ 
0 
cr 
'010 
001 CS 
ca 
jcr 
+ /oio pP- 1 " (S'oio + fm) ^ /)io 0 
0/100 05 'ioo ^S'oio 
+ (/^oio + *^ 100 ) 
'001 
fool 
^010 00 + ^010 
uoo 
0^100 
0cr 
0^100 
Ocr 
0^ 
001 
jcr 
0/1 
+ 0010 + 0 
100 
0/; 
0O- _ n 
'001 00- -ffi 
010 
(-) = i+/ i + ^ 3^'+ iL +47« + 
0cr . /^0cr . da- 
^ 3 3cr 
"h (*^^001 ffi '^9ioo) ST t“ ^.'^oio ST I” 2.7 ooi 
da 
100 
0 a, 
010 
0 a 
I 7 0 o" I 
+ 0001 Ti-r r 
'001 
06 
001 
100 
001 
0cr 
0'/’ioo 
0cr 
0'-^ioo 
+ fool pT^ + (.'S/ool + <^ 100 ) 
q/100 
icr I 0<r _1_ . 0_PL 
s-r Cqio "T Cqoi ^ 
d9ioo ^9oio ^9ooi 
+ (0001 ffi fioo) 00 /oio 
jcr 
+ /ooi 00-^ - 
r’^Hioi 
^=P) = “3i + "'‘3!. 
0cr 
“ 'p y 010 "sL V" p 001 p 
100 ^''010 ^ 
0cr . 0fr . 0O- . . . 0cr . , 0cr . . 0o- . . 0cr 
+ g 'fi + 2(/)iio + fiQo fj -h 4*101 / + ^Joo 
+ a^ 
UOO 
0'^6ho 
, 0cr 
+ .6100 
¥ 
+ 27hc» 
0*^O2C 
0(^ 
no 
06 
100 
3 3cr 
+ (0100 + 20oio) pT 1" 26001 070 + ^'kio 0 
oc»oio riUgni ^''Oio 
0^011 
0c 
00001 
0^^010 
da 
0/100 
\0^i 0cr| 0cr 
+ (/lOO + .'7oio) p> r ^'ooi ST r fhoo 007“^ 
0/010 °/ooi ^voio 
0cr . rda . da 
—h a 
0cr 
100 0!^ + (®oio + ^hoo) 00 ’ + « 
jcr 
001 
noo 
‘010 
dh 
= 0 , 
001 
0cr 
¥¥) = </ / + 2/^7 + T7 + In; + bIu sVi» 
dh 
+ <^001 
06 ‘ “0/ 
0 cr j_ 9 /• 0 cr 
n -^Pioo 
020 
+ c 
0 c /010 
0cr 
06 
100 
0<^iio 
+ (0001 H~ 2 / 010 ) 00-' 
L O /■ 0^ I . 0^ 
"T'^/OOIS/, “T <-001 
’010 ^^001 
0 c 
010 
100 
pp— + (/ool + Oolo) 0 P 
0/100 vfc 
0cr I ^ 0^ J_ r, 0^ 
+ Oool "T Pool p 
010 0/001 OPolO 
7)a / I 7 \ 0cr I da _ ^ 
+ Pioo Sr - 0 + ^^ 001 ) 00 ^ 9ooi si ~ 
dh. 
.00 
■010 
dh 
001 
