142 
where « = (y’ dt + y” ao gas hy ase). and 
} 2 2 
po~aty’S see eg dey ey 
Arranging R according to positive powers of dt, dr, ds, and omitting super- 
fluous terms, we find c 
R= 45 dtd f r) ia 
( mera pen * ai 
iv SS et lS 4/ 3 
seat dee tau) Se ee SD (ese 
yY y” ye" ( oe i } 2 iM a y/// 
t (ds? — dr? aa Apes 
spate id i Q4(y’)? By” J l Qy’ J —— “By? le 
From these coefficients we may determine the differential invariants. 
$, =x. 
I ie x, pais ) 2 - (x’)? 274 Y3— 3y2” a: x’ ae Ee 2 
7 rT en ae 12 ¥i2 6x’ Det ee 
‘6, = 2¥1 Ys — 3Y2” 
Yi2 
4 cally fae dyn V3 by 2° eat > He 
Aa 24 te 7, a AW Bs yi? J 24 $2 + 1, (x), 
$= ts 472% ses 
1 Yi 
(x* 75 = Vora Ya Vins Vios 
is = _ == — 4 = 1 —-— 9 —— 
: 120 | yi Yar ya vie 5 A ses 
(x yee (x’)* nets 
ai 24 ?3 720 2% +- 72 , +1, (x); 
y Yay a AN Pe Yo" 3 Vig 
Sp ee Op aa aah esl 7 22 Ys gf Ye 1* 
‘ va Ly, J ie Ya Ly, J 
In some of the following paragraphs we shall need the forms I,, I,, here 
computed. Incidentally we have computed the differential invariants ¢,, $4. 
10. The group 
| 4, ¥4, ¥7q, P 
has the same differential invariants as 9 above, with the exception of ¢,, which 
must be omitted. We shall have, therefore, ¢,, 03, 04, as defined above. 
