OF A SURFACE, AND THEIR GEOxMETRIC SIGNIFICANCE. 
oDo 
U). As regards these equations, we replace (Ij) and (I^) by two ecpiatlons composed 
f their sum and their difterence. The former Is 
¥ 
¥ M n ¥ 
k/ = 2(e54 + fh4 + g^) + 2(l^^ + mU + nU 
0E ' ' SF ■ 0G 
?./ n I T? 
3/ 
01 
4GS/+«?a , a.c 
0a 0/8 ■ ('y 
+ ^Is + I, + K, + F'" K; + «■» K„ + «"' I 
10 '-■''01 '-'*^10 '-‘^01 
-P 4 ( F -I- F 4- F -I- F ^ ^ -1- F 4- F 
+ ■+1 ;^-rw -r y-cT + Go-: Sp H" T „ - + to: >^A - 
oT^.^o clt.n cUa-’ <^'t.,o dt|, cTaa 
+ ^^-20 si- + (^11 + Gtoj 
i; j_ J \ I ^’f \ t 
t’9io t'9oi ci/ijo oi//oi 
0G,o 
11 
AL\ 
^^^dCrJ 
■^10 
^4>20 
-I- O / ^ Al' I ^ _J_ A _L 1 _L 1 
+ - ( 9i0 + 911 ^ + "fo:+ '/':o ^G;.- + ’/hi N.1~ + ’Ao: , 
0(^11 ' '^'^'^0(^03 ‘ '^'~'’^-20 
4-oIa C/’iA -L A S/j-A 3/ 
+ ■" /'30 A, - + 9:i + <f>i-2 yd- + <^03 ydy- 
1)930 d</)33 d9o3 
'-Vll 
, , 3/’ , , 0/’ , 0/" . , 0/'^ 
+ '/'oo + V':! ^r,.' + 'Ai: ^i- + ’/'03 , 
The latter is 
?'A:i ' ' '^'''''’S'Aun. 
= 2 / 1 ] — G 4- L _N -'M 4- hP 4- O — P o»j S./ 
0E 0G + 0L 0N / + '^^0? + 0Q 011 ~ 0S 
4- 4a 4- ‘^>8 — •a'S — 4e 
^ ^0/8 0S " 
ca 
0e 
0 , 
+ + Kn "^ 4 / 4- F 30 ypW 01 
dE]o eEox 0130 f^Fo] 
OJ1,AO (41,33 ~ dtjo ■ cToa 
+ 9io 5Q-9oi ' + ’Aio — '/'oi Ad ' 
f’9io hi//oi 
-1 0/ 
op ^ / 
" 3Cto, 
■^10 -,A 
oGjo 
— ‘^G 
-OTii 
—^ — 4G 
-'./'"I '^'-^03 
dCT33 
3/ 
c-Go: 
' ^ j 'rui 'd / 
O9]0 d(/)03 
^ ~ ‘Ao: G-- + 4:o 
0r^O3 ' 
+ NJ~ + <A:i a^;A “ ^12 —- 
^9:i 
'Ao: 
13 :1J, — ^'Ao3 
iz: 
01^Q.'1 , 
i/ 
^‘Ao3 
-Lit/ h/^i, 0/ , 0/ 0/ 
+ ^'Aso Ad— + ’A:! -lAi: a-;-34o3 a • 
ClAoo 04.33 01 //] o 04 o.o 
{!,)• 
(F). 
\'OL. CCT. 
