OF A SUKFACE, AND THEIR GEOMETRIC SIGNIFICANCE. 
839 
9. Ill particular, we have 
clE 
dt 
dE, 
MO _ q 
+ Vio (Eqi + 2 F 10 ) + 2ryo|jF 
''ni 
— 2fioEoi + ^oiEio + + >?o]Eui + ^i^joEoi + 2i?nF 
— ^^ioEoq + o^ooE^q -f 24 oE 
dt 
f/E., 
' dt ^ 3?20-I^10 
+ 2i?io (Eji + F 20 ) + >730 (Eq] + iFjo) + 2 F 7730 
rZEi 
dt 
(' ’ 
■'ll 
— S^iqEh + ^oiEoo + 2^ooE,ji + + 2|^2iE 
+ ’?io (Eo 3 + 2Fji) + '>?()iEn + 21720F01 + (E,ji + 2Fiij) + 2%^F 
^0? 
dt 
“ — 2?i(jEo 3 + 2^oiEn + 4 ^iiEq 3 + ^usEio + 2^i2E 
+ 2 i7oiEu3 + 2i7ioFoo + 47;nF,ji + r^o.Eoi + 2r7ioF 
- — 2^ioFio + ^uiEio + ^3 oE + fiiE 
+ ’^lo (Eol + Gjo) + i?oiFio + + ^iiE 
- = f.oFoi + 4, (E„, + F,„) + f„F + f„,E 
+ '710^^01 + 27701F01 + 'i?iiCt + i^ooF 
]-C' 
- = S^.oFeo + ^oiE3o + 34,Fio + 2^nEjo + ^3iE + ^^oF 
+ >7oiF3o + ^Vio^n + ”>710^^20 + ^2o(2G]o + Fyi) + 2t)^^E^q + 773„G + y].yE 
~ = 2fioFji + ^oi(Eii + F2o) + ^o(jFQ^ + ^3i(E(ji + 2FiJ + fy2Eio+4iF + ^ioE 
+ 2i?oiFn + ^io(Fo2+ Gt] i) + 1730^01 + ’ 7 ii( 2 Foi + Gio)+ 1700F10+ %iG + 7713F 
- - = fioF„. + fo. (E„, + 2F„) + 2f„F„, + f„, (2E„, + F,„) + f,,,F + f^jE 
? 1 
( ’ 
dt 
dG- 
dt 
dG< 
+ '5^oiFo2 + ’710^02 + 2i7iiGqj^ + ^rjQ.EQ^ + t^^oG + 7]q^E 
■ = + 2^oiFio + 2^"iiF + ’7iu^Ri + “^Voi^io + 2r7iiG 
' = ^ui (^Do + 2 F 01 ) + 2|^q2F + 3>7oiG^,^ + 2-)7,joG 
dt 
dC' 
- ""a = 2fi„Gj„ + 2f„F,„ + + 4f„F.„ + 2ft,F 
f/Gi 
+ 2i7oi^Eo + 2r7i(,Gii + 17 .,oGoi + irj-^iG^f^ + 27;oiG 
~ — ^10^11 + ^01 (CGq + 2 F 11 ) + (2F^,^ + Gjo) + 2|’ooF^y + 2^ioF 
+ 3i7oiGii + ^710^^0 + 3t7iiGoi + 27703^10 + ^i^G 
- = 2ft, (F,. + G„) + ft, (G,„ + 4F„,) + 2 ft 3 F 
H“ I^OiFtiio ~ 1 “ ^^03^^01 “h 2170 : 51 ^ 
