1207 
0Z 0Z 0Z 07 
A vo) = ze = by + + An dn + Ld? +o] 
Jy Oy ee dy i 
Herein the sign d indicates that we have to differentiate according 
to all variables, which the function contains. Further is: 
04 WA 0Z 
Den AP+d~ acs are endde P= ahaa tom 
oP Oy : 
WA Pp Dn OZ 
&Z = d* — Pp „AP + a — NEE — ie Ay +... 
oF a7 
When we neglect in @?7 and d°Z ha terms ae are infinitely 
small with respect to AP and A7, then we may write: 
read ioe Ay + 
ING ea „22 RE yt. 
EE Oy 
From a form: 
OZ OZ : 
Zw ane ERN == 
it follows, therefore: 
0Z OZ 
—VAP+ HAT + («+Az) (a +. Juan) Ge + .)-| ‘ 
(_ (9) 
BE iy ese. AE 
Now is 
VA 7 0Z 0Z 
Relea’ sya? ER Aap de EO IE ae 
Ox Ow Oy Oy 
so that we may write for (5) 
WA A 
SE teat wo de a ded. RAE 
+4@027Z1+4¢@74+...=—AK 
Now we apply this to the m equations (2) and we differentiate 
further also the mn (n—1) equations (8). First, however, we shall 
introduce the following notation; we put viz: 
ee OZ. 0°Z, ; 0°Z, : 
TE ed 7), ; aia ; OE ay )s ; me erie 
Oy Ow, & Va 
The geen aa the parentheses indicates, therefore, which of 
the functions Z,...Z, has to be differentiated; the letters within 
the parentheses indicate according to which variables we have to 
differentiate. 
Then it follows from the » equations (2): 
