29 
and solving 2,, @,, @, out of them we find 
vh US Vy, oh UE, + Vis e= 8 U6, + Vi, 
from which ensues immediately 
1 
i Sy (U°*k’? + V*), 
and also 
ASoids, ==} Udh + VER den 
AZ dn, = hk UEn ds, + 4 Vdd, 
A{VEo ds, —-UZe dn} = (Uk + V’) Sy, dé, . 
The reduction of the differential dJ now takes place as follows. 
We have 
Pree ithe Oe EE Es | 2de, nde, ZA de, 
1 
at = EN EAS elen MS MSA eN 0 0 k? 
Ge ge ees oe LER U ug 0 
and therefore 
ke | dU—Za,d8, dV—2Z2,dm, | 
/ Ek Se She, 
wh U iS 
k?(VdU — UdV i? 
a El ee =n, dé, , 
Uk} V? A 
so finally 
1 
BT 
ds, ds, ds, 
Abe! Ae oA 
£8 & | 
The second term of the righthand member corresponds in form 
entirely to the original form dH; however the independent variables 
Bids Tt, are replaced now by &,,&,,§,, functions of A,, A,, A, 
On account of the equations 
eS ee a al, 
we may consider A,,A,,A, as functions of one variable ¢ only, 
which implies that also §,,§,,§, appear as functions of that variable 
t, whilst this variable itself is determined by the equation 
en Ae oe) 
Vv 
dH = ktang— — 
ang Di + 
ae an fanelion. Of 25:25, 2, 
Substituting the expression found for dH we now find 
| ds: 45, ds, 
V 1 
dz == kd tang”! Uk 4- SE? A. A, lie 
1 
5: $2: Ss 
d ze Crees 
+ nine 
u 
