28 
remark that the three quantities A,, A,, A, are entirely determined 
as functions of x,,2,,7, by the three equations 
he Nig A ne Sagas A; St eA) 
and now we express. p,, Pa, Ps iN 41, 2,2, Ay, Ay, As. 
So by eliminating p, and p, out of the equations 
EP — & Ps = As 
ED PPA en 
Dy Pat Pe m* 
we find that p, is determined by the equation 
pa? — 2(A,e,—A,2,) — em + A,’ + Ag? ls 
from which follows after some reduction 
| A. oe aes + dU, Vm Ea —k? 
ONE 
= Po Pa 
We find for p, and p, similar expressions; by putting 
Dn, 
we get the total differential equation 
a = ae | 
da 1 dite da 3 | 
it | BY ing ge 
dE Ae ea V m?u?—l?. 
u” u 
De Etn 
da, de, de, | 
A 
Bes 
dH = — 
u 
1 
| 
| | 
[@, & %3 
we consider three functions &, 8, & of A,, A,, As, satisfying the 
condition 
SATS} ie 
but otherwise arbitrary. 
Putting moreover 
Ny = (4.8: —A,§,), Ye =e (A,§,—A,8§;), VE == (A,§,—A,§,); 
we get 
Zin =0, SAn,=0, AHR? = yt 
We still introduce two quantities U and V determined by the 
equations 
Bye, Sra — 
By adding to these the equation 
Sa A= 0; 
