ALF GULDBERG. M.-N. Kl 
SJ BO Tn 
IG = — im 
G=—m.m 
en 
LE 1h. 
From the third and sixth equations, we find that 
m=1, m=—G. 
Substituting these values in the seventh and eighth equations, we find that 
=, n=AE, 
values which will be found to satisfy the second and fifth equations, and 
which reduce the fourth equation to the form 
EGi? + (AF + BG) å + HG — AD=0 
Supposing 4 to be thus determined, the equation (A) becomes 
(4) 
A êu 
pels] later 
If A, and A, be the roots of the equation (A), we have 
peu A ou 
pr lat Pa] [a +) Ga] 
ou ou ou ou 2 A ou 2 
LE = tr] Br, — 33 |= 
and these two equations are manifestly together equal to the second and 
third equations of system (II). 
In the same manner, we may substitute two new equations for the 
second and fourth equations of system (II). Eliminating first = from the 
first and the fourth equation, we find 
au]? FD [au|?_ ED + CG UM ¢ 
pies | G ort cele a + a an 
