40 ALF GULDBERG. M.-N. Kl. 
and where 
(AF + BG) [(AF + BG)F + G?C]= G3(AD— HG). 
The corresponding systems of total differential équations are then 
AGdy — (AF + BG)dx + G?dt = 0 
Ddx + uFdy — Fds + Gdr = 01 
2. Letting A=o, £ + 0, G + 0, we had the systems 
eu eu 
DE + BG eu eu eu 
Zee = | )= 
where 4 was determined by the quadratic 
EG}? + BGi + HG — AD— 0, 
and where 
(DE + CG) [DE + CG)E + G?B)] = GYAD — HG). 
The corresponding systems of total differential equations are 
DG dx — (DE + CG)dy + Gdr = 0 
Ady + LEdx — Eds + Gdt =o, 
3. Letting G=0, £ + 0, F + 0, we had the system 
eu eu 
(EBF 4. BD" 4 apa pes (PÅ =, 
et es ey 
eu en eu 
AF + CE)— — DE — — EF |—|=0 
( D ) et es ox L 
1 We omit here and in the following systems of total equations, the equations 
dp —rdx — sdy = 0 
dg — sdx — tdy = 0 
da — pdx — qdy = 0. 
