( 424 ) 
whilst the indices 1, 2, 3 refer to differentiations according to #, y 
or z of the functions, with which they are connected. 
If these conditions are satisfied the first intermediate integral is 
found by connecting the two common integrals of the system 
dp ( u+ 1 DE 2u o' dp 
ae f Lenk a: Sie EBs eee ge 
dz cvz(u—l) v3 
dz ON 7 du 
op ( u+ 1 de 2u 0 Ap kad 
oy hvzlu—l)  v3/ dz he oon 
where 
1+c¢G(v) 1+’ AH (v) 
u : : 
OE CREE 
Bn vg ie 
A first common integral pj=g ; of this system is easy to find, 
u — 
the second g¢ however cannot be found without v and v = g (v) 
being known. 
In the same way the second intermediate integral is deduced by 
connecting the two common integrals of the system 
ow de a ae de 
ox cv3(w—1) v5 he Baie 
de GO Opie 
ow Tee | nye 2we dw ay 
dy hv3 (w— 1) vs 
OE 
where 
SES 1—h H(v) 
EN 1+hH(v)° 
4 PEA Ww) \ : 
Here too a common integral yw; = : a is directly known, whilst 
w— 
the second wz requires the functions v and v to be known. 
