( 526 ) 
OR deo / ie 
der En 7 RO atin zer 
rr Bud k on dudV 
==. 
E dg dqdy Coz ade 
Special cases : 
L. stAt=0 
1 
Here uw =— H(pe+v)=0; therefore 
Q 
H(o)=0 and H(v)=0, 
whilst the differential equation for v reduces to 
du de 
de dw 
Let o be any function of 2, q, w=2—qy. We then find here 
1 do do 020 020 
i do E Ga oq 15) 27 dw dq mr 4 ; 
ae 
The differential equation s + Àt=0 now possesses the two inter- 
mediate integrals 
06. Oa do do 
Dan Td and Vonn 
where f represents an arbitrary function. 
These results are more general than those formerly communica- 
ted sub 1V; we find these back by putting 
o=eSI@)d , v= — fe P (9) dq w (a, 7) dq 
I. s+ a= 6. 
Pag 
Here 4 = — — (pe+v)=0; therefore 
g dg 
dg du 
— =0 and — = 0, 
dg eit a8 
