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Mathematics. — Prof. W. KAPTEYN presents a supplement to 
his communication of the Meeting of November 25, 1899: 
“On some special cases of Monae's differential equation”. 
In my last communication was mentioned sub I that the equation 
r—hs=0 possesses two intermediate integrals, if 4 is given by 
the relation 
wp) 
g—p(yp)' 
in which supposition these intermediate integrals were deduced. 
However a closer examination shows that this result represents only 
1 : 
a particular case. In the most general one “= T presents itself 
in the form 
dU dU hl PR 
LEN ode du + W(p,y)s 
Pau Op yo 6 ET a dp 5) meat 
where = U(upy) and W(p,y) denote arbitrary functions of u, p, y 
and p, y respectively, whilst u stands for 2 — pz. 
The corresponding intermediate integrals are 
UQ 
gev fo du +f W(r.0 =F) 
wet fo Sdn + [Won 
By putting 
Ca ea Vues [in pe el 
W(p) w(p) 
the first mentioned case reappears, as is easily demonstrated. 
