( 423 ) 
to the well-known analogy, given by E. Fiscner, there are keys, 
which consist of a ring with different pieces attached to it, which 
each fit into a different lock. Even when one or more of those 
pieces are bent or made useless in some other way, those that are 
left can still be used. 
While the gastric juice of the dog used by me, showed very 
clearly the fat-decomposing action, described by VorLLHARD!), the 
pure pepsin, prepared out of it, had not the slightest action on fat, 
neither by neutral nor by acid reaction. 
Mathematics. — “The differential equation of Monen.” By Prof. 
W. KAPTEYN. 
In our communication of June 6 1901 we gave the results of 
our investigation of the differential equation 
rdt dt u=0, 
in which À and w were supposed to be dependent only on p and g 
or on #, y and z 
If we now assume no limiting conditions with respect to À and w, 
we shall find that the above mentioned equation can possess two 
intermediate integrals in the following case only. 
Suppose ¢, 4, v and g to be any functions respectively of 2, of 
y, of «, y, 2 and of v; then putting 
P 
4 must be equal to @ and « equal to A? Q + Pi, 
where 
c? G(v) — 1 ge! 
Cc V3” h V3” 
p= 
7 1 
Poe eee ME 1 
Oe C U3 V3 
ey ee HO + — HH) 
Q h h ve 
2) Münch. med. Woehenschr., 1901, 8. 141 and Zeitschr. f. klin. Med. Bd. XLII, S. 414, 
28* 
