( 499 ) 
From a comparative ontogenetical point of view, therefore, also 
the value of the urethra before and behind the fossa navicularis is 
different. For, whereas behind the fossa navicularis only a very small 
portion of the wall can be considered as a production of the phallus- 
frame, perhaps the vertical part of the lumen as it is found in the 
urethra of man, this changes before the fossa navicularis in such a 
way that there the greater part of the wall originates from that 
frame; therefore behind this fossa the urethra is principally homolo- 
gous to the “Harnurethra”’, before it to the “Samenurethra”. 
Mathematics. — “On bicuspidal curves of order four.” By Prof. 
JAN DE VRIES. 
1. It is easy to see, that each curve of order four, C,, with two 
cusps can be represented by the equation 
Be, + 22,0,0,’ + 26,0,2,° + 2b,2,2,° + ew, = 0. 
The triangle of reference has then the cusps O,, 0, and the point 
of intersection 0, of the cuspidal tangents as vertices. 
From the equation 
(zie, + «,°)? + 2(6,2, + b,c, + bewo), = 0, 
where 26, —c— lI, is evident that 
b, = b,#, + 6,4, + 6,7, = 0 
represents the double tangent d of C, and that the conic 
tbe) 
passes through the tangential points D,, D, of d and osculates C, 
in the cusps QO, and 0, 
By combining the equations 
i aie =O oand w= 26,0, 
we understand that the conics A, through O, , O, , D, and D, generate 
a system of pairs of points on C,, which are lying in pairs on the rays 
2x, + Abr — 0 
of the pencil, having the point of intersection H of k= 0,0, andd 
as vertex. 
As this system of points with the curve is given we shall denote 
it as the fundamental involution F,. 
If we put 2? = u, it follows from 
oy. fo, = 0, 0? = pd,*4,*, 
that C, can be generated by a pencil of conics (0,0, D,D,) arranged 
in the pairs of an involution and a pencil of lines (47) between which 
