( 763 ) 
5. When each ray throngh a singular point determines a system 
of tangents with index two, then the equation is projectively reducible 
to an equation of the form 
dy N(a)y? + Ploy + Qa) 
dz R(«)y + S(x) 
For, this equation determines for «=m the tangents of a conic 
and by the substitution 
ESS, y= 
i Y 
(see $ 1) it is transformed into an equation having in a= 0, y=0 
a singular point, whilst each ray of the pencil « = my possesses the 
above indicated property. 
The equation 
dy a + y® — 2a°y? — ay 
ET y”? — 2e y — « 
is in this case, for each ray y= me furnishes a system of tangents 
with index two. By the substitution 
1 u 
av Tete 9 y En 
Vv 
it passes into the equation (of Riccart) 
dv . 
— = 2u— wv v’. 
du 
This can be reduced with the aid of the solution v= uw’ to the 
equation (of BERNOULLI) 
ae =wuww+t w? 
du j 
where w =v —u’. By w=2z—! we then arrive at a linear differen- 
tial equation. 
Botany. — Mr. vaN DER STOK presents in behalf of S. H. Koorpers 
a communication entitled: “Polyporandra Junghuhnii, a hitherto 
undescribed species of the order of Icacinaceae, found in’s Rijks 
Herbarium at Leiden by S. H. Koorpers”’ (Plantae Jung- 
huhnianae ineditae IT)*). 
(Communicated in the meeting of February 27, 1909). 
Polyporandra Junghuhnii, Kps n. spec. Hrutee? scandens, ramulis 
teretiusculis novellis pubescentibus. Folia opposita, oblonga, basi acuta 
vel obtusa, apice sensim acuminata; 12—13 em. longa et 4—5 em. 
lata, petiolo 1—14 em. longo, subcoriacea, supra praeter costam 
1) Continuation of Plantae Junghuhnianae ineditae I in Proceedings of the 
Mathematical and Physical Section, of June 27 1908, p. 158—162. 
