( 6fi2 ) 



to tlie oapitnliim of the female or of the hermaphrodite is one at 

 eaeh side only, in some species it is two or three and the largest 

 number I have observed was five. How can we explain that there 

 is a species with such a large number as the case mentioned? I 

 have tried in vain to find an explanation. We do not know much of 

 the habits of these animals. It is hardly admissible that tlie great 

 numlier of males should be connected with the depth at which they 

 live, for (1) the same species which is found in the Malay Archipe- 

 lago at a depth of 200—400 m. lives in the Japan sea in shallow 

 water, and (2) we know species living in coastal waters and others 

 found in depths of over 1800 m., all of which have two males 

 only. A connection exists no doubt between the place where the 

 little males are found attached and their great number - but I 

 am at a loss to understand what the relation may be. The eggs 

 of these Cirripedes ai-e fecundated at the moment they are excluded 

 and form two leaves (the so-called ovigerous lamellae) which remain 

 in the sack or mantle-cavity of the female until the eggs hatch out. 

 If the males are attached at the margin of the mantle-cavity, the 

 chance that the eggs will be impregnated is of course larger than 

 in the case when they are attached at a greater distance, as in 

 Sc. Stearmi. So it is easily understood that in the latter case a 

 greater number of males would be required — but why did they 

 choose for attachment a place which is less favourable for impregnation? 

 Because they were so numerous and did not find space enough at 

 the ordinary place? 



Mathematics. — "A group of complexes of rays irhose singular 

 surfaces consist of a scroll and a numher of planes". By 

 Prof. Jan de Vries. 



1. The generatrices of a rational scroll can be arranged in the 

 groups of an involution Ip-, to this end we have but to arrange 

 their traces on an arbitrary plane in the groups of an Ip. If we 

 consider each pair of lines /, /' of Ij, as directrices of a linear con- 

 gruence, it immediately occurs to us to examine the complex of 

 rays r which is the compound of the go' congruences determined 

 by it. 



Let the scroll (*" be of order n and let it have an {n — J)-fold 

 directrix d. The generatrices I form a fundamental involution /„_i, 

 each group of which consists of the (n — Ij right lines, coinciding 

 in a point of (/. Tliis /„_i has evidently [ii — 2) (p — 1) pairs in 



