39 



duration that cliaages in accordance witli tlie metabolic situation of 

 the ventricle-nuisculatnre. I found in fact that the duration of the 

 7?-F-interval (this name T gave to the interval between the beginning 

 of the /^-oscillation of the venlricieelectograra and the beginning of 

 the venlriele-suspensioncurve belonging to it) increases considerably 

 after poisoning witii veratrine ; vvlien tlien the ventricie-rliythm halves 

 this R- F-interval decreases again, and increases afterwards again 

 when the poisoning-process continues. ') 



Mathematics. — ".4 pariiculur bilinear congruence of rational 

 hoisted quintics". By Prof. .1. de A'ries. 



(Communicated in the meeting of April 23, 1915). 



1. In a communication in these Proceedings of March 27''' last, 

 (volume XVII, p. 1250) I considered a congruence of rational twisted 

 quintics, q\ which is determined by a net of cubic surfaces the base 

 of whicli consists of a twisted cubic, a straight line and three fun- 

 damental points. We arrive at a [^*] differing from this by starting 

 from a net of cubic ruled surfaces /?' having a straight line q as 

 nodal line. Two arbitrary surfaces of that net have anotiier q^ in 

 common, which is rational, because it has q as a quadri.secant. An 

 arbitrarily chosen tliird surface intersects (,>' eight times on ![, con- 

 sequently seven times outside q ; hence all base-curves q' of the 

 pencils (/i') comprised in the net have seven fundamental points 

 Fk in common. 



The congruence [(>*] consists therefore of the curves q\ which 

 intersect the straight line q four times and pass through seven points F. 



2. The hyperboloid /i!^^ containing the straight line q and the 

 six points Fk{lc=z2 to 7), has with an W of the net another 

 rational curve (>/ in common of whicli q is a trisecant. This (>/ is 

 a component part of a degenerate curve of the congruence; the 

 second component part is the straight line /•,, which coiniects F^ 

 with the point R^, where p/ moreover intersects the plane [F^q). 

 To each ray of the plane pencil (r,) belongs on the otiier hand a 



1) Erelong an elaborate communication about tliis subject will appear in "The 

 Journal of Pliysiology." (.lompare tig. '2, 3, 4 and 5 of communication I: 'On tlic 

 heart rhythm" by Dr. S. de Boer. Koninisl. Akademie van Wetenschappen at 

 Amsterdam. Verslag van de gewone vergadering der Wis- en Naluurk. Afdeehng 

 van 30 Januari l'J15. Deel XXII, p. 102G and 1027. Proceedings of the meeting 

 of Saturday February 27 1915. Vol XVII p. 1075. 



