( 255 ) 



changed in corisequencc of the moinentiim of (lie "new mass", which 

 is added to it. Tiie vahie of lü being- nnknown in many eases it will 

 be impossible to perform the separation between force and transport, 

 and we will simply call -Jv the force exei'ted on the body. 



In some cases however it will be useful to take the ditFerence 

 between force and transport into account. An electrical condensor 

 e. g. sharing the motion of the earth is suddenly charged, heat is 

 generated in a wire according to the law of Joule, or a body receives 

 heat from another body. The momentum of these bodies is increased. 

 Is a force required in order to keep the motion of these bodies 

 uniform, and will they sutler a retardation when this force is not 

 applied ? The answer to this question will undoubtedly be : If they 

 receive their energy from a stationary source, this will be the case, 

 but not if they receive their energy from a source moving along 

 with the earth. 



Mathematics. — ".4 bilinear congruence of (jiiartic twisted curves 

 of the first species." By Prof. Jan de Vries. 



1. If we allow each quadric Q^ of a pencil {Q-) to bisect each 

 surface of a second pencil {Q")', a congruence r* is formed of biqua- 

 dratic twisted curves, q*, of order one; for through an arbitrary 

 point F passes one q\ the intersection of the two (2^ which is 

 determined by P in the two pencils. 



An arbitrary line / is cut by the pencils into two quadratic in- 

 volutions, which have, in general, one pair in connnon ; the con- 

 gruence r is thus of class one fan arbitrary line is bisecant of one 

 curvej. 



2. The base-curves j5^ and /5'^ of the pencils are singular curves; 

 each of their points bears go^ curves q^. As ji" and q^ lie on a (2^, 

 they cut each other in eight points. So we can determine F also 

 as the system of the 9'' cutting each of two given biquadratic twisted 

 curves in eight points. 



Each bisecant b of /i'' is a singular line. For the surface Q" deter- 

 mined by a point of b contains b and the pencil {Q"^)' cuts b in the 

 pairs of an involution, so that b is bisecant of co^ curves q\ 



3. Besides the two congruences (2,6) of singular bisecants deter- 

 mined by ^i^ and ■^'\ the congruence r has a congruence of singular 

 bisecants on which {Q^) and {Q-)' describe tJie same involution. 



18 . 

 Proceedings Royal Acad. Amsterdam. Vol. XiV. 



