( 31J ) 



be necessary, liowevei-, at least Coi- low temperatures, to take ^reat 

 care that the temperature is kept euuslaiit (liiriii,i>- the time recpiired 

 for a iiieasiii-ement. In these measurements the determination of the 

 temperature was less accurate than seemed desii'ahle with a A'iew 

 to the accuracy of the determination of tlu; ratio dui-inii,' the measure- 

 ments on one day. 



In the results there is a slrikinu,' dilfei-ence i)etween the gold and 

 the platinum. Thouiih the \ahies found do not help us to ti\ the 

 temperature function for gold foi* want of certainty altout the zero 

 to whieh they helonii", yet they show that the curvature ot" the liue 

 which for gold represents that temperature function is much smaller 

 than in the case of jtlatinum and that the cui-ve is hent more towards 

 the absolute zero. Hence a gold wire would be more suited for 

 extrapolation than a platinum wire, because here the deviations 

 which we cannot but exjject, arc much smaller. 



Mathematics. — "A coi/r/rdt'ncc of orde t- t/ro and cfas.s two fortned 

 by conk's'. By Prof. J. de Vkies. 



For a twofold iidinite system of conies (congruence) ordi'P is called 

 the number of conies through an arbitrary point, class the number 

 of conies w^itli an arbitrary i-iglit line for bisecant. 



The congruences of order one aiid class one arise from the pro- 

 jectixe coordination of a net of planes to a net of quadrics^). Under 

 investigation were furthernKjre the congruences of order one and 

 class two and those, the conies of which cut a fixed conic twice "). 



In this communication the characteristic inunbers are deduced of 

 the congruence determined by the tangent planes of a (juadric Q^ 

 on the planes of a net [Q^'] of (_[uadrics to which they are project- 

 ively conjugate. 



2. To obtain this conjugalioji >ve ])rojcct the points P of (^^ out 

 of a fixed point 1\, of Q'~ on a plane 0. A projectivity between 

 the points P' of 4^ and the surfaces of | ^/' | furnishes then imme- 

 diately a projectivity IxMweeu [^/"] ^i''"' ^1'^' system [-r].^ of the 

 tangent planes rr of (}'-. 



To a pencil {Q-) in [_W'] coi-responds a range of [toints (/-'') in 



1) D. MoNTESANO, Su di un si.stoina linoare di coniclie ncllo sjiazin, Atti di 

 Torino, 1891 — 189iï, t. XXVll, p. (iGO. 



') M. PiEKi, Sopi'ii alcuiuï coiiti.i'iK'ii/.c di cuniclic, Alii ili Tofint), 180:2 — 1893, 

 t. XXVIII, p. 135. 



21 



Proceedings Royal Acad. Amsterdam. Vol. VII. 



