( 2(33 ) 



1",, ar.d both pencils contain at the same time the ray at infinity 

 of the plane ~JI7 1 he latter is a line through which the bitangen- 

 tial planes of C^ pass; the point in 2^ corresponding to it is /)„. So 

 the point Cu is found by constructing the plane T'^ ^T-i; D^ and 

 determining its point of intersection with K-\, . 



Physics. — „On the vihraiions of electrified systems, placed in a 

 magnetic field. A contribniion to the tltcory of the Zeeman- 

 rffect". By Prof. H. A. Lorentz. 



(Will be published in the Proceedings of the next meeting.) 



Mathematics. — „On Trinodal Qnartics". By Prof. Jan de Vkies. 



1. If we consider the nodes 7),, D„, D.^ of a trinodal plane 

 quartic as the vertices of a triangle of reference, that curve has an 

 equation of the form : 



r^ = «n ^2^ ^•3''^ + ^22 ■'•3^ •'•1* + «33 -^'l- •^■2® + 



+ 2 3-1 3-2 .rg («12 ■'T-i + «23 '«l + «31 ^2) = . . (1) 



The equations 



02 = ^'1 -''2 ■'■■6 + h -'S ^'1 + ^-3 a'l .'s = , . . . . (2) 



W.2 = c'l .12 .fg + C.2 x-i .i'l + f3 .Ci .r.2 = (:5) 



then represent two conies passing through the nodes. 



If the coefficients of these equations satisfy the conditions 



^1 <■] = "11 1 ^2 ^2 = «22 ) ^3 «'s = «33 1 • • • (4) 

 it is evident from the identity 



that the two new couples of points common to F^ and each of the 

 two associated conies (f>„ and 'f2 ^^^ situated on the right line 

 corresponding to the equation 



-(^'l'-2 + ^'2''l-2«io).'-3 = ((3) 



IS* 



