( H17 ) 



The magnetisation of the speetral lines enables us to determine the 

 ma.xinuim value of the force with phenomena varying rapidly with 

 the time, and with non-uniform fields. 



h\ some cases it is of great importance to follow the behaviour of 

 a spectral phenomenon with dilferent strengths of field. The above 

 described method miglit then be called t/ie method of the non-uniforin 

 field. 



In a future commujiieatiun 1 hope to stutly in this manner the 

 fisi/ininetrij of the separation of spectral lines in weak magnetic 

 fields, predicted from theory by Voigt. On a former occasion I have 

 communicated some experiments giving rather convincing evidence of 

 the existence of this asymmetry '). 



In the mean time, I think that the developments lately given by 

 LoHEXTZ ") make it desirable to corroborate the reasons for accepting 

 the existence of this extremely small asymmetry. 



Mathematics. — "Some properties of penciL- of algebraic curves". 

 l>y Prof. Jan de Vries. 



§ 1. Let A be one of the n'' basepoints of a pencil (c") of curves 

 c" of order n, B one of the remaining basepoints. If we make to 

 correspond to each f' the right line c' touching c" in A, then we 

 get as product of the projective pencils (c") and (c'), a curve 1\ of 

 order (?t -|- 1) forming the locus of the tangential points of A, i. e. 

 of the points which are determined by each c" on its tangent c^. 

 This tangential curve has in A a threefold point where it is touched 

 by the inflectional tangents of three c" having in A an inflection ; 

 it has been considered for the first time hy Emil Weyr (Sitz. Ber. 

 Akad. in Wien, LXI, 82). 



I shall now consider more in general the locus Tm of the )/i"> 

 tangential points of A. The order of this curve is to be represented 

 by t(»;). whilst «(/») and ^{m) are to indicate the number of branches 

 which Tm has in A and B. 



Prof. P. H. ScHOUTE has drawn my attention to a paper inserted 

 by him in the Coniptes Rendus de l'Académie des sciences, tome CI, 

 736, where the corresponding curve is treated for a cubic pencil. 

 I found that the numbers obtained there for ?i ^ 3 appear from the 

 results to be deduced here. 



1) Zeeman. Tfiese Proceedings, December 1899. 

 '^) LoRENTz. These Proceedings, December 1905. 



