( 573 ) 



that the deviations for a part considerably exceed the limits ofaccu- 

 rateness of the statements. 



It should be observed that the charts refer to currents near the 

 surface, whereas the values of the table derived from our observations 

 refer to a depth of 5 M. 



Finally we may mention that the observations at station H2 up 

 till now have been continued in the same way, that is to say, they 

 are still made every quarter of a year, as far as possible, during 

 24 hours. Moreover, owing to the kind co-operation of His 

 Excellency the Minister of Marine, a current-meter of Pettkrsson has 

 been placed on the lightship "Noord-Hinder", with which since 

 November 1906 daily, in so far as the state of the weather permits, 

 with intervals of three hours, measurements at various depths ate 

 made by the ordinary staff of the lightship. The lists of observation 

 are forwarded to the "Rijksinstituut" and promise to yield important 

 material, especially for the inquiry into the way in which the tidal 

 and residual currents differ in layers of different depth. 



Mathematics. "The locus of the pairs of common points of 



n-\-l pencils of {n — lydimensional varieties in a space of 

 n dimensions." By Dr. F. Schuh. 



(Communicated by Prof. P. H. Schoute). 



1. Let ( Vi) 0' = 1, 2, . . . , n + 1) be n -f 1 pencils of (n -- 1)- 

 dimensional varieties in the space of operation Sp n of n dimensions and 

 let Vi be the order of the varieties F;of the pencil (Vi). Let moreover 

 a t be the number of points of intersection of the n varieties 

 V lt V t , ..., Vi- U Vi+ i,r« + 2, ... ,r„ + i not of necessity lying in 

 the base-varieties. 



When considering the locus of pairs of points P,P' through which 

 a variety of each of the pencils passes we have exclusively such 

 pairs in view of which neither of the two points lies of necessity 

 on a base-variety of one of the pencils and we call the locus thus 

 arrived at the locus proper L. 



We determine the order of L out of its points of intersection with 

 an arbitrary right line /. To this end we take on /an arbitrary point 

 Qi2...n and we bring though it varieties V lt V t ,V t , . . ,V„, having 

 a n _l_i — 1 points of intersection not lying on Qi 2 .. n and the base- 

 varieties. Through each of those points we bring a V n + x and arrive 

 in this way at a„+i — 1 varieties V n +\ intersecting together line / 

 in (</„+i — 1) /•„ + ! points Qn+i-Soto Qi2...« correspond {fln+\ — 1)^+1 

 points Qn + i- 



