( o45 ) 



tour axes given in the first row are axes OE for C'g and C'l,, axes 



4 



OR for C'l,, C'la and C.,,\ moreover the coefficients 2,-, 2 of 



o 



4 

 2 /?, - R,2R indicate that the quadruples of coordinates appearing 



o 



in this row relate to the point which is obtained by multiplying 

 the observed axis R of C\^, C'\^, C,^ as far as the length from 



goes by 2, |, 2. 



With the preceding we have pointed out the position of each axis 

 of one of the cells of the three nets (Cj, (CiJ, (CjJ with reference 

 to each of the two systems of coordinates and so we have furnished 

 in connection with the preceding the material by which it is possible 

 to deduce easily all the spacial sections of these three regular nets 

 connected in a simple way with these axes. To give an example 

 here already we observe that a- space normal to one of the twelve 

 axes Fg is normal to an axis K ïov all the cells of the net (Ci,); 

 if it now proves possible to determine such a space in such a way 

 that it is equally distant from the centres of all the cells C^ which 

 are intersected, then in the intersecting space a more or less regular 

 space- filling is generated by a selfsame body in three different positions. 



In a future part we hope to commence with the determination 

 of the remarkable spacial sections of the nets (Cj, (6\g), (C,J. 



Mathematics. — ''Contribution to the knowledge of the surfaces 

 with constant mean curvature" . By Dr. Z, P. Bouman. (Com- 

 municated by Prof. Jan de Vries). 



(Communicated in the meeting of January 25, 1908). 



§ 1. As is known the great difficulty connected with the study 

 of the surfaces with constant mean curvature is the integration of 

 the differential equation 



^r 1- :r = sinh 6 . COsk 6. 



The course followed here leads to two simultaneous partial diffe- 

 rential equations of order one and of degree two. 



In Gauss' symbols the value of the mean curvature^ of a surface 

 is indicated by 



2 i^i>' — ED'' — GD 



~ EG — F' ' 



