( 481 ) 



Cad mi tun, Magnesium, Calcium and iAIcrcury. Moreover tlic i)rin- 

 oiple of combination appears to point here to summational and 

 differential vibrations of the intensest (first) lines of the already known 

 series, so that we can account for the new lines without making 

 use of a spectral formula. In Paschen's recent paper on the systems 

 of series in the spectra of Zinc, Cadmium and Mercury it is parti- 

 cularly the very intense lines Zn 2138,6, Cd 2288,1 and Hg 1849, 

 which occur in combinations; they must be considered as first line 

 of a principal sei'ies, lying in the ultra-violet. This principal series 

 is indicated M by 1,5 S—mP, a second subordinate series being 

 indicated by IP — mS. The series 2,5 aS—?/?/^ is a differential vibration 

 of the lines of the principal series with the first line of the 2"'^ S.S. 

 2,5 S—mP=\{\,b S—mP) — (1,5 S—2P)\ — (2P— 2,5 S) 



— m^'' line P.S. — l^t line P.S. - l^t jjne H S.S. = 



= ;?^th line D.S. - 1st line II S.S. 

 In this I luive called 1^^ line II S.S. [m =. 2,5), what is con- 

 sidered the 2"^' line by Ritz. 



Mathematics. — ''On the conoids belonging to an arhitranj surface.'' 

 By Prof. Hk. de Vrtes. (1"^ part). 



§ 1. Among the examples current in Descriptive Geometry of 

 non-developable scrolls we meet the so-called right sphere conoids, 

 formed by all the lines which intersect a given directrix, run parallel 

 to a plane perpendicula» on that directrix, and touch a given sphere; 

 it is a surface of ordei four, which has the given directrix as well 

 as the line at infinity of the director plane as nodal lines, and the 

 points of intersection of these two straight lines with the sphere 

 as cuspidal points; the generatrices passing through these points coincide 

 namely in so-called torsal lines, distinguished from the other genera- 

 trices on account of the tangential planes coinciding in all their points. 



If we substitute for the sphere an arbitrary surface of order n, 

 then the right conoid appears belonging to this arbitrary surface, 

 which conoid seen from a mathematical point of view does not differ 

 from the scroll formed by all the lines intersecting two arbitrary 

 directrices r, , r, , crossing each other, and touching a surface ^/>" 

 of order n; on this surface some observations follow. 



§ 2. We suppose the surface 0" to be point general. A plane 



1) F. Paschen, Ann. d. Phys. 35, 1911, p. 863. 



