( 57 ) 



If the surfaces S^ and S^ have an ordinary contact in cf points, 

 the common tangent planes in these d points are ordinary double 

 tangent planes of the developable D circumscribing S^ and ^Sa ^). The 

 surfaces S\ and S\ will also have in ö points an ordinary contact. 



If the surfaces S^ and S^ have in x points a stationary contact 

 the tangent planes in these / points are stationary tangent planes 

 of the developable D^). The surfaces >S'i and S\ have thus also 

 in / points a stationary contact. 



So the rank of the curve of intersection d' of the surfaces S\ and 

 S\ is according to formula (A), just as the rank of the curve s, 

 r =z m^}i^ -\- 171^71^ — 2Ö -— 3/. 



The curve d' being the reciprocal polar figure of the circum- 

 scribing developable D, the rank of D is equal to the rank of d'. 

 Whence the theorem: 



For two arbitrary/ algebraic surfaces the rank of the curve of 

 intersection is equal to the rank of the circumscribing developable. 



Here we have supposed that the points of contact ö and x ^I'e 

 ordinary points on both surfaces and the tangent planes ordinary 

 tangent planes in tliese points^). 



1) Versluys, Mém. de Liège. 3™*? série t. VI. De l'iiifluence d'un contact etc. 



2) Versluys, loc. cit. 

 8) Versluys, loc. cit. 



(June 21, 1905). 



