( 761 ) 



A^A^A,: I\v dcteniiiniii.ü; for cacli of tlie pairs of projective series of 

 points on each of llie bearers the point corresponding to the point 

 of intersection of the bearers reckoned to belong to the other series it 

 becomes evident that this conic tonches the sides in the centres, so that 

 it is the inscribed circle c". The point of contact being the point of 

 intersection L^ of /, and /',, the locus of this point is at the same 

 time the locus of the point of intersection of the corresponding rays 

 of the pencil (/j) of order one and the pencil {/\Y of order two 

 formed by the tangents /', of c', tinis a cnrve c^ of order three with 

 ()j as node and the tangents from (J^ to c^ i.e. the isotropic lines 

 tlirongh 0^ as nodal lines. This curve represented in tig. 4 touches 

 the sides of the triangle A^A^A^ in the centres and has the points at 



Fis. 4 



infinity of the sides as inflectional points; tlie inflectional asymptotes 

 run parallel to the sides at distances of four ninths of the height. 

 In normal coordinates its equation with respect to triangle .4,^3^1, is 



whilst the Pliicker numbers are 



n = 3 , d=l , c = , 

 7/1 zr: 4 , t =z , i = S . 



As is known we mean by the three characterizing numbers of a 

 simple infinite series of surfaces the numbers n, v, q indicating 

 successively how many surfaces of the series pass through any given 



53* 



