( 542 ) 



Fig. 4. 



rotation of multiples of 60° round ()', for then ,r 5 -j- y* and ij(if 

 are transformed into themselves. 

 Out of the equation 



3.c' 



SM 3<£> 



± 2?^ l - r * 



on polar coordinates it is evident that the curve c' (with the excep- 

 tion of its four isolated points) is included between the circles de- 

 scribed out of O with the radii 1 and —1/3. 



If we pass from the Jocus of the cusps to the parabolic curve of 

 >S S we must notice that the last curve has the node of S 3 as 

 threefold point, because c* has separated itself three times from the 

 locus c 1 '. So this parabolic curve is an s' of order nine, a result 

 which will presently be arrived at in an other way. 



We shall give without wishing in the least to exhaust this 



case of the six basepoints situated on a conic - - some degenerations 

 of the remaining curve c" corresponding to some definite coincidences 

 of the basepoints. 



a) The cases (2,2,2), (4,2), (6). If the six basepoints coincide 

 two by two in three points of the conic, then c" consists of the sides 

 of the triangle of the basepoints counted double, originating from 

 compound cubies with a double line; there is not a locus proper. 

 In reality the case (2,2,2) of a conic touching in three points cannot 

 occur for a genuine cubic with a cusp. 



