46 DISCONTINUOUS VARIATION. 



species would become an almost hopeless task. The 

 degree to which local races may vary is well shown by 

 some of Ludwig's determinations. For instance,* four 

 groups of specimens of Torilis anthriscus, obtained 

 from various spots near Schmalkalden, had the follow- 

 ing numbers of branches of the main umbels : 



34 5 67 89 10 11 12 13 Total 



In the first group, the 8 branch form occurred the 

 most frequently, the variations from this number being 

 distributed more or less evenly around it. In the next 

 group, the 10 branch form was the commonest; in the 

 third group the 8 and 10 branch forms were both com- 

 mon, whilst in the last group of all, collected in a wood 

 at Wolfsberg, near to Schmalkalden, a quite distinct 

 race having five branches presented itself. 



In determining the variations of a plant, therefore, 

 it is probably best to obtain a very large amount of ma- 

 terial, from various sources, and submit this to examina- 

 tion. Though the curve thereby obtained may be very 

 composite, yet at least it will indicate something as 

 to the range of variation of the flower in many of its 

 local races, and also what number of branches or other 

 parts occur on the whole most frequently. For in- 

 stance, Ludwig f has had made enumerations of the 

 number of ray florets in 17,000 specimens of the Ox-eye 

 Daisy, Chrysanthemum leucanthemum. The material 



*Bot. Centralb., vol. Ixiv. p. 40. 

 fBot. Centralb., vol. Ixiv. p. 1, 1895. 



