Laws of Fluctuations 739 



heads in our particular case. It is the 

 series to which we have already alluded 

 when dealing with the arrangement of the leaves 

 on the twisted teasels. It commences with 

 1 and 2 and each following figure is equal to 

 the sum of its two precedents. The most com- 

 mon figures are 3, 5, 8, 13, 18, 21, higher cases 

 seldom coming under observation. Now the 

 secondary summits of the ray-curves of the 

 composites are seen to agree, as a rule, with 

 these figTires. Other instances could readily be 

 given. 



Our second heading includes those cases 

 which exhibit two summits of equal or nearly 

 equal height. Such cases occur when dif- 

 ferent races are mixed, each retaining its own 

 average and its own curve-summit. We have al- 

 ready demonstrated such a case when dealing 

 with the origin of our double corn-chrysanthe- 

 mum. The wild species culminates with 13 rays, 

 and the grandiflomm variety with 21. Often 

 the latter is found to be impure, being mixed 

 with the typical species to a varying extent. 

 This is not easily ascertained by a casual in- 

 spection of the cultures, but the true condition 

 will promptly betray itself, if curves are con- 

 structed. In this way curves may in many in- 

 stances be made use of to discover mixed races. 



Double curves mav also result from the inves- 



