738 ' Fluctuations 



another. Furthermore, whenever an empirical 

 curve agrees in this manner with the theoretical 

 one, the fluctuation agrees with Quetelet's law, 

 and may be ascribed to quite ordinary and uni- 

 versal causes. But if it seems to diverge from 

 this line, the cause of this divergence should be 

 inquired into. 



Such abnormal curves occur from time to 

 time, but are rare. Unsymmetrical instances 

 have already been alluded to, and seem to be 

 quite frequent. Another deviation from the 

 rule is the presence of more than one summit. 

 This case falls under two headings. If the ray- 

 florets of a composite are counted, and the fig- 

 ures brought into a curve, a prominent summit 

 usually corresponds to the average. But next 

 to this, and on both sides, smaller summits are 

 to be seen. On a close inspection these summits 

 are observed to fall on the same ordinates, on 

 which, in the case of allied species, the main 

 apex lies. The specific character of one form 

 is thus repeated as a secondary character on an 

 allied species. Ludwig discovered that these 

 secondary summits comply with the rule discov- 

 ered by Braun and Schimper, stating the rela- 

 tion of the subsequent figures of the series. 

 This series gives the terms of the dis- 

 position of leaves in general, and of the 

 bracts and flowers on the composite flower- 



