Laws of Fluctuations 111 



stain from the use of methods which are not 

 necessary for the furtherance of experimental 

 work. 



Fortunately, Quetelet's law is a very clear 

 and simple one, and quite sufficient for our con- 

 siderations. It claims that for biologic phe- 

 nomena the deviations from the average comply 

 with the same laws as the deviations from the 

 average in any other case, if ruled by chance 

 only. The meaning of this assertion will be- 

 come clear by a further discussion of the facts. 



First of- all, fluctuating variability is an al- 

 most universal phenomenon. Every organ and 

 every quality may exhibit it. Some are very 

 variable, while others seem quite constant. 

 Shape and size vary almost indefinitely, and the 

 chemical composition is subject to the same law, 

 as is well known for the amount of sugar in 

 sugar-beets. Numbers are of course less liable 

 to changes, but the numbers of the rays of um- 

 bels, or ray-florets in the composites, of pairs of 

 blades in pinnate leaves, and even of stamens 

 and carpels are known to be often exceedingly 

 variable. The smaller numbers however, are 

 more constant, and deviations from the quinate 

 structure of flowers are rare. Complicated 

 structures are generally capable of only slight 

 deviations. 



From a broad point of view, fluctuating varia- 



