Laws of Fluctuations 731 



scale with sugar in beets and sugar-cane, with 

 -starch in potatoes and in other instances. 

 These figures are also found to-f oUow the same 

 law. 



All qualities which are seen to increase and 

 to decrease may be dealt with in the same man- 

 ner, if a standard unit for their measure- 

 ment can be fixed. Even the colors of flowers 

 may not escape our inquiry. 



If we now compare the lines, compiled from 

 the most divergent cases, they will be found to 

 exhibit the same features in the main. Ordi- 

 narily the curve is symmetrical, the line sloping 

 down on both sides after the same manner. But 

 it is not at all rare that the inclination is 

 steep on one side and gradual on the other. This 

 is noticeably the case if the observations relate 

 to numbers, the average of which is near zero. 

 Here of course the allowance for variation is 

 only small on one side, while it may increase 

 without distinct limits on the alternate slope. 

 So it is for instance with the numbers of ray- 

 florets in the examples given. Such divergent 

 cases, however, are to be considered only as ex- 

 ceptions to the rule, due to some unknown cause. 



Heretofore we have discussed the empirical 

 side of the problem only. For the purpose 

 of experimental study of questions of hered- 

 ity this is ordinarily quite sufficient. The in- 



