Laws of Fluctuations 1^1 



the case of symmetrical curves, perhaps in two 

 figures. 



Also in comparing different curves with one 

 another, the quartiles are of great importance. 

 Whenever an empirical fluctuation-curve is to be 

 compared with the theoretical form, or when 

 two or more cases of variability are to be con- 

 sidered under one head, the lines are to be 

 drawn on the same base. It is manifest that 

 the averages must be brought upon the same 

 ordinate, but as to the steepness of the line, 

 much depends on the manner of plotting. Here 

 we must remember that the mutual distance of 

 the ordinates has been a wholly arbitrary 

 one in all our previous considerations. And 

 so it is, as long as only one curve is considered 

 at a time. But as soon as two are to be com- 

 pared, it is obvious that free choice is no longer 

 allowed. The comparison must be made 

 on a common basis, and to this effect the quar- 

 tiles must be brought together. They are to lie 

 on the same ordinates. If this is done, each 

 division of the base corresponds to the same 

 proportionate number of individuals, and a 

 complete comparison is made possible. 



On the ground of such a comparison we may 

 thus assert that fluctuations, however different 

 the organs or qualities observed, are the same 

 whenever their curves are seen to overlap one 



