with Remarks on the Law of Frequency of Error. 39 



these two processes have to be protracted, as in figure 2, 

 the unit of vertical measurement in the case of a series of bino- 



700 soo goo 



mial grades will be a single grade, or, what comes to the same 

 tiling, the difference of the effect produced by the plus and 

 minus phase of any one of the alternative elements, upon the 

 value of the whole. The unit of the exponential curve will 

 be q— m of fig. 1, or the probable error. This latter unit is 

 equally applicable to what we may call the binomial ogive, which 

 is the curve drawn with a free hand through the grades. The 

 •justification for such a conception as a binomial ogive will be 

 fully established further on. Suffice it for the present to re- 

 mark that, by the adoption of a unit of this kind, the middle 

 portion of a binomial ogive of 999 elements is compared in the 

 figure with one of 17. 



The first three of the above-mentioned conditions may occur 

 in games of chance, but they assuredly do not occur in vital and 

 social phenomena ; nevertheless it has been found in numerous 



