344 



order that the curve may represent a series of probability 

 curves with changing moduli with the value \j = A for a,- = 0. 



It is therefore inappropriate in such case to introduce 

 the term x m , or in other words to make ft or m other than 

 zero, if the y axis is to coincide with the maximum value 

 of the ordinate. On the other hand, if the ordinate to the 

 curve at its origin is to be zero, the term ft log «, with ft 

 positive, ensures this, since log = - oo . It is obvious 

 that suitable manipulation of the values of 7, s, a and ft 

 enables the curve to be fitted to a very wide range of 

 results, without departing from the conception that it may 

 be regarded as being built up of elements of ordinary 

 probability curves with different moduli. 



A close examination of a large number of graduated 

 statistical curves will disclose the fact that the variation 

 of frequency with change of the value of the variable can- 

 not ordinarily be subsumed under the conception of a curve 

 of unchanging modulus, or even of moduli progressively 

 changing in any very uniform manner. 



2. Synthesis of the curve.— Neglecting the general factor 

 A in expression (1) the curve represented by it has ordinates 

 which are the product of two variable factors, viz. .v lu and 



