472 Theory of the Average. [CHAP. xix. 



great certainty as by any a priori rule. That is, if we took 

 another hundred thousand measurements from the same 

 class of population, we should feel secure that the average 

 would not be altered by any magnitude which our measuring 

 instruments could practically appreciate. 



8. But the mere assignment of the mean or central 

 value does not here, any more than in the preceding case, 

 give us all that we want to know. It might so happen that 

 the mean height of two populations was the same, but that 

 the law of dispersion about that mean was very different : 

 so that a man who in one series was an exceptional giant or 

 dwarf should, in the other, be in no wise remarkable. 



To explain the process of thus determining the actual 

 magnitude of the dispersion would demand too much mathe 

 matical detail ; but some indication may be given. What 

 we have to do is to determine the constant h in the equation 1 



7 

 V 



TT 



In technical language, what we have to do is 



to determine the modulus of this equation. The quantity ^ 



in the above expression is called the modulus. It measures 

 the degree of contraction or dispersion about the mean 

 indicated by this equation. When it is large the dispersion 

 is considerable; that is the magnitudes are not closely 



1 When first referred to, the genera I as usual, by unity. In this form of 

 form of this equation was given (v. p. expression h is a quantity of the 

 29). The special form here assigned, order x~ l ; for lix is to be a numerical 



in which * is substituted for A t is ^^ Banding as it does as an 



fj-rr index. The modulus, being the reci- 



commonly employed in Probability, procal of this, is of the same order 



because the integral of ydx, between f quantities as the errors themselves. 



+ 00 and- 30, becomes equal to unity. ^ n fact, if we multiply it by 4769... 



That is, the sum of all the mutually we nave the so-called probable 



exclusive possibilities is represented, error. 



