454 Averages. [CHAP. xvni. 



them. In fact, if they be averages of a few only they 

 most probably will not have anything thus corresponding 

 to them. Anything answering to a type can only be sought 

 in the limit towards which they ultimately tend, for this 

 limit coincides with the fixed point or object aimed at. 



17. Fully admitting the great value and interest of 

 Quetelet s work in this direction, he was certainly the first 

 to direct public attention to the fact that so many classes of 

 natural objects display the same characteristic property, it 

 nevertheless does not seem desirable to attempt to mark 

 such a distinction by any special use of these technical 

 terms. The objections are principally the two following. 



In the first place, a single antithesis, like this between 

 an average and a mean, appears to suggest a very much 

 simpler state of things than is actually found to exist in 

 nature. A reference to the three classes of things just 

 mentioned, and a consideration of the wide range and di 

 versity included in each of them, will serve to remind us 

 not only of the very gradual and insensible advance from 

 what is thus regarded as fictitious to what is claimed as 

 real ; but also of the important fact that whereas the real 

 type may be of a fluctuating and evanescent character, the 

 fiction may (as in games of chance) be apparently fixed 

 for ever. Provided only that the conditions of production 

 remain stable, averages of large numbers will always prac 

 tically present much the same general characteristics. The 

 far more important distinction lies between the average of 

 a few, with its fluctuating values and very imperfect and 

 occasional attainment of its ultimate goal, and the average 

 of many and its gradually close approximation to its ulti 

 mate value : i.e. to its objective point of aim if there happen 

 to be such. 



Then, again, the considerations adduced in this chapter 



