SECT. 4.] Arrangement and Formation of the Series. 27 



Here the statistical elements under consideration are, as 

 regards their origin at any rate, optional or brought about 

 by human choice. They would, therefore, be commonly 

 described as being mainly artificial, but their results ulti 

 mately altogether a matter of chance. 



Again, in the second place, we might take the accurate 

 measurements i.e. the actual magnitudes themselves, of 

 a great many natural objects, belonging to the same genus 

 or class ; such as the cases, already referred to, of the heights, 

 or other characteristics of the inhabitants of any district. 

 Here human volition or intervention of any kind seem to 

 have little or nothing to do with the matter. It is optional 

 with us to collect the measures, but the things measured are 

 quite outside our control. They would therefore be com 

 monly described as being altogether the production of nature, 

 and it would not be supposed that in strictness chance had 

 anything whatever to do with the matter. 



In the third place, the result at which we are aiming 

 may be some fixed magnitude, one and the same in each 

 of our successive attempts, so that if our measurements 

 were rigidly accurate we should merely obtain the same 

 result repeated over and over again. But since all our 

 methods of attaining our aims are practically subject to 

 innumerable imperfections, the results actually obtained 

 will depart more or less, in almost every case, from the 

 real and fixed value which we are trying to secure. They 

 will be sometimes more wide of the mark, sometimes less 

 so, the worse attempts being of course the less frequent. 

 If a man aims at a target he will seldom or never hit it 

 precisely in the centre, but his good shots will be more 1 



1 That is they will be more densely cessive circle, the number of shot 

 aggregated. If a space the size of the marks which it contains will be suc- 

 bulVs-eye be examined in each sue- cessively less. The actual number 



