IECT. 16.] Arrangement and Formation of the Series. 45 



reneous elements is illustrated by the figure annexed, of 

 :ourse in a very exaggerated form. 



16. In the above case the nature of the heterogeneity, 

 and the reasons why the statistics should be so collected and 

 arranged as to avoid it, seemed tolerably obvious. It will be 

 seen still more plainly if we take a parallel case drawn from 

 artificial proceedings. Suppose that after a man had fired a 

 few thousand shots at a certain spot, say a wafer fixed some 

 where on a wall, the position of the spot at which he aims 

 were shifted, and he fired a few thousand more shots at the 

 wafer in its new position. Now let us collect and arrange all 

 the shots of both series in the order of their departure from 

 either of the centres, say the new one. Here we should 

 really be mingling together two discordant sets of elements, 

 either of which, if kept apart from the other, would have 

 been of a simple and homogeneous character. We should 

 find, in consequence, that the resultant law of error betrayed 

 its composite or heterogeneous origin by a glaring departure 

 from the customary form, somewhat after the fashion indi 

 cated in the above diagram. 



The instance of the English and French heights resem 

 bles the one just given, but falls far short of it in the strin 

 gency with which the requisite conditions are secured. The 

 fact is we have not here got the most suitable requirements, 

 viz. a group consisting of a few fixed causes supplemented by 

 innumerable little disturbing influences. What we call a 

 nation is really a highly artificial body, the members of 



