6 On certain kinds of Groups or Series. [CHAP. i. 



of things which can be traced almost everywhere, to a 

 greater or less extent, throughout the whole field of our ex 

 perience. Fires, shipwrecks, yields of harvest, births, mar 

 riages, suicides; it scarcely seems to matter what feature we 

 single out for observation 1 . The irregularity of the single 

 instances diminishes when we take a large number, and at 

 last seems for all practical purposes to disappear. 



In speaking of the effect of the average in thus diminish-! 

 ing the irregularities which present themselves in the details,, 

 the attention of the student must be prominently directed to 

 the point, that it is not the absolute but the relative irregu 

 larities which thus tend to diminish without limit. This 

 idea will be familiar enough to the mathematician, but t 

 others it may require some reflection in order to grasp i 

 clearly. The absolute divergences and irregularities, so fa 

 from diminishing, show a disposition to increase, and this (i 

 may be) without limit, though their relative importance show 

 a corresponding disposition to diminish without limit. Thu 

 in the case of tossing a penny, if we take a few throws, sa 

 ten, it is decidedly unlikely that there should be a differenc 

 of six between the numbers of heads and tails; that is, tha 



1 The following statistics will give (fluctuation 1*85), and the numbe 



a fair idea of the wide range of ex- of pounds of manufactured tobacc 



perience over which such regularity taken for home consumption (fluctug 



is found to exist: &quot;As illustrations tion 1-89); or out-door paupers (flu 



of equal amounts of fluctuation from tuation 3-45) and tonnage of Britis 



totally dissimilar causes, take the vessels entered in ballast (fluctuatio 



deaths in the West district of London 3-43), &c.&quot; [Extracted from a pap* 



in seven years (fluctuation 13-66), in the Journal of the Statistical S&amp;lt; 



and offences against the person (flue- ciety, by Mr Guy, March, 1858 ; tl 



tuation 13-61); or deaths from apo- fluctuation here given is a me: 



plexy (fluctuation 5-54), and offences sure of the amount of irregularit; 



against property, without violence that is of departure from the averag 



(fluctuation 5-48) ; or students regis- estimated in a way which wall 



tered at the College of Surgeons described hereafter.] 



