94 Modes of establishing the Groups or Series. [CHAP. iv. 



of such series. But it is not possible to keep the two enquiries 

 apart, for here, at any rate, the old maxim prevails that to 

 know a thing we must know its causes. Recur for a minute 

 to the considerations of the last chapter. We there saw 

 that there was a large class of events, the conditions of pro 

 duction of which could be said to consist of (1) a comparatively 

 few nearly unchangeable elements, and (2) a vast number 

 of independent and very changeable elements. At least if 

 there were any other elements besides these, we are assumed 

 either to make special allowance for them, or to omit them 

 from our enquiry. Now in certain cases, such as games of 

 chance, the unchangeable elements may without practical 

 error be regarded as really unchangeable throughout any 

 range of time and space. Hence, as a result, the deductive 

 method of treatment becomes in their case at once the most 

 simple, natural, and conclusive ; but, as a further consequence, 

 the statistics of the events, if we choose to appeal to them, 

 may be collected ad libitum with better and better ap 

 proximation to truth. On the other hand, in all social 

 applications of Probability, the unchangeable causes can only 

 be regarded as really unchangeable under many qualifica 

 tions. We know little or nothing of them directly ; they are 

 often in reality numerous, indeterminate, and fluctuating; 

 and it is only under the guarantee of stringent restrictions of 

 time and place, that we can with any safety attribute to 

 them sufficient fixity to justify our theory. Hence, as a 

 result, the deductive method, under whatever name it may 

 go, becomes totally inapplicable both in theory and practice ; 

 and, as a further consequence, the appeal to statistics has to 

 be made with the caution in mind that we shall do mischief 

 rather than good if we go on collecting too many of them. 



19. The results of the last two chapters may be 

 summed up as follows : We have extended the conception 



