SECT. 28.] Fallacies. 361 



ance in the proportion will be brought about simply by the 

 continual influx of fresh terms in the series. These will in 

 the long run neutralize the disturbance, not by any special 

 adaptation, as it were, for the purpose, but by the mere 

 weight of their overwhelming numbers. At every stage 

 therefore, in the succession, whatever might have been the 

 number and nature of the preceding terms, it will still be 

 true to say that one in ten of the terms will be an X. 



If we had to do only with a finite number of terms, 

 however large that number might be, such a disturbance as 

 we have spoken of would, it is true, need a special alteration 

 in the subsequent proportions to neutralize its effects. But 

 when we have to do with an infinite number of terms, this 

 is not the case ; the limit of the series, which is what we 

 then have to deal with, is unaffected by these temporary 

 disturbances. In the continued progress of the series we 

 shall find, as a matter of fact, more and more of such dis 

 turbances, and these of a more and more exceptional character. 

 But whatever the point we may occupy at any time, if we 

 look forward or backward into the indefinite extension of the 

 series, we shall still see that the ultimate limit to the pro 

 portion in which its terms are arranged remains the same ; 

 and it is with this limit, as above mentioned, that we are 

 concerned in the strict rules of Probability. 



The most familiar example, perhaps, of this kind is that 

 of tossing up a penny. Suppose we have had four heads in 

 succession; people 1 have tolerably realized by now that head 

 the fifth time is still an even chance, as head was each 



1 Except indeed the gamblers. Ac- it will not be repeated at the next 



cording to a gambling acquaintance coup: this is the groundwork of all 



whom Houdin, the conjurer, describes theories of probabilities and is term- 



himself as having met at Spa, &quot;the ed the maturity of chances&quot; (Card- 



oftener a particular combination has sharping exposed, p. 85). 

 occurred the more certain it is that 



