SECT. 16.] Modes of establishing the Groups or Series. 91 



assert with some confidence that these conditions cannot well 

 be altogether independent of the health, circumstances, man 

 ners aod customs, &c. (to express oneself in the vaguest way) 

 of the parents ; and if once these influencing elements are 

 introduced, even as very minute factors, the results cease to 

 be dependent only on fixed and permanent conditions. We 

 are at once letting in other conditions, which, if they also 

 possess the characteristics that distinguish Probability (an 

 exceedingly questionable assumption), must have that fact 

 specially proved about them. That this should be the case 

 indeed seems not merely questionable, but almost certainly 

 impossible ; for these conditions partaking of the nature of 

 what we term generally, Progress and Civilization, cannot be 

 expected to show any permanent disposition to hover about 

 an average. 



16. The reader who is familiar with Probability is of 

 course acquainted with the celebrated theorem of James 

 Bernoulli. This theorem, of which the examples just ad 

 duced are merely particular cases, is generally expressed 

 somewhat as follows : in the long run all events will tend 

 to occur with a relative frequency proportional to their 

 objective probabilities. With the mathematical proof of this 

 theorem we need not trouble ourselves, as it lies outside the 

 province of this work; but indeed if there is any value in the 

 foregoing criticism, the basis on which the mathematics rest 

 is faulty, owing to there being really nothing which we can 

 with propriety call an objective probability. 



If one might judge by the interpretation and uses to 



something to do with the sex of the to 100 does not seem by any means 



offspring. If this were so, it would universal in all countries or at all 



quite bear out the above remarks. times. For various statistical tables 



As a matter of fact, it should be on the subject see Quetelet, Physique 



observed, that the proportion of 106 Sociale, Vol. i. 166, 173, 238. 



