REMARKS 



ON THE FUNDAMENTAL PRINCIPLE OF 

 THE THEORY OF PROBABILITIES*. 



I WISH to make an addition to the remarks on the foundation 

 of the theory of probabilities which were offered some years since 

 to the notice of the Societyf. My intention in doing so is to 

 consider, in what way the proposition, which I conceive to be 

 the fundamental principle of the theory, may be the most clearly 

 and conveniently expressed. This principle may for the moment 

 be thus stated : " On a long run of similar trials, every possible 

 event tends ultimately to recur in a definite ratio of frequency." 

 Our conviction of the truth of this proposition is, I think, intui- 

 tive, the word being used, as in all similar cases, with reference 

 to the intuitions of a mind, which has fully and clearly appre- 

 hended the subject before it, and to which therefore to have 

 arrived at the truth and to perceive that it has done so are 

 inseparable elements of the same act of thought. If we endeavour 

 to translate the proposition just stated into ordinary philosophical 

 language, we may in the first place remark that the phrase 

 "similar trials," expresses the notion of a group or genus of 

 phenomena to which the different results are subordinated as 

 distinct species. If the trial is the throwing of a die, this may be 

 regarded as the generic character; the occurrence of ace, deuce, 

 &c. constituting different species. Thus much is clear ; but it 

 is less obvious how the idea expressed by a " long run of trials" 

 in " definite series of experiments," and the like, is to be ex- 

 pressed, so as to make the analogy between the fundamental 

 principle of the theory of probabilities and those of other sciences 

 more obvious than it has hitherto been. The idea in question 



* Transactions of the Cambridge Philosophical Society, Vol. ix. p. 605. [Read 

 Nov. 13, 1854.] 



t Transactions of the Cambridge Philosophical Society, Vol. vm. p. r. [p. i of 

 this volume.] 



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