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VII. The Measurement of Chance. 

 By Norman Campbell, Sc.D.* 



Summary. 



IT is maintained that the chance of an event happening 

 is always a physical property of a system, measured 

 by a process of derived measurement involving the two 

 fundamental magnitudes — number of events and number 

 of trials. 



Chances are not measurable by a process of fundamental 

 measurement. But the calculation of chances is analogous 

 to fundamental measurement. It is usually theoretical, and 

 is valuable only in so far as the calculated chances are 

 confirmed by measurement. 



When a proposition concerns a system characterized by a 

 chance, it may sometimes (but by no means always) be 

 regarded as having a definite probability determined by that 

 chance. The probability of propositions which do not 

 concern systems characterized by chances has nothing: to do 

 Avi tli chance. 



1* It is generally recognized that there are two kinds of 

 " probability.'-' There is (1) the probability (of the 

 happening) of events, and (2) the probability (of the truth) 

 of propositions. Etymologically the term belongs more 

 properly to the kind second of probability, and it will be 

 confined to that kind in this paper. For the first kind, the 

 term " chance,''' often used in some connexions as a synonym 

 of probability, is available. Accordingly we shall speak 

 throughout of the chance of an event happening and of the 

 probability of a proposition being true. 



Various opinions have been entertained concerning the 

 relation between chance and probability and between the 

 methods of measuring them. Some have held that chance, 

 some that probability, is the more fundamental conception, 

 and that the measurement of the less fundamental depends 

 on that of the more fundamental conception. Others have 

 held that only one of the two, or neither, is measurable. 

 The conclusion towards which this paper is directed is that 

 chance, in the sense primarily important to physics, is a phy- 

 sical property measurable by ordinary physical measurement. 

 This view is similar to that held by Venn ; indeed, it is 



* Communicated by the Author. 

 F2 



