﻿72 Dr. Norman Campbell on the 



subject-matter of science is objective, that is the characteristic 

 of the objective c'hance which is physically measurable. 

 Chance is applicable only to events which contain an element 

 which is wholly and completely random to everybody *. 



6. We shall then base our further discussion on the 

 assumption that any physically significant chance (of the 

 happening of an event) is a measurable derived magnitude, 

 a property of the system concerned in that event, determined 

 by a linear numerical law relating the fundamental magni- 

 tudes, number of events and number of trials. It is thereby 

 implied that the " errors " from the law are random, for 

 otherwise the law would not be linear. The definition of 

 chance as the limiting ratio of the fundamental magnitudes 

 as they tend to infinity is identical with that given, if it is 

 known as an experimental fact that the magnitudes of the 

 errors fulfil certain conditions which need not be discussed 

 in detail here ; these conditions are not inconsistent with 

 the randomness of the errors. 



Chance as a fundamental magnitude. 



7. Another important question may be raised, again 

 suggested by the analogy with resistance, Resistance means 

 the derived magnitude defined by Ohm's law. But actually 

 resistance is measured nowadays, not as a derived, but as a 

 fundamental magnitude, in virtue of the Kirchhotf laws for 

 the combination of resistances in series and parallel f. Can 

 chance, though meaning the derived magnitude, be measured 

 independently as fundamental ? 



In order that a property may be measured as a funda- 

 mental magnitude, it is necessary that satisfactory definitions 

 of equality and of addition should be found (P. Ch. x.). 

 In addition, some numerical value must be assigned arbi- 

 trarily to some one property, which with all others can 



* In this sense the last figure of the logarithm is not wholly dictated 

 by chance ; for we know that there must be some regularity in the 

 distribution of the points about the straight line, even if we cannot say 

 exactly what it is. In the strictest sense, therefore, there is no such 

 thing as the chance of the last figure being 1. But there are events 

 which are, at present at least, wholly dictated by chance in this sense, 

 e. g. the disintegrations of a radioactive atom. Here I do not think 

 anyone has imagined what kind of regularity there can be, except the 

 falling of the plotted points about the straight line which determines 

 the chance. 



f Ultimately measured, that is to say, by the makers who calibrate 

 our resistance boxes. In the laboratory we use a method which is 

 essentially that of judgment of equality with a graduated instrument. 



