﻿Measurement of Chance. 69 



straight line passing through the origin shows that a 

 numerical law of a certain form holds, and therefore that the 

 die is characterized by a single definite magnitude, which is 

 what we mean by resistance ; the slope of the line tells us 

 the numerical value of this magnitude. When we proceed 

 to measure the chance of turning up six, we make several 

 groups of trials, measure in each group the number of trials 

 and the number of those in which six turns up. We plot 

 these two fundamental magnitudes against each other, and 

 find that a straight line can be drawn through (or among) 

 the points. The fact that the graph is straight and passes 

 through the origin tells us that the die is characterized 

 by a definite magnitude, which is what we mean by chance ; 

 the slope of the line tells us the numerical value of this 

 magnitude. 



3. The resemblance is exact in all essentials. But as the 

 conclusion that chance is an ordinary physical magnitude 

 does not seem to be universally accepted, some objections 

 may be considered. 



The first may be (though I am not sure that it will be) 

 raised by those who denounce the "frequency theory " of 

 probability. They might say that, though the derived 

 magnitude, estimated in the manner described, is a true or 

 approximate measure of the chance, yet it is not what is 

 meant by the chance — that is something much more abstruse. 

 Such an objection can only be met by stating more clearly 

 what is asserted, and recognizing any difference of opinion 

 that remains as insoluble. What I assert is (1) that all 

 chances determined by experiment are determined by a 

 relation between frequencies, and (2) that chances are 

 important for physics only in so far as they represent 

 relations between frequencies. Few examples can be cited 

 in support of (1), for chance in physics is usually a theo- 

 retical and not an experimental conception ; but it may be 

 suggested that anyone who proposed to attribute to the 

 chance of a given deflexion of an a-ray in passing through 

 a given film any value other than that determined by fre- 

 quency, could convince us of nothing but his ignorance of 

 physics. In support of (2) it may be pointed out that 

 the chance, which is such an important conception in the 

 statistical theories of physics, enters into the laws predicted 

 by those theories only because it represents a relative 

 frequency. 



