﻿70 Dr. Norman Campbell on the 



4. A second objection may be based on the fact that the 

 straight line has to be drawn among and not through the 

 experimental points. It may be readily admitted that this 

 fact shows that the chance cannot be estimated with perfect 

 accuracy. But there is also some uncertainty in determining 

 the resistance ; and since I am concerned only to enforce the 

 analogy between chance and resistance, the admission is 

 innocuous. If it is urged that this uncertainty shows that 

 the derived magnitude cannot be the chance, because chance 

 is something to which a numeral may be attached with 

 mathematical accuracy, then it is replied (as in answering 

 the first objection) thnt such a chance, to which no experi- 

 mental error is attached, is something totally irrelevant to 

 physics. 



But the objection may be put in a less crude form. It 

 may be urged that, in the matter of experimental error, there 

 is a fundamental difference between resistance and chance. 

 For in the latter, but not in the former, the error is something 

 essential to the magnitude ; we can conceive of a resistance 

 measured without error, but not of a chance measured with- 

 out error ; if all the points lay accurately on the line, then 

 the magnitude measured by its slope would not be a chance. 

 Again, there is a simple relation between the average error 

 about a point on the " chance " line and the co-ordinates of 

 that point ; while in the " resistance " line the relation is 

 much more complex, and depends on the exact method of 

 measuring the current and potential. All this is quite true, 

 and would be important if we were considering the theory of 

 chance or of resistance. There is a great difference in those 

 theories; we suppose that the "real" Ohm's law holds between 

 the real and not the measured magnitudes of the current and 

 potential, while there is no real magnitude involved in the 

 chance relation. But w T e are not considering theory but 

 experiment; I am only asserting that chance is an experi- 

 mentally measured magnitude. The fact that the errors in 

 the two cases are differently explained does not affect the 

 fact that there are errors in both cases, and that the problem 

 of determining the derived magnitude in spite of these errors 

 is precisely the same. 



5. As a third objection it might be urged that the two 

 measurements are not really similar, because ihe chance is 

 not really determined by the slope of the line, but by the 

 ratio of the two numbers when they are sufficiently great. 

 Here is a misconception which it is important to correct. 

 If we know that the happening of the events is determined 



