ON THE STUDY OF PHYSICS. 61 



In the language of paradox, the physicist is exact because he 

 knows how inexact he is. The phrase 'exact value' is a term with 

 which many well meaning people deceive themselves and others. 

 Every measure is imperfect. Mathematical precision is a fatuous 

 term, except as qualified by the limits within which a statement is true. 



In the face of some teaching a denial that physics is an experimental 

 science seems almost to be justified. No law can be proved by one or 

 by a hundred experiments. Suppose, as is sometimes done, that a 

 student is given a bar, a knife edge and a couple of weights, and that he 

 is asked to prove to law of the lever. He balances the bar, determines 

 the weights, measures the lever arms and finds what? That the prod- 

 uct of each weight by its corresponding lever arm is constant ? By no 

 means. For every time, and with whatever pains he has taken to secure 

 accuracy, the product of the weight by its lever arm will be found dif- 

 ferent on each side, which proves, if literal interpretation of the figures 

 is demanded, that the law of the lever is false. It is very important to 

 recognize the fact that scientific laws are not proved by perfect cor- 

 roboration of measurements. The proof of any law is of a negative 

 character. Not even the law of gravitation nor the law of the conserva- 

 tion of energy is proved by any positive demonstration. The probable 

 truth of any proposition is assumed from inability to disprove it. 

 Whence it follows that there is nothing more fundamental to the cor- 

 rect understanding of the science of physics, or indeed of science in gen- 

 eral, than the interpretation of measurements according to the theory 

 of probabilities and a rational discussion of the inherent errors. 



Now the difficult art of physical measurement can neither be taught 

 nor learned apart from some sort of work in the physical laboratory. 

 In this connection the student should be taught something concerning 

 the different sorts of errors that may arise: (1) Errors of construc- 

 tion or of fluctuations in the measuring instruments. Many otherwise 

 instructed people always start with the assumption that their instru- 

 ments are correct. A little wholesome yet not unsettling distrust of 

 makers' markings can be taught in a brief examination of scales 

 and thermometers. (2) The limitations of the senses and observa- 

 tional errors may be clearly studied from a series of readings made 

 upon almost any instrument having a moderate degree of sensitiveness. 

 (3) Errors of definition, the personal equation, other constant errors 

 and even out and out blunders demand full illustration and recogni- 

 tion. All these things may be taught from the simplest or from any 

 available apparatus, and the knowledge of them is, in the writer's opin- 

 ion, of more value to the apprehension of pure science than the exhibi- 

 tion or the so-called verification of any law that may be named. 



In this insistence that the chief use of the physical laboratory is in- 

 struction in the difficult art of physical measurement, an art difficult on 



