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 product 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 different 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 corroboration of measurements. The proof of any law is of a negative character. Not even the law of gravitation nor the law of the conservation 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 correct understanding of the science of physics, or indeed of science in general, 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 construction or of fluctuations in the measuring instruments. Many otherwise instructed people always start with the assumption that their instruments 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 observational 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 recognition. All these things may be taught from the simplest or from any available apparatus, and the knowledge of them is, in the writer's opinion, of more value to the apprehension of pure science than the exhibition or the so-called verification of any law that may be named.
In this insistence that the chief use of the physical laboratory is instruction in the difficult art of physical measurement, an art difficult on