90 THE PRINCIPLES OF SCIENCE. 



but those of reflection and refraction, and the only diffi- 

 culty consisted in developing their full consequences. 



There is one instructive result of the theory of error 

 which should always be borne in mind, namely that when 

 a large variable error is combined with a small variable 

 error, the uncertainty of the final result, as measured by 

 its probable error, is scarcely at all affected by the small 

 variable error s . Accordingly our efforts at accuracy must 

 be devoted to the sources of error in the order of their 

 magnitude. There is no use in making instruments to 

 measure the heat of the sun with the last degree of 

 accuracy, when the varying transparency of the atmo- 

 sphere produces uncertainties of far greater amount. It 

 is needless to observe a comet or other heavenly body with 

 the very finest instruments if it appears low down on the 

 horizon, where the atmospheric refraction is not accurately 

 determinate. In short, minuter variable sources of error 

 may be entirely neglected, so long as those of a consider- 

 ably greater amount remain beyond our powers of correc- 

 tion. 



Discovery of Hypothetically Simple Laws. 



In some branches of science we meet with natural laws 

 of a simple character which are in a certain point of view 

 exactly true and yet can never be manifested as exactly 

 true in natural phenomena. Such, for instance, are the 

 laws concerning what is called a perfect gas. The gaseous 

 state of matter is that in which the general properties of 

 matter are exhibited in the simplest and most general 

 manner. There is much advantage accordingly in ap- 

 proaching the question of molecular mechanics from this 

 side. But when we ask the question What is a gas ? 

 the answer must be a hypothetical one. Finding that 



8 Airy, 'Philosophical Transactions,' (1856) vol. cxlvi. p. 324. 





