380 Dr. Dorothy "VTrinch and Dr. H. Jeffreys on Certain 



simplicity fits our observations, running "perhaps into tens 

 or hundreds of thousand*, with errors never greater than 

 a millionth of the total range of variation o£ the quantities 

 involved. The Newtonian law of gravitation accounts for 

 the motions of the planets with such accuracy ; and there 

 are others in electricity and optics scarcely less simple and 

 accurate. Is the prevalence of these simple and accurate 

 laws due to the nature of our investigation, or to some 

 widespread quality in the external world itself? 



It may be suggested that the former alternative is correct, 

 and that only the simplest laws would ever have been dis- 

 covered. We think, however, that this possibility disappears 

 when the method of discovery of physical laws is examined 

 more closely. The investigator does not set out to discover 

 an empirical instance of a particular formal law ; he starts 

 by making observations on topics chosen simply because 

 they interest him, and he then chooses the law to suit the 

 observations. It is a matter of logical necessity that a law 

 can always be found — indeed, that an infinite number of 

 laws can be found — that satisfy a particular set of obser- 

 vations. The remarkable fact that emerges from the results 

 is that it is so often possible to find a simple one ; for there 

 is no mathematical necessity for this. Many important 

 cases are, of course, known where no simple law fits the 

 observations : such as, for example, fhe permanent defor- 

 mation of metals under stress and the relation of the velocity 

 of a shell to the air resistance. Yet complex empirical laws 

 are well known in such cases. Thus the possibility of finding 

 laws is not dependent on their simplicity. 



The existence of simple laws is, then, apparently, to be 

 regarded as a quality of nature; and according^ we may 

 infer that it is justifiable to prefer a simple law to a more 

 complex one that fits our observations slightly better. In 

 other words, the simple law may be supposed to be ipso 

 facto more probable than a complex one. Some such tacit 

 assumption evidently underlies the widespread use of 

 inference from simple laws, and the great confident e 

 usually placed in the results ; for the only alternative 

 reason for the adoption of the simple law is its convenience, 

 and one would hardly place much reliance on an inference 

 dependent on a hypothesis chosen merely for convenience. 

 Thus scientific practice seems to require the assumption that 

 an inference drawn from a simple scientific law may have a 

 very high probability, often not far from unity. It cannot 

 be exactly unity, for that would mean that no other law w as 

 possible; and this is never the case. 



