BEGINNINGS OF MODERN MATHEMATICAL SCIENCE 295 



only two mutually attracting bodies. Newton of course appreci- 

 ates that such a case is purely ideal and that, since every body 

 attracts every other, the result of dealing with only two is merely 

 a first approximation to the reality. 



All planets he says are mutually heavy, therefore, for example ; Jupiter 

 and Saturn will attract each other in the vicinity of their conjunction 

 and perceptibly disturb each other's motion. Similarly the Sun will dis- 

 turb the motion of the Moon, and Sun and Moon will disturb our ocean. 



Newton prefaced these applications of the theory with four rules 

 which should guide scientific men in making hypotheses. These in 

 their final shape, are to the following effect : (1) We should not assume 

 more causes than are sufficient and necessary for the explanation of 

 observed facts. (2) Hence, as far as possible, similar effects must be 

 assigned to the same cause ; for instance, the fall of stones in Europe 

 and America. (3) Properties common to all bodies within reach of 

 our experiments are to be assumed as pertaining to all bodies ; for 

 instance, extension. (4) Propositions in science obtained by wide in- 

 duction are to be regarded as exactly or approximately true, until 

 phenomena or experiments show that they may be corrected or are 

 liable to exceptions. The substance of these rules is now accepted 

 as the basis of scientific investigation. Their formal enunciation here 

 serves as a landmark in the history of thought. Mathematical 

 Gazette, July, 1914. 



Every new satellite, says Brewster in his Life of Newton, every 

 new asteroid, every new comet, every new planet, every new star 

 circulating round its fellow, proclaims the universality of Newton's 

 philosophy, and adds fresh lustre to his name. It is otherwise however 

 in the general history of science. The reputation achieved by a great 

 invention is often transferred to another which supersedes it, and a 

 discovery which is the glory of one age is eclipsed by the extension of 

 it in another. ... It is the peculiar glory of Newton, however, 

 that every discovery in the heavens attests the universality of his 

 laws, and adds a greener leaf to the laurel chaplet which he wears. 



Shrinking always from publicity 1 and controversy, Newton like 

 Copernicus had gradually perfected his great work, but, like Co- 



1 In one instance he authorized publication of one of his works "so it be without 

 my name to it : for I see not what there is desirable in public esteem, were I able 



