THE ASTRONOMICAL VIEW OF NATURE. 333 



focus, is replaced by a larger or a smaller circle, the 

 contours of the image become less and less distinct, 

 and with the possible light which we gain there is 

 mingled much darkness, the source of many mistakes 

 and errors. But the tendency of all scientific thought 

 is towards clearer and clearer definition ; it lies in the 

 direction of a more and more extensive use of mathe- 

 matical measurements, of mathematical formulae. 



There is probably no science which has come so per- 

 fectly under the control of this kind of mathematical ex- 

 pression as has astronomy since the time of Newton or of 

 Laplace, and, we may add, there exists probably no mathe- 

 matical formula which has stood the test of application to 

 existing phenomena so long and so thoroughly as the 

 gravitation formula of Newton. It possesses two unique 

 properties which no other formula possesses so far as we 

 can now see it is universal l and it is accurate. 2 These 



1 The law of gravitation can be 

 called the first and most general 

 physical law or statement of uni- 

 versal application. The laws of 

 motion may be called mechanical 

 or dynamical statements. Both 

 the law of gravitation and the 

 laws of motion describe facts, and 

 have been found by experience ; 

 but the laws of motion con- 

 tain no physical constant i.e, t 

 no quantity which requires to be 

 fixed and measured by observa- 

 tion, and the absolute value of 

 which has for us at present no 

 ulterior meaning. The law of gra- 

 vitation has one physical constant, 

 the universal gravitation constant 

 (see p. 320). As it measures what 

 we call matter, it need not be de- 

 termined, and its actual determin- 

 ation, which has been accurately 

 made only in recent times, has not 



in any direction advanced our gen- 

 eral physical knowledge. For all 

 practical purposes of physics the 

 unit of mass is a weight, just as for 

 all commercial purposes gold is the 

 standard of value. The astrono- 

 mical view permits us to go a step 

 further and express the mass of a 

 pound of matter in units of time 

 and space, and the political econo- 

 mist may seek for a real standard 

 of value for instance, an article 

 of food like wheat. Other funda- 

 mental physical laws or general 

 statements involve other physical 

 constants, as we shall see later on. 

 2 The accuracy of the so-called 

 laws of nature, or, more correctly, 

 of the expressions which science 

 gives to the laws of nature, is a 

 very important question. Little is 

 said on this point in the ordinary 

 text - books. It is only in very 



