THE ASTRONOMICAL VIEW OF NATURE. 375 



the basis of 

 cal 

 lomy. 



of confirmation occupied a long period, during which it 

 became more and more satisfactory and complete. In 

 fact, so great has the coincidence of calculation with 

 observation turned out to be, in all problems of physical 

 astronomy, that no astronomer at the end of this century 40. 



The Newton- 

 doubts that the gravitation formula alone will suffice to ian formula 



explain all anomalies which still exist in great number 

 in the movements of cosmic bodies such, for instance, 

 as the moon. 



Moreover, in the whole wide range of physical and 

 chemical, not to speak of other natural phenomena, there 

 is probably no instance of a simple mathematical rela- 

 tion having been applied to so large a field of facts, 

 found so trustworthy a guide, and been so unfailingly 

 verified. 



And yet the very extent of this field must not blind 

 us to the fact that for the explanation of molecular 1 



1 This is indeed not to be won- 

 dered at when we consider that in 

 all molecular and molar phenomena 

 such a variety of elements and forces 

 come into play that it is impossible 

 to isolate any special quantities as 

 we do when from the cosmic point 

 of view we lose sight of everything 

 except mass, time, and distance 

 i.e., the elementary factors of our 

 system of measurement. In the 

 phenomena of electricity, for in- 

 stance, it is merely by a process of 

 mental abstraction, which has no 

 counterpart in the observable phe- 

 nomena, that we speak of electrical 

 masses, be they one or two ; of 

 fluids ; of elements of currents, 

 which in nature cannot exist alone ; 

 of velocities of a something which 

 as yet cannot be clearly denned. 

 Any mathematical formula can 

 under such conditions be merely 



tentative, and the preciseness of it 

 must not hide from us the fact that 

 it is based upon hypothetical rela- 

 tions and artificial definitions. This 

 was, for the gain of scientific 

 thought, very clearly brought out 

 in the theoretical discussions which 

 followed upon Helmholtz's critical 

 examination of Weber's and kindred 

 formula;, and is well expressed by 

 Carl Neumann: "Electrical mat- 

 ters" if such there be "never 

 exists alone, but only in combina- 

 tion with ponderable matter." Any 

 law like that of Weber can there- 

 fore be merely a " particular," not 

 a "fundamental" or "universal" 

 law, for it refers merely to a small 

 portion of the properties, forces, 

 and relations of electric and pon- 

 derable matter, leaving others as, 

 for instance, those between electric- 

 ity and heat, electricity and light, 



