THE ASTRONOMICAL VIEW OF NATURE. 377 



for the purpose of discovering the forces which exist in 

 the universe between cosmic bodies we had been con- 

 fined to experiments in the laboratory, as we are in all 

 other departments of physics and chemistry, it is very . 



J The Newton- 



doubtful whether this universal law of gravitation would ian formula 



unique as to 



ever have been discovered. And yet it stands there as and V acc^- ty 

 almost the only formula universally applicable to all acy ' 

 matter throughout the visible and tangible universe. 



In the foregoing pages I have sometimes spoken of this 

 great discovery of Newton, on which is based the astron- 

 omical view of nature, as a formula, sometimes as a law. 

 A formula is merely the expression in definite terms of 

 certain relations of measurable quantities. By a law 

 we are apt to understand something more viz., the 

 statement of some fundamental, all-pervading property 

 of the things of nature, which, so far as we are con- 

 cerned, is final. 1 Whether the human mind is at all 



this expression would give an in- 

 finite value for the force between 

 electrical particles in motion. 

 Weber replied that the same argu- 

 ment could be used against the 

 gravitation formula, and hinted at 

 the possibility that a correction 

 might have to be added to the New- 

 tonian formula to make it appli- 

 cable to molecular distances ( ' Elec- 

 trodyn. Maasb.,' 1871, p. 60). This 

 idea was taken up by several Con- 

 tinental mathematicians (see Isen- 

 krahe, ' Das Rathsel von der Schwer- 

 kraft,' p. 33, &c. ; Paul du Bois- 

 Reymond, ' Ueber die Qrundlagen 

 der Erkenntniss,' p. 50 ; Tisserand, 

 'Comptes Rendus,' September 1872). 

 1 Helmholtz says, referring to 

 Weber's so - called law : "If we 

 are to consider Weber's law as an 

 elementary law, as an expression 

 of the ultimate cause of the phe- 



nomena to which it refers, and not 

 merely as an approximately correct 

 expression of facts within narrow 

 limits, then we must demand that, 

 if applied to objects of the largest 

 imaginable dimensions, it should 

 give results which are physically 

 possible" (1873, ' Wissenachaf tliche 

 Abhandlungen," vol. i. p. 658). This 

 sentence raises a philosophical ques- 

 tion as to the demands which we 

 can legitimately expect to be satis- 

 fied by any so-called law of nature 

 expressible in the symbols of hu- 

 man thought, be these words or 

 algebraic signs. I venture to think 

 that nowadays, and largely in con- 

 sequence of discussions similar to 

 those carried on over Weber's law, 

 physicists do not any longer expect 

 to find laws of that general and 

 fundamental character which the 

 words given above describe. 



