Januaey 12, 1906.] 



SCIENCE. 



55 



have been foreseen long ago by Gauss' and 

 Riemann," requires a generalization of, or 

 even a direct departure from, the ordinary 

 laws of mechanics : the law of the relativity 

 of motion, the conservation of linear and 

 angular momentum and of energy in a 

 closed system, the instantaneous equality 

 of action and reaction. 



It is now pretty generally recognized 

 that Newton's 'laws of motion,' including 

 his definition of ' force, ' are not unalterable 

 laws of thought, but merely arbitrary pos- 

 tulates assumed for the purpose of inter- 

 preting natural phenomena in the most 

 simple and adequate manner. Unfortu- 

 nately, nature is not very simple. "As the 

 eye of the night-owl is to the light of the 

 sun, so is our mind to the most common 

 phenomena of nature," says Aristotle. 

 And if since Newton's time we have made 

 some progress in the knowledge of physics 

 it is but reasonable to conclude that the 

 postulates which appeared most simple and 

 adequate two hundred years ago can not be 

 regarded as such at the present time. 



This does not mean, of course, that the 

 mechanics of Newton has lost its value. 

 The case is somewhat parallel to that of 

 the postulates of geometry. Just as the 

 abandonment of one or the other of the 

 postulates of Euclidean geometry leads to 

 a more general geometry which contains 

 the old geometry as a particular, or limit- 

 ing, ease, so the abandonment or general- 

 ization of some of the postulates of the 

 older mechanics must lead to a more gen- 

 eral mechanics. The creation of such a 

 generalized mechanics is a task for the 

 immediate future. It is perhaps too early 

 to say at present what form this new non- 

 Newtonian mechanics will ultimately as- 

 sume. Generalization is always possible in 



'Gauss, Werke, Vol. 5, p. 627. Compare 

 Encykloplidie der niathematischen Wissenschaften, 

 Vol. 12, ppi' 45-46. 



'Riemann, Werke, 2(1 edition, 1892, p. 288. 



a variety of ways. In the pres nt ease, 

 the object should be to arrive at a mechan- 

 ics, on the one hand sufficiently general for 

 the electron theory, on the other such as to 

 include the Newtonian mechanics as a spe- 

 cial ease. 



After the searching criticism to which 

 Poincare, especially in his St. Louis ad- 

 dress,^" in 1904, has subjected the founda- 

 tions of mechanics and mathematical phys- 

 ics, almost the only one of the fundamental 

 principles that appears to remain intact 

 is the principle of least action. It seems, 

 therefore, natural to take this principle as 

 the starting point for a common foundation 

 of mathematical physics and of a general- 

 ized mechanics, but with a broader defini- 

 tion of 'action,' or what amounts to the 

 same, with a generalized conception of 

 'mass' so as to make the latter a function 

 of the velocity. 



A very notable attempt has recently been 

 made in this direction by E. and F. Cos- 

 serat.^^ And although only a first instal- 

 ment of their investigation has so far been 

 published, the able way in which the diffi- 

 cult problem is here attacked seems full of 

 promise for a solution as complete as the 

 nature of the case may warrant. 



It may, perhaps, be said that, in de- 

 manding a generalization of the founda- 

 tions of mechanics on such broad lines, I 

 have attached undue importance to the 

 electron theory as developed by Lorentz 

 and Abraham, a theory which is still in 

 the formative stage. There exist electro- 

 magnetic theories that appear less i^adical 

 in their departures from the older views 



^"Bulletin des sciences matMmatiques (2), 28, 

 pp. 302-324; English translation in the Bulletin 

 of the American Mathematical Society, Vol. XIII., 

 February, 1906. 



^^ Comptes rendus, Vol. 140, pp. 932-934; for a 

 more detailed development see the notes con- 

 tributed by E. and F. Cosserat to the French trans- 

 lation of 0. D. Chwolson's ' Traite de physique,' 

 Paris, Hermann, 1905. 



