MEMOIR OF KIRCHHOFF. 539 



fimdaineutal notions of space, time, and matter, Kirch hoft" tries to make 

 Ills way to the description of the facts of experience and i>oes beyond 

 his predecessors by delineating" by means of pure geometry the sup- 

 l)osed logically fundamental notions of force and mass. Force is to him 

 the accsleratioii (change of velocity) experienced by a material particle 

 in a unit of time; the knowledge of all these accelerating forces in a 

 given moment of time would suffice to describe the world ; experience 

 has shown however that the description gains in simplicity, if we mul- 

 tiply the acceleration by a certain positive constant, called mass of the 

 moving particle. 1 have mentioned this abstract train of thought be- 

 cause it is very characteristic of Kirchhoff. The necessity of looking at 

 natural forces as something really existing, or the mass as something 

 really constant, remaining equal to itself, he does liot recognize. It is 

 only a fact of experience that the movements in nature hitherto observed 

 have taken place in such a way that they seem to be represented in the 

 simplest manner by making those suppositions. We can build up me- 

 chanical systems on quite different bases, but it would not help us to 

 describe simply the real movements. The problem of mathematical 

 physics will be solved when the observed phenomena will be described 

 by means of the simplest possible supposition as to the nature of forces 

 and distribution of matter. There is nothing impossible in it; it can be 

 proved in fact that all that men can observe in tinite time must be sus- 

 ceptible of being described mathematically. 



Even an outsider will not fail to notice, I think, that something is not 

 inclmded in Kirchhotf's programme. The simplest description can not 

 produce the conviction that the i)henomena, even in future time, shall 

 run in accordance with the description ; its equations are, so to say, not 

 laws. There exists a stand-point differing somewhat from that of Kirch- 

 hoff; it looks for what is in accordance with a law in the change of 

 phenomena. Experience teaches us that nature acts according to laws; 

 because without laws experience would be impossible. Experience is 

 the collecting of what is similar in different particular perceptions. 

 That the laws exist is accordingly an observed fact and not a hypothe- 

 sis. We feel them acting at every moment independently of our will. 

 We must ascribe to them the same reality as to our will; these two 

 things are opposite to one another, power against power. We desig- 

 luite them accordingly by the names of forces, and forces as causes of 

 motion ; they have the same reality as the motion itself. Up to this 

 point nature nmy be said to be intelligible. What a force is we know 

 not ; we can only say that it nuinifests itself in the acceleration it im- 

 ])arts to the mass, and de facto accordingly, we do not go beyond Kirch- 

 hoflf's description of nature. As to results, the search after a law and the 

 endeavor after the simplest description of nature is one and the same 

 thing; the difference lies only in the formulation of the problem and 

 sometimes possibly in the way towards its solution. It follows for in- 

 stance from Kirchhoflf's definition, that it must be permitted (not only 



