34Q POPULAR SCIENCE MONTHLY 



Neither has this conception been useless; it has rendered us an 

 inestimable service, since it has contributed to make precise the funda- 

 mental notion of the physical law. 



I will explain myself; how did the ancients understand law? It 

 was for them an internal harmony, static, so to say, and immutable; 

 or else it was like a model that nature tried to imitate. For us a law 

 is something quite different; it is a constant relation between the 

 phenomenon of to-day and that of to-morrow; in a word, it is a differ- 

 ential equation. 



Behold the ideal form of physical law; well, it is Newton's law 

 which first clothed it forth. If then one has acclimated this form in 

 physics, it is precisely by copying as far as possible this law of New- 

 ton, that is by imitating celestial mechanics. This is, moreover, the 

 idea I have tried to bring out in chapter VI. 



The Physics of the Principles 



Nevertheless, a day arrived when the conception of central forces 

 no longer appeared sufficient, and this is the first of those crises of 

 which I just now spoke. 



What was done then? The attempt to penetrate into the detail of 

 the structure of the universe, to isolate the pieces of this vast mechan- 

 ism, to analyze one by one the forces which put them in motion, was 

 abandoned, and we were content to take as guides certain general prin- 

 ciples the express object of which is to spare us this minute study. 

 How so? Suppose we have before us any machine; the initial wheel 

 work and the final wheel work alone are visible, but the transmission, 

 the intermediary machinery by which the movement is communicated 

 from one to the other, are hidden in the interior and escape our view; 

 we do not know whether the communication is made by gearing or by 

 belts, by connecting-rods or by other contrivances. Do we say that it 

 is impossible for us to understand anything about this machine so long 

 as we are not permitted to take it to pieces? You know well we do 

 not, and that the principle of the conservation of energy suffices to 

 determine for us the most interesting point. We easily ascertain that 

 the final wheel turns ten times less quickly than the initial wheel, 

 since these two wheels are visible ; we are able thence to conclude that 

 a couple applied to the one will be balanced by a couple ten times 

 greater applied to the other. For that there is no need to penetrate 

 the mechanism of this equilibrium and to know how the forces com- 

 pensate each other in the interior of the machine; it suffices to be 

 assured that this compensation can not fail to occur. 



Well, in regard to the universe, the principle of the conservation of 

 energy is able to render us the same service. The universe is also a 

 machine, much more complicated than all those of industry, of which 



