606 APPLIED MATHEMATICS 



or it was like a model that nature constrained herself to imitate. A 

 law for us is not that at all; it is a constant relation between the 

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

 differential equation.' 



The ideal form of physical law is the law of Newton which first 

 covered it; and then how has one to adapt this form to physics? 

 by copying as much as possible this law of Newton, that is, in imi- 

 tating celestial mechanics. 



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. 



Then investigators gave up trying to penetrate into the detail 

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

 mechanism, to analyze one by one the forces which put them in 

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

 ciples which have precisely for their object the sparing us this minute 

 study. 



How so? Suppose that we have before us any machine; the ini- 

 tial wheel-work and the final wheel-work alone are visible, but the 

 transmission, the intermediary wheels 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 dis- 

 positives. 



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 compensate each other in the interior of the 

 machine; it suffices to be assured that this compensation cannot fail 

 to occur. 



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

 of energy is able to render us the same service. This is also a machine, 

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

 almost all the parts are profoundly hidden from us; but in observing 

 the movement of those that we can see, we are able, by aid of this 

 principle, to draw conclusions which remain true whatever may be 

 the details of the invisible mechanism which animates them. 



The principle of the conservation of energy, or the principle of 

 Mayer, is certainly the most important, but it is not the only one; 



