704 SCIENCE AND HYPOTHESIS 



mathematical physics. We recognize at the outset that the efforts of 

 men of science have always tended to resolve the complex phenomenon 

 given directly by experiment into a very large number of elementary 

 phenomena, and that in three different ways. 



First, with respect to time. Instead of embracing in its entirety 

 the progressive development of a phenomenon, we simply try to 

 connect each moment with the one immediately preceding. We admit 

 that the present state of the world only depends on the immediate 

 past, without being directly influenced, so to speak, by the recollection 

 of a more distant past. Thanks to this postulate, instead of studying 

 directly the whole succession of phenomena, we may confine ourselves 

 to writing down its differential equation; for the laws of Kepler we 

 substitute the law of Newton. 



Next, we try to decompose the phenomena in space. What experi- 

 ment gives us is a confused aggregate of facts spread over a scene of 

 considerable extent. We must try to deduce the elementary phenom- 

 enon, which will still be localized in a very small region of space. 



A few examples perhaps will make my meaning clearer. If we 

 wished to study in all its complexity the distribution of temperature in 

 a cooling solid, we could never do so. This is simply because, if 

 we only reflect that a point in the solid can directly impart some of 

 its heat to a neighboring point, it will immediately impart that heat 

 only to the nearest points, and it is but gradually that the flow of 

 heat will reach other portions of the solid. The elementary pheno- 

 menon is the interchange of heat between two contiguous points. It 

 is strictly localized and relatively simple if, as is natural, we admit 

 that it is not influenced by the temperature of the molecules whose 

 distance apart is small. 



I bend a rod: it takes a very complicated form, the direct investi- 

 gation of which would be impossible. But I can attack the problem, 

 however, if I notice that its flexure is only the resultant of the 

 deformations of the very small elements of the rod, and that the 

 deformation of each of these elements only depends on the forces 

 which are directly applied to it, and not in the least on those which 

 may be acting on the other elements. 



In all these examples, which may be increased without difficulty, it 

 is admitted that there is no action at a distance or at great distances. 

 That is an hypothesis. It is not always true, as the law of gravitation 

 proves. It must therefore be verified. If it is confirmed, even ap- 

 proximately, it is valuable, for it helps us to use mathematical physics, 

 at any rate by successive approximations. If it does not stand the 

 test, we must seek something else that is analogous, for there are 

 other means of arriving at the elementary phenomenon. If several 

 bodies act simultaneously, it may happen that their actions are inde- 

 pendent, and may be added one to the other, either as vectors or as 



