702 SCIENCE AND HYPOTHESIS 



greatness or the smallness of certain quantities which allow of certain 

 terms to be neglected in no case is it due to chance. This simplicity, 

 real or apparent, has always a cause. We shall therefore always be 

 able to reason in the same fashion, and if a simple law has been ob- 

 served in several particular cases, we may legitimately suppose that it 

 still will be true in analogous cases. To refuse to admit this would 

 be to attribute an inadmissible role to chance. However, there is a 

 difference. If the simplicity were real and profound it would bear 

 the test of the increasing precision of our methods of measurement. 

 If, then, we believe Nature to be profoundly simple, we must conclude 

 that it is an approximate and not a rigorous simplicity. This is what 

 was formerly done, but it is what we have no longer the right to do. 

 The simplicity of Kepler's laws, for instance, is only apparent; but 

 that does not prevent them from being applied to almost all systems 

 analogous to the solar system, though that prevents them from being 

 rigorously exact. 



Role of Hypothesis. Every generalization is a hypothesis. Hy- 

 pothesis therefore plays a necessary role, which no one has ever con- 

 tested. Only, it should always be as soon as possible submitted to 

 verification. It goes without saying that, if it cannot stand this test, 

 it must be abandoned without any hesitation. This is, indeed, what 

 is generally done ; but sometimes with a certain impatience. Ah well ! 

 this impatience is not justified. The physicist who has just given 

 up one of his hypotheses should, on the contrary, rejoice, for he found 

 an unexpected opportunity of discovery. His hypothesis, I imagine, 

 had not been lightly adopted. It took into account all the known 

 factors which seem capable of intervention in the phenomenon. If 

 it is not verified it is because there is something unexpected and 

 extraordinary about it, because we are on the point of finding some- 

 thing unknown and new. Has the hypothesis thus rejected been 

 sterile? Far from it. It may be even said that it has rendered more 

 service than a true hypothesis. Not only has it been the occasion of 

 a decisive experiment, but if this experiment had been made by chance, 

 without the hypothesis, no conclusion could have been drawn ; nothing 

 extraordinary would have been seen ; and only one fact the more would 

 have been catalogued, without deducing from it the remotest conse- 

 quence. 



Now, under what conditions is the use of hypothesis without dan- 

 ger ? The proposal to submit all to experiment is not sufficient. Some 

 hypotheses are dangerous, first and foremost those which are tacit 

 and unconscious. And since we make them without knowing them, we 

 cannot get rid of them. Here again, there is a service that mathemat- 

 ical physics may render us. By the precision which is its character- 

 istic, we are compelled to formulate all the hypotheses that we would 

 unhesitatingly make without its aid. Let us also notice that it is 



