NATURE 699 



aspects. This is enough to free us. He is no longer a slave who can 

 choose his master. 



Thus, by generalization, every fact observed enables us to predict 

 a large number of others; only we ought not to forget that the first 

 alone is certain, and that all the others are merely probable. How- 

 ever solidly founded a prediction may appear to us, we are never 

 absolutely sure that experiment will not prove it to be baseless if we 

 set to work to verify it. But the probability of its accuracy is often 

 so great that practically we may be content with it. It is far better 

 to predict without certainty, than never to have predicted at all. We 

 should never, therefore, disdain to verify when the opportunity pre- 

 sents itself. But every experiment is long and difficult, and the la- 

 borers are few, and the number of facts which we require to predict 

 is enormous; and besides this mass, the number of direct verifications 

 that we can make will never be more than a negligible quantity. Of 

 this little that we can directly attain we must choose the best. Every 

 experiment must enable us to make a maximum number of predic- 

 tions having the highest possible degree of probability. The problem 

 is, so to speak, to increase the output of the scientific machine. I may 

 be permitted to compare science to a library which must go on in- 

 creasing indefinitely ; the librarian has limited funds for his purchases, 

 and he must, therefore, strain every nerve not to waste them. Exper- 

 imental physics has to make the purchases, and experimental physics 

 alone can enrich the library. As for mathematical physics, her duty 

 is to draw up the catalogue. If the catalogue is well done the library 

 is none the richer for it; but the reader will be enabled to utilize its 

 riches ; and also by showing the librarian the gaps in his collection, it 

 will help him to make a judicious use of his funds, which is all the 

 more important, inasmuch as those funds are entirely inadequate. 

 That is the role of mathematical physics. It must direct generaliza- 

 tion, so as to increase what I called just now the output of science. 

 By what means it does this, and how it may do it without danger, is 

 what we have now to examine. 



The Unity of Nature. Let us first of all observe that every gen- 

 eralization supposes in a certain measure a belief in the unity and 

 simplicity of Nature. As far as the unity is concerned, there can be 

 no difficulty. If the different parts of the universe were not as the 

 organs of the same body, they would not re-act one upon the other; 

 they would mutually ignore each other, and we in particular should 

 only know one part. We need not, therefore, ask if Nature is one, 

 but how she is one. 



As for the second point, that is not so clear. It is not certain that 

 Nature is simple. Can we without danger act as if she were? 



There was a time when the simplicity of Mariotte's law was an argu- 

 ment in favor of its accuracy : when Fresnel himself, after having 



