696 SCIENCE AND HYPOTHESIS 



And even the probable reason why our geometry seems convenient to 

 us is, that our bodies, our hands, and our limbs enjoy the properties 

 of solid bodies. Our fundamental experiments are pre-eminently phy- 

 siological experiments which refer, not to the space which is the object 

 that geometry must study, but to our body that is to say, to the 

 instrument which we use for that study. On the other hand, the fun- 

 damental conventions of mechanics and the experiments which prove 

 to us that they are convenient, certainly refer to the same objects or 

 to analogous objects. Conventional and general principles are the 

 natural and direct generalizations of experimental and particular prin- 

 ciples. Let it not be said that I am thus tracing artificial frontiers 

 between the sciences; that I am separating by a barrier geometry 

 properly so called from the study of solid bodies. I might just as well 

 raise a barrier between experimental mechanics and the conventional 

 mechanics of general principles. Who does not see, in fact, that by 

 separating these two sciences we mutilate both, and that what will 

 remain of the conventional mechanics when it is isolated will be but 

 very little, and can in no way be compared with that grand body of 

 doctrine which is called geometry. 



We now understand why the teaching of mechanics should remain 

 experimental. Thus only can we be made to understand the genesis 

 of the science, and that is indispensable for a complete knowledge of 

 the science itself. Besides, if we study mechanics, it is in order to 

 apply it ; and we can only apply it if it remains objective. Now, as we 

 have seen, when principles gain in generality and certainty they lose 

 in objectivity. It is therefore especially with the objective side of 

 principles that we must be early familiarized, and this can only be 

 by passing from the particular to the general, instead of from the 

 general to the particular. 



Principles are conventions and definitions in disguise. They are, 

 however, deduced from experimental laws, and these laws have, so to 

 speak, been erected into principles to which our mind attributes an 

 absolute value. Some philosophers have generalized far too much. 

 They have thought that the principles were the whole of science, and 

 therefore that the whole of science was conventional. This paradoxi- 

 cal doctrine, which is called Nominalism, cannot stand examination. 

 How can a law become a principle? It expressed a relation between 

 two real terms, A and B; but it was not rigorously true, it was only 

 approximate. We introduce arbitrarily an intermediate term, C, more 

 or less imaginary, and C is by definition that which has with A exactly 

 the relation expressed by the law. So our law is decomposed into an 

 absolute and rigorous principle which expresses the relation of A to C, 

 and an approximate experimental and revisable law which expresses 

 the relation of C to B. But it is clear that however far this decom- 

 position may be carried, laws will always remain. We shall now enter 

 into the domain of laws properly so called. 



