MOLECULAR THEORIES AND MATHEMATICS BOEEL. 169 



The atomic theory, whose tradition goes back to the Greek plii- 

 losophers, was not abandoned durmg that period Independent of the 

 confirmation that it found in the properties of gases and in the haws 

 of chemistry, it was by means of that theory that one was obliged to 

 explam certain phenomena, such as the compressibiUty of liquids or 

 the permeability of sohds, in spite of the apparent continuity of 

 these two states of matter. But the atomic theory was placed in 

 juxtaposition with physical theories based on continuity; it did not 

 affect them. The rapid advances in thermodynamics and in the 

 theories of energy contributed to mamtam this sort of jmrtition 

 between the physical theories and the hypothesis of the existence of 

 atoms, which became so fruitful m chemistry. To the majority of 

 physicists half a century ago the problem of the reality of atoms was 

 a metaphysical question properly beyond the domam of physics; it 

 mattered little to science whether atoms exist or are simple fictions, 

 and one niight even doubt if science were able to affirm or deny their 

 existence. 



However, thanks especially to the labors of Maxwell and of Boltz- 

 mann, the definite introduction of molecules in the theory of gases 

 and solutions showed itself fruitful. Gibbs created the new study, 

 to winch he gave the name "Statistical mechanics." But it is only 

 in the last 20 years that all physicists have been forced, by the study 

 of new radiations on the one hand and the study of the Brownian 

 movement on the other, to consider the molecular hypothesis as one 

 that is necessary to natural pliilosophy. And, more recently, the 

 thorough study of the laws of radiation has led to the milooked-for 

 theory of the discontinuity of energy— or of motion. It does not 

 come withm my subject to expound the experimental proofs through 

 which these hypotheses are each day becoming more probable. The 

 most striking of such experiments are perhaps those which have 

 made it possible to observe the individual emission of the a particles, 

 so that one actually obtains one of the concrete units with which 

 the physicist constructs the sensible universe, just as the abstract 

 universe of mathematics can be constiaicted by means of an abstract 

 unit. 



For definitely formulating their hypotheses and deducing there- 

 from results susceptible of experimental verification the theorists 

 of modern physics make use of mathematical symbols. These 

 symbols are those which have been created ui starting out with the 

 notion of continuity. It is, therefore, not astonishing that diffi- 

 culties sometunes appear, the most real of which is the contradiction, 

 apparent at least, between the hypothesis of the quanta and the older 

 hypothesis that plienomena are governed by differential equations. 

 But these difficulties of principle do not prevent the success of what 

 one might call partial theories, by which a certaui number of exj^eri- 



