December 16, 1904.] 



SCIENCE. 



835 



equality of two forces, and this implies the 

 principle of the equality of action and reac- 

 tion. " Hence, this principle should no 

 longer be regarded as an experimental law, 

 but as a definition" (p. 122). The result 

 reached is that the ' law of ISTewton ' as to 

 acceleration must be regarded as a definition, 

 in which mass is still undefined. " We are 

 driven to the following definition, which is 

 simply an avowal of impotence : Masses are 

 coefficients which it is convenient to introduce 

 into calculations" (p. 12Y). 



While the principles of dynamics are defini- 

 tions, they can be approximately verified by 

 experiment. A more precise experiment would 

 show simply that the law was only approxi- 

 mately true in that case; which we knew 

 already. Thus we see how experience has 

 served as basis for the principles of mechanics 

 and still can never contradict it. 



The analogy between geometry and me- 

 chanics would at first glance seem complete. 

 In each the fundamental principles are merely 

 conventions which experience has led us to 

 set up as convenient. But there is a dif- 

 ference. The laws of geometry are set up 

 in consequence of experiments in mechanics, 

 in optics, in physiology; they are in no sense 

 experiments in geometry; they do not relate 

 to space (which geometry studies), but to ma- 

 terial objects. On the other hand, the funda- 

 mental conventions of mechanics and the ex- 

 periences which show that they are convenient, 

 relate to the very same objects or to analogous 

 objects. This is not an artificial barrier be- 

 tween sciences but a real distinction. The 

 teaching of mechanics should, therefore, re- 

 main objective, experimental. 



The fourth part, devoted to ' Force,' eon- 

 tains chapters on : ' Hypotheses in physics ' ; 

 ' The theories of modern physics ' ; ' The theory 

 of probabilities, optics and electricity,' and 

 ' Thermodynamics.' In this part the relation 

 of observation to hypotheses and generaliza- 

 tion is taken up. Experience is the s6l6 

 source of truth, but one must use his observa- 

 tions; he must generalize. A mere accumu- 

 lation' of facts is no more a science than a 

 pile of stones is a house. Above all, the scien- 



tist must foresee. A good experiment teaches 

 more than an isolated fact; it permits us to 

 foresee, i. e., it permits us to generalize. In- 

 terpolation is necessary. ' Experiments give us 

 only a certain number of isolated points ; gen- 

 eralization traces a curve. This curve does 

 not pass exactly through all the points given 

 by experiment. We not merely generalize 

 experience, but correct it. Experimental 

 physics furnishes the facts; mathematical 

 physics orders them, makes the generalizations 

 and points out the needs. In this generaliza- 

 tion the unity of nature and the simplicity of 

 its laws is presiipposed. The curve does not 

 follow all the zigzags indicated by the points 

 given by experiment. Nevertheless, it is not 

 certain that nature is simple, but generaliza- 

 tion, and with it science, could not exist if 

 the hypothesis of simplicity were entirely 

 abandoned. 



Generalization requires hypotheses. There 

 are three categories of hypothesis : (1) Those 

 which are natural and which can hardly be 

 avoided, as that the influence of very distant 

 bodies is negligible; (2) those that are indif- 

 ferent, as that matter is continuous or that it 

 is composed of atoms. These indifferent hy- 

 potheses are never dangerous, provided their 

 true character is recognized. The hypotheses 

 of the third category are true generalizations 

 which experience should either confirm or in- 

 validate. 



The hypotheses of physics lead to physical 

 theories which, though apparently well estab- 

 lished, are in turn displaced by others. Vari- 

 ous examples are discussed. 



" No theory seemed more solid than that of 

 Fresnel which attributed light to movements of 

 ether. But now that of Maxwell is preferred. 

 Does this mean that the work of Fresnel was in 

 vain? No, because the real aim of Fresnel was 

 not to find out whether there really is ether, 

 whether it is or is not formed of atoms, whether 

 these atoms I'eally move in this or that sense; 

 his object was to foresee optical phenomena. 



Now the theory of Fresnel always permits this, 

 to-day as well as before Maxwell. The differ- 

 ential equations are always true; they can always 

 be integrated by the same procedure and the 

 results always retain their value. 



Let no one say that thus we reduce physical 



