734 SCIENCE AND HYPOTHESIS 



structions, between which communication is difficult and sometimes 

 impossible. Take, for instance, the chapter in which electrostatic at- 

 tractions are explained by the pressures and tensions of the dielectric 

 medium. This chapter might be suppressed without the rest of the 

 book being thereby less clear or less complete, and yet it contains a 

 theory which is self-sufficient, and which can be understood without 

 reading a word of what precedes or follows. But it is not only inde- 

 pendent of the rest of the book; it is difficult to reconcile it with 

 the fundamental ideas of the volume. Maxwell does not even attempt 

 to reconcile it ; he merely says : " I have not been able to makie the 

 next step namely, to account by mechanical considerations for 

 these stresses in the dielectric." 



This example will be sufficient to show what I mean; I could quote 

 many others. Thus, who would suspect on reading the pages devoted 

 to magnetic rotatory polarization that there is an identity between 

 optical and magnetic phenomena? 



We must not flatter ourselves that we have avoided every contra- 

 diction, but we ought to make up our minds. Two contradictory 

 theories, provided that they are kept from overlapping, and that 

 we do not look to find in them the explanation of things, may, in 

 fact, be very useful instruments of research ; and perhaps the reading 

 of Maxwell would be less suggestive if he had not opened up to us 

 so many new and divergent ways. But the fundamental idea is 

 masked, as it were. So far is this the case, that in most works that 

 are popularized, this idea is the only point which is left completely 

 untouched. To show the importance of this, I think I ought to 

 explain in what this fundamental idea consists; but for that purpose 

 a short digression is necessary. 



The Mechanical Explanation of Physical Phenomena. In every 

 physical phenomenon there is a certain number of parameters which 

 are reached directly by experiment, and which can be measured. I 

 shall call them the parameters q. Observation next teaches us the 

 laws of the variations of these parameters, and these laws can be 

 generally stated in the form of differential equations which connect 

 together the parameters q and time. What can be done to give a 

 mechanical interpretation to such a phenomenon? We may endeavor 

 to explain it, either by the movements of ordinary matter, or by those 

 of one or more hypothetical fluids. These fluids will be considered as 

 formed of a very large number of isolated molecules m. When may 

 we say that we have a complete mechanical explanation of the phe- 

 nomenon? It will be, on the one hand, when we know the differen- 

 tial equations which are satisfied by the co-ordinates of these hypo- 

 thetical molecules m, equations which must, in addition, conform to 

 the laws of dynamics; and, on the other hand, when we know the 

 relations which define the co-ordinates of the molecules m as func- 



