A MODEL OF NATURE. 187 



unequal spherical bodies in the particular case in which the sizes are 

 distributed according to the law of errors, which would involve far 

 greater inequalities than can occur amongatoms. Without discussing 

 the precise details of his problem, it is sufficient to say that in the case 

 considered by him the length of the main free path is seven-elevenths 

 of what it would be if the particles were equal. Hence, were the ine- 

 qualities of atoms as great as in this extreme case, the reduction of 

 the mean free path in hydrogen could only be from 185 to 119 fAf*; 

 but they must be far less, and therefore the error, if any, due to this 

 cause could not approach this amount. It is probably inappreciable. 



Such examples might be multiplied, but the one I have selected is 

 perhaps sufficient to illustrate my point, viz, that considerable and 

 fairly accurate knowledge can be obtained as to molecular quantities 

 by the aid of theories, the details of which are provisional and are 

 admittedly capable of improvement. 



IS THE MODEL UNIQUE? 



But the argument that a correct result may sometimes be obtained 

 by reasoning on imperfect hypotheses raises the question as to whether 

 another danger may not be imminent. To be satisfactory our model 

 of nature must be unique, and it must be impossible to imagine any 

 other which agrees equally well with the facts of experiment. If 

 a large number of hypotheses could be framed with equal claims to 

 validity, that fact would alone raise grave doubts as to whether it were 

 possible to distinguish between the true and the false. Thus, Professor 

 Poincare has shown that an infinite number of dynamical explanations 

 can be found for any phenomenon which satisfies certain conditions. 

 But though this consideration warns us against the too ready accept- 

 ance of explanations of isolated phenomena, it has no weight against 

 a theory which embraces so vast a number of facts as those included 

 by the atomic theory. It does not follow that because a number of 

 solutions are all formally dynamical they are therefore all equally 

 admissible. The pressure of a gas may be explained as the result of 

 a shower of blows delivered by molecules, or by a repulsion between 

 the various parts of a continuous medium. Both solutions are expressed 

 in dynamical language, but one is and the other is not compatible with 

 the observed phenomena of expansion. The atomic theory must hold 

 the field until another can be found which is not inferior as an expla- 

 nation of the fundamental difficulties as to the constitution of matter 

 and is, at the same time, not less comprehensive. 



On the whole, then, the question as to whether we are attempting 

 to solve a problem which has an infinite number of solutions may be 

 put aside until one solution has been found which is satisfactory in all 

 its details. We are in a sufficient difficulty about that to make the 

 rivalry of a second of the same type very improbable. 



