ADDRESS. 21 



discredit the atomic theory by pointing out that the strong statements 

 which have sometimes been made as to the equality, among themselves, 

 of atoms or molecules of the same kind may not be justified, as the 

 equality may be that of averages only, and be consistent with a consider- 

 able variation in the sizes of individuals. 



Allowing this argument more weight than it perhaps deserves, it is 

 easy to show that it cannot affect seriously our knowledge of the length 

 of the mean free path. 



Professor George Darwin ^ has handled the problem of a mixture of 

 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 among atoms. Without discussing 

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

 considered by him the length of the mean free path is -^^ of what it 

 would be if the particles were equal. Hence were the inequalities 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 /j/x ; 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 acceptance 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 



' Phil. Trans., 180. 



