A MODEL OB^ NATURE. 187 



mioqual sphorical l)0(li(>s in tln^ ])ai-ticiil:u' casi^ in which tho sizes arc 

 distributed accordino- to the law of (mtots. which would involve far 

 o-reator inequalities than can occur anionj>- atoms. AN'ithout discussino- 

 the precise details of his proldem, it is sufiicient to sa}' that in the case 

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

 of what it would ])e if the particles were equal. Hence, were the ine- 

 qualities of atoms as g-reat as in this extreme case, the reduction of 

 the mean free path in hydrogen could only be from 185 to 119 /i/^/ 

 but the}^ must be far l(\ss, and therefore the error, if any, due to this 

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



Such examples might l)e multiplied, but the one I ha\'e 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 proN'isional and are 

 admittedly capable of improvement. 



TS THE MODEL UNIQUE? 



But the argument that a correct result may sometimes l)e 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 impossil)le to imagine an}^ 

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

 a large numl)er 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 num])er 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 luuuber 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 ma}" 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. lioth solutions are expressed 

 in dynamical language, l)ut one is and the other is not compatible wdth 

 the observed phenomena of expansion. The atomic theory must hold 

 the Held 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 ma}' 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. 



