186 A MODEL OF NATURE. 



Society a resume of what was then known on those subjects,* and I 

 must refer to thai lecture or to the most recent edition of (). E. 

 Meyer's work on the kinetic theory of gases" for the evidence that 

 various independent lines of argument enable us to estimate quantities 

 very much less than four millionths of an inch, which is perhaps from 

 500 to L, 000 times greater than the magnitude which, in the present 

 state of our knowledge, we can best describe as tin- diameter of a 

 molecule. 



Confining our attention, however, to the larger quantities, I will 

 give one example to show how strong is the cumulative force of 

 the evidence as to our knowledge of the magnitudes of molecular 

 quantities. 



We have ever}' reason to believe that though the molecules in a gas 

 frequently collide with each other, yet in the case of the more perfect 

 gases the time occupied in collisions is small compared with that in 

 which each molecule travels undisturbed by its fellows. The average 

 distance traveled between two successive encounters is called the mean 

 free path, and. for the reason just given, the question of the magni- 

 tude of this distance can be attacked without any precise knowledge of 

 what a molecule is, or of what happens during an encounter. 



Thus the mean free path can be determined, by the aid of the theory, 

 either from the viscosity of the gas or from the thermal conductivity. 

 Using figures given in the latest work on the subject.' and dealing 

 with one gas only, as a fair sample of the rest, the lengths of the mean 

 free path of hydrogen, as determined by these two independent 

 methods, differ only by about 3 per cent. Further, the mean of tin 1 

 values which I gave in the lecture already referred to differed only by 

 about f, pei- cent from tin 1 best modern result, so that no great change 

 has been introduced during the last thirteen years. 



It may. however, be argued that these concordant values are all 

 obtained by means of the same theory, and that a common error may 

 affect them all. In particular, some critics have of late been inclined 

 to discredit the atomic theory by pointing out that the strong state- 

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

 themselves, of atoms or molecules of the same kind may not be justi- 

 fied, as the equality may be that of averages only, and be consistent 

 with a considerable variation in the sizes of individuals. 



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

 easy to show that it can not affect seriously our knowledge of the 

 length of the mean free path. 



Prof. George Darwin' 1 has handled the problem of a mixture of 



'('licin. S,,c. Trans., LIII, March, 1888, pp. _!^-262. 



b Kinetic Theory of Gases, < >. I' 1 .. Meyer, L899; translated by R. E. Bayiies. 



c Meyer's Kinetic Theory of Gases (see above). 



d Phil. Trans., 180. 



