September 20, 1901.] 



SCIENCE. 



439 



change in films of average thickness of 106 

 millionths of a millimeter (,«/^), and quite 

 recently Rudolph Weber found it in an oil- 

 film when the thickness was 115, a/^'-.* 



Taking the mean of these numbers and 

 combining the results of different variants 

 of the theory we may conclude that a film 

 should become unstable and tend to rupture 

 spontaneously somewhere between the 

 thicknesses of 110 and 55 //,a, and Professor 

 Reinold and I found by experiment that 

 this instability is actually exhibited between 

 the thicknesses of 96 and 45 //./-t.-j- There 

 can therefore be little doubt that the first 

 approach to molecular magnitude is sig- 

 nalled when the thickness of a film is some- 

 what less than 100 ,a,y., or 4 millionths of an 

 inch. 



Thirteen years ago I had the honor of 

 laying before the Chemical Society a resume 

 ofwhat was then known on these subjects, | 

 and I must refer to that lecture or to the 

 most recent edition of O. 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 4 millionths of an 

 inch, which is perhaps from 500 to 1,000 

 times greater than the magnitude which, in 

 the present state of our knowledge, we can 

 best describe as the 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 every 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 



*Annalen der Physik, 1901, IV., pp. 706-721. 



tPhil. Trans., 1893, 184, pp. 505-529. 



tChem. Soe. Tmiis., LIII., March, 1888, pp. 222- 

 262. 



§ 'Kinetic Theory of Gases,' O. E. Meyer, 1899. 

 Translated by K. E. Baynea. 



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 magnitude 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 deter- 

 mined, 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 inde- 

 pendent methods differ only by about 3 

 per cent. Further, the mean of the values 

 which I gave in the lecture already referred 

 to differed only by about 6 per cent, from 

 the 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 com- 

 mon error may affect them all. In par- 

 ticular, some critics have of late been in- 

 clined to 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 

 considerable variation in the sizes of in- 

 dividuals. 



Allowing this argument more weight 

 than it perhaps deserves, it is easy to show 

 that it cannot affect seriously our knowl- 

 edge of the length of the mean free path. 



Professor George Darwin f has handled 

 the problem of a mixture of unequal spher- 



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

 t Phil Trans., 180. 



