20 REPORT — 1901. 



of a millimetre (/xju), and quite recently Rudolph Weber found it in an 

 oil-film when the thickness was 115 ^i/j.* 



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 fifi, and Professor Reinold and I found 

 by experiment that this instability is actually exhibited between the 

 thicknesses of 96 and 45 ^^..^ There can therefore be little doubt that 

 the first approach to molecular magnitudes is signalled when the thick- 

 ness of a film is somewhat less than 100 /.i/.!, or 4 millionths of an inch. 



Thirteen years ago I had the honour of laying before the Chemical 

 Society a resum^ of what was then known on these subjects,^ and I must 

 refer to that lecture or to the most recent edition of 0. E. Meyer's work 

 on the kinetic theory of gases "* for the evidence that various independent 

 lines of argument enable vis 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 desci'ibe 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 collisions is small compared with that in which 

 each molecule travels undisturbed by its fellows. The average distance 

 travelled 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 mole- 

 cule 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 the values which I 

 gave in the lecture already referred to diflfered only by about 6 per 

 cent, from the best modern result, so that no great change has been intro- 

 duced 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 



' Annalen der Physili, 1901, iv. pp. "06-721. 

 - Phil. Trans., 189.3, 184, pp. 505-529. 



* Cliem. Soc. Travis., liii., March 1888, pp. 222-2G2. 



* Kinetic Theory of Gases, O. E. Meyer, 1899. Translated by R. E. Baynes. 

 5 Meyer's Kinetic Theori/ of Gases (see above). 



