272 ProF. McLennan and Mr. Shaver on Permeability of 



where the A's are, in general, functions of the co-ordinates 

 Qi> Q2 — J an( i the a's are likewise functions of the <?'s. 

 Whence at once there is obtained for the / form. Jexp — AT. 

 As before, we may pass from this expression for the law of 

 distribution of the genus to that of the universe *. 



III. The third argument in the simple form so far adopted 

 is not applicable to cases in which the co-ordinates are 

 changed by an encounter. Recourse must be had to that 

 theorem of Liouville which leading writers have called in at 

 an earlier stage. 



E. It would be possible to advance further in other 

 directions — in particular, where a held of force occurs — on 

 the lines of the first and second arguments, without the aid 

 of Hamiltonian Dynamics, by mere Probabilities. 



XXX. On tlie Permeability of Thin Fabrics and Films to 

 Hydrogen and Helium. By Prof. J. 0. McLennan", 

 F.R.S., and W. W. Shaver, P. A., University of Toronto^. 



I. Introduction. 



IN a recent paper by R. T. El worthy J and V. F. Murray 

 the diffusion of hydrogen and helium through thin 

 rubber fabrics was discussed, and the results of measurements 

 made by them on several samples of balloon fabrics were 

 given. In these experiments the amount of gas diffusing 

 through the fabrics was measured by a Shakespear Katharo- 

 meter and by a Jamin Interferometer. As the method was 

 one capable of wide application it was decided to use it in 

 determining the permeability of liquid films to various gases, 

 and the following paper describes some experiments made 

 upon the passage of hydrogen and helium through soap 

 films. The study of gas transfusion through membranous 

 tissues is an important physiological problem, and it was 

 thought on this account that it would be useful and might 

 prove interesting to measure the rate of gas diffusion through 

 films of various materials, with a view to formulating a more 

 exact theory of the process of gas transfusion than exists at 

 present. 



* Above, p. 264. 



t Communicated bv the Authors. 



I Proc. Roy. Soc. Can., May 1919. 



