798 Mr. T. Carlton Sutton on the 



mathematician, and it would be interesting to have the con- 

 ditions worked out on which such an integral would give as 

 limit the result (xii.) above arrived at. 



The question, however, is closely bound up with the ex- 

 pansion o£ an arbitrary function not in terms of sines and 

 cosines as in the ordinary Fourier expansion, but in terms of 

 what may be called exponentially damped sines and cosines. 



§ 7. The results above obtained indicate that in the random 

 impulses that constitute natural radiation, we may be led 

 mathematically to a certain distribution of energy in the 

 spectrum, provided that the time-interval T contains a 

 sufficiently large number of any periods considered. Thus 

 between the values p and p-\-dp we shall have an amount of 

 energy e[/(p)] 2 dp/ST per unit volume. If we identify this 

 with the steady distribution obtained by experiment, we are 

 led to suppose that the harmonic analysis of a component of 

 (say) the electric force X over a sufficiently long time T, 

 must yield ultimately results of a steady type in such a way 

 that e. g. if X be given by (ii.), [/(p)] 2 tends to become 

 proportional to T, the time over which the original dis- 

 turbance is analysed. Of course the exact character oif(p) 

 cannot be settled by the considerations adduced. 



LXXXVII. On the Mechanism of Molecular Action. (A Con- 

 tribution to the Kinetic Theory of Gases.) By T. Caklton 

 Sutton, B.Sc, Government Research Scholar in the Uni- 

 versity of Melbourne* . 



Introduction. 



THERE are a number of problems which may be attacked 

 by means of either thermodynamics or the kinetic 

 theory ; and the results obtained by each method should be 

 in good agreement with experiment and with one another. 



Up to the present, much more has been done by means of 

 the thermodynamical than the kinetic method. This is due 

 no doubt to the fact that, while the elements of thermo- 

 dynamics are well known, there is as yet no knowledge of 

 those mechanisms of ultimate molecular action on which the 

 further development of the kinetic theory must be based. 



Accepting the thermodynamical results, it should be 

 possiole to find certain such mechanisms which will yield 

 kinetic results in agreement with the thermodynamical. 



If, in addition, these results are in good agreement with 

 experiment, there is strong evidence in favour of the assumed 

 mechanisms. 



* Communicated by Professor Lyle, M.A., D.Sc, F.K.S. 



