706 Mr. R. J. A. Barnard on Direct Application of 



frictionless piston, both cylinder and piston being imper- 

 meable to heat, and the axis of the cylinder being vertical 

 with the piston uppermost. If, as a first approximation, 

 we neglect the inertia of the gas in comparison with that of! 

 the piston, the single working coordinate is the height (z) of 

 the piston above the bottom of the cylinder, the kinetic 

 energy being made up of ^Ms 2 (where M is the mass of the 

 piston) and the \s } the %'s being the coordinates necessary 

 for the complete specification of the distribution of gas- 

 molecules when z is given. On differentiating with respect 

 to the various %'s it is evident that the momenta thus obtained 

 are homogeneous linear functions of the ^'s, so that the x's 

 are likewise homogeneous linear functions of the momenta, 

 and the whole kinetic energy is equal to ^Mi; 2 together with 

 a h.q.f. of the ^-momenta. The further condition which is 

 sufficient to ensure that the energy of the ^-momenta shall 

 have the potential character is that, when these momenta are 

 given, none of the %'s shall involve z (though they may and 

 do involve z). This is consonant with the assumptions which 

 we make when we propose to treat as potential energy the 

 translational energy of the gas-molecules. 



39. Similar considerations are readily applied to a differ- 

 ential volume-element of a gas through which sound-waves 

 are travelling. That energy of the element which we com- 

 monly treat as kinetic is its energy of translational motion, 

 corresponding to velocity-components x, y, z of its mass- 

 centre : while the energy of the momenta corresponding to 

 the remaining (ignored) coordinates of the gas-molecules- 

 which make up the element is independent of #, y, z, as are 

 also the velocities of the ignored coordinates when the corre- 

 sponding momenta have assigned values. 



LXIV. Direct Application of the Electron Theory to Induction 

 Currents. By R. J. A. Barnard, M.A., Melbourne *. 



AMOVING charge of electricity in a magnetic field is 

 acted on by the electromagnetic force e(y x H) in 

 Gibbs's Vector notation, where v is the velocity. Conse- 

 quently, if electrons are moving about in a conductor, even 

 when no current is flowing an electromagnetic force is acting 

 on each electron when there is an external magnetic field. 

 But since the electrons are moving in such a case impartially 

 in all directions, there can be no resultant effect produced by 

 these forces. Even if a current is flowing, the resultant 

 effect of the electromagnetic force will be perpendicular to 

 * Communicated by the Author. 



