122 Mr. S. H. Burbury on Diffusion of 



As an example, consider the question of the stability of la 

 symmetrical top spinning in small oscillation about the 

 vertical when acted on by a periodic force through a point 

 in the axis. If the force is vertical the equations of motion 

 are : 



— A?) + Cmf + 3%7i(l -f a cos nt)y =0, 



Af + Cm'rj — Mgh(l + a cos ntyt; = 0, 



so that the effect of the applied force, to this degree of 

 approximation, is to produce a variation in the spring alone ; 

 hence a comparatively large oscillation is generated if n lies 

 near to a certain value in the vicinity of 2/x : /r or 2fjL 2 /r, where 

 Hi and /x 9 are the natural frequencies and r any integer. If, 

 on the other hand, the force is horizontal the spring is not 

 affected, and there is instability only when g=fii or fi 2 . 

 When the horizontal and vertical forces act together, 



— A?7 + Cmf + Mgh(l + a cos nt)ri = Mgh a sin (qt + e), 



Af + Gm'j] — Mgli(l + a cos nt)% = ; 



so that the joint action produces a large effect when 

 q = \c + rn \ , where c represents either of the frequencies 

 under the vertical force alone. 



The spring and direct disturbances may be produced by 

 giving the point of suspension periodic motions in the vertical 

 and horizontal directions respectively ; and for readily ap- 

 preciable magnification it would be necessary to have the 

 vertical vibration of large amplitude, 



VI. Diffusion of Gases as an Irreversible Process. 

 . By S. H. Burbury, F.R.S.* 



PROFESSOR G. H. Bryan in his recent work on Thermo- 

 dynamics (Leipzig, Teubner & Co.) states (p. 125), 

 " when two gases at equal pressure and temperature mix by 

 diffusion, the loss of available energy and consequent gain of 

 entropy is the same as would occur if each component were 

 to expand by rushing into vacuum till it occupied the same 

 volume as the mixture." This statement appears to present 

 some difficulties. 



If in a cylinder of volume 2v, one half on one side of the 

 piston is occupied by oxygen at given pressure and tempera- 

 ture, and the other half is vacuum, we have in that 

 arrangement available energy. We might, by placing the 

 axis of the cylinder vertical with the oxygen at the bottom, 



* Communicated by the Author. 



