TRANSACTIONS OF SECTION A. 635 



determined by the sign of tlie inequality. This last is unaltered by reversing the 

 Telocity componeuts of all the particles. 



In order that a stationary distribution of energy may be possible^ certain con- 

 ditions represented by inequalities must hold good, and further conditions, which 

 may or may not be identical with these, must be satisfied in order that the distri- 

 butions may be stable. These properties may pf rbaps have a physical interpretation 

 in the notion that change of state takes place when the conditions in question 

 cease to hold good. Finally, the fact that the Newtonian potential satisfies 

 Laplace's equation may possibly give an exceptional character to the phenomena of 

 energy-partition in the cosmic universe. It is also evident that expressions for the 

 second differential coefficients of squares and products of velocity components may 

 theoretically be written down for a dynamical system of the most general character, 

 and applied to determine the partition of energy between the molecules and the 

 ether. 



3. Note 011 the Propagation of Electric Waves along Parallel Wires. 

 By Prof. W. B. Morton, M.A. 



In the ' Annalen der Physik ' for June 1900, a very complete investigation of 

 this problem has been published by G. Mie. He finds expressions for the wave- 

 length and damping of the oscillations, involving a series of ascending powers of the 

 ratio of radius of wires to distance apart. The object of this note is to point out 

 that the approximate solution, in which the square of this ratio is neglected, can 

 be very easily obtained from the known solution for a single wire, as worked out 

 by Professor J. J. Thomson and by Sommerfeld. The formula for the damping 

 agrees with that given by Heaviside's simple theory when Lord Rayleigh's high- 

 frequency values are used for the resistance and inductance. Attention is called 

 to an error in the formula for the K^ function in the work of Thomson, Sommerfeld, 

 and Mie, arising probably from an erratum in Heine's 'Kugelfuuctionen.' It afl'ects 

 the numerical values worked out in Sommerfeld and Mie's papers. 



4. On the Vector Potential of Electric Currents in a Field lohere Disturb- 

 ances are propagated with Finite Velocity. By S. H. Burbuey, F.R.S. 



1 . If u' v' lo' be the components of the total electric current at x' y' rJ in a 

 homogeneous isotropic transparent medium, the components of vector potential 

 F G II at any point .r y s at a given instant are usually defined as follows, 



F =. (((^*^f7.i'r?^'rf2 = \''^dr Sec, where r = ^/(,^•' - .vf+Qf^'^(z''^^' and the 



integration is over all space. Also ti' v' lo' are the values of u' v' w' at the given 

 instant, and therefore all at the same instant. Hence follow Poisson's equations 



^'■F,,,j, = -irrtCry, Sec (1) 



2. If 



dy dz 



^ dz dx ' 



^t?G _d¥ 

 ' dx dy 



Then 



dy dz dx\dx dy dz J 



