1900.] on the Dynamical Theory of Heat and Light. 391 



to the value of q in case (/?) ; in case (a), whether of § 46 or § 47, the 

 time-integrals of the kinetic energies to he compared are as \ 2 q 1 

 to 2 (1 — q 2 ), and in case (/?) they are as ^ 2 q 3 and 2 q (1 — q 2 ). 

 § 49. Hence with the following notation — 



In § 46 i time-integral of kinetic energy perpendicular to F, = V 

 \ „ „ parallel to F, = U 



j n *£j \ „ translatory energy = V 



I „ rotatory „ = B 



we have ( 2 (i q 2 — 1) . , x 



v.u| = s(i^) lncsse(a) 



V + U l_2 (|- g 3 - g ) 

 Ste-fa 3 ) 



S( fg 2 -1) 

 2(1 -i 9 2 ) 



_ S ($g»-g ) 



08) 



§ 49. By the processes described above, q was calculated for the 

 single particle and corrugated floor (§ 46), and for the rotator of 

 two equal masses each impinging on a fixed plane (§§ 41, 42), and 

 for the biassed ball (central and eccentric masses 100 and 1 respec- 

 tively, §§ 41, 43). Taking these values of q, summing q, q 2 and 

 q 3 for all the flights, and using the results in § 48, we find the 

 following six results : 



Single particle bounding from corrugated floor (semicircular 

 hollows), 143 flights :— 



V — U ( = + • 197 for isochronous sinusoidal flights. 

 V-j-U \ = + '136 for gravitational parabolic „ 



Eotator of two equal masses, 110 flights : — 



V — B, ( = — • 179 for isochronous sinusoidal flights. 



V -f- E i = — * 150 for gravitational parabolic „ 



Biassed ball, 400 flights :— 



V — E C = + • 025 for isochronous sinusoidal flights. 



V + E ( = — "014 for gravitational parabolic „ 



The smallness of the deviation of the last two results from what 

 the Boltzmann-Maxwell doctrine makes them, is very remarkable 

 when we compare it with the 15 per cent, which we have found 

 (§ 43 above) for the biassed ball bounding free from force, to and 

 fro between two parallel planes. 



