On the Bates of a Rocling Watch. 595 



The mean value of this expression for u l u. 2 + i\t\ 2 -{-w l w^ 



is ^rr t^i where D 12 denotes the anaxial minor of D 1? and 

 la D 



contains terms in the first degree of the b's. But now 



w l£l = ( m l + m 2) l>\2 u l U 2 + & C - 



And if we form u x u^ in the same way, the expression will 

 contain only second and higher powers of the Vs. It follows 

 that 2(iig + vi] + w£) does not represent the stream energy. 

 And therefore the law of equal partition is not proved in the 

 sense above explained. 



If, however, as a mere question of definition, and "without 

 prejudice " to the facts, we call £("i£i + r i 7 ?i + w 'i£'i) ^he 

 energy of stream-motion for mj, there is much to be said for 

 the definition. By so doing we should in a measure preserve 

 the symmetry, while unable to maintain the accuracy, of the 

 Maxwell-Boltzmann theory of equal partition of energy. 



21. I think the conclusions to be drawn are as follows :— 



I. The law of equal partition of energy among the trans- 

 lation velocities is not proved by the Maxwell-Rayleigli 

 method. 



II. It is not proved by Boltzmann's method, because the 

 fundamental assumption on which that method is based is 

 not proved. 



III. Subject to any proof that may be given hereafter of 

 Boltzmann's assumption, which, however, I think can be 

 disproved, the law is not generally true in any sense 

 whatever. When, however, the density is very small,' 

 mu 2 will differ from m'vl' 1 only by small quantities of the 

 second order. 



The law may therefore be asserted for the limiting case of 

 an infinitely rare gas. 



LVIII. The Rates of a Rocking Watch, with Remarks on a 

 Gravitational Pendulum. By 0. Barus *. 



(1) A FTER mounting the works of an old watch in a 

 J_~\. hard-wood ring, 1 noticed that the period of the 

 watch and case when suspended loosely from a pin a (after- 

 wards, see fig. 4, replaced by a knife-edge), was almost 

 identical with that of the balance-wheel. As a result, the 

 watch when left to itself rocked permanently to and fro, 

 the excursions amounting to as much as 9°, in later experi- 



* Communicated by the Author. 



