1905 - 6 .] Dr W. Peddie on Vibrating Systems. 
139 
(4), we must suppose that the divisor A is included in each A. 
The inequalities then reduce ’ to 
and must be negative. A four-fold infinity of examples is possible 
The Boltzmann-Maxwell Law holds in the three-fold infinity of 
cases obtained by changing the inequalities to equalities. 
13. Although the case of a self-contained system of n masses 
vibrating in one-dimensional space ; or, say, of a system of k masses, 
where n— 3k, vibrating in three-dimensional space ; and not subject 
to the law of equi-partition, is of great interest, the other case in 
which a preponderating mass has to be placed effectively at the 
origin is of even greater interest as embodying Kelvin’s view, § 1, 
that “each atom must have satellites connected with it (or ether 
condensed into it or around it) and kept (by the collisions) in 
motion relatively to it with total energy exceedingly small in 
comparison with the translational energy of the whole system of 
atom and satellites.” When the mass of each satellite is. so small 
that the forces which act on it produce accelerations which are large 
in comparison with the accelerations to which the central mass 
is subject, communication of energy to the satellites may have little 
direct connection w r ith communication of energy to the central mass. 
And, in any case, there is no necessary observance of equi-partition 
of energy amongst the satellites, since the effects of collisions appear 
only in the squared coefficients such as A x 2 , etc., in equation (4). 
The above results apply at once to the case of a luminous gas, 
provided that we postulate (1) that the time of description of the 
average free path is long relatively to the longest constituent period 
and to the time of impact ; (2) that the temperature is such that 
only a small proportion of collisions give rise to disintegration of the 
molecules or to change of their essential configurations ; (3) that the 
fractional loss of energy by radiation during free intervals is small. 
14. The object of the investigation, as stated in § 2, is to 
determine systems in which equi-partition of energy, of vibrational 
type, cannot take place. And, as we have just seen, the systems 
"T > 1 _3 > I . 
m 2 < 9 ’ m 2 < J 
and the common value of - n x 2 , - n 2 2 , - n B 2 , is 
