950 Prof. J. II. Jeans on Non^Newtonian Mechanical 



vanish separately. It follows that when the matter is suffi- 

 ciently reduced in amount, the value of each term on the 

 left is infinitesimal . 



We accordingly suppose as an approximation that 



b^ + mr (10) 



f >r each v;ilu j of a and proceed to examine the nature of the 

 co-ordinates Q,, K\, E3quation (10) is the condition that 



<w/W_K,/n .!,;,]! be a perfect differential. Calling this 



f /(/>,* we have 



The rate of change of $ t is given by 



: c></>, • 30, • 



by equations (11). Thus </>, does not vary with the time. 



Tl nergy E # of the »th vibration is some function, at 



presenl anknown, of Q t and !( v . [ts rate of change is 



dE,_3E, . 3E, . 



dQ,dR, 9R.3Q, 



_ 9(E S , *.) 



~3(Q.,R.)' 



Since the energy must remain unaltered with the time, 

 the Jacobian must vanish, so that 6 S must be a function 

 of E,. 



* An exception would occur if the matter were arranged so as to have 

 free periods of it* own, so introducing- resonance effects j then the right 

 hand of (9) might ba mainly balanced by a few terms only on the left 

 hand. But even if this is the case, there is no difficulty ; we can confine 

 our attention to wave-lengths for which the resonance effects are 

 nenrlijrible. 



