POLYATOMIC MOLECULES 87 



and a frequency, v, such that 



vy{n,ni,7i2, ••• ns-i,hj) (3) 



is the rate at which molecules transfer Ikj quanta from the kth to the 

 jth oscillator. The total number of ways that n quanta can be distributed 

 among s distinguishable oscillators is 



(n + s - 1) ! 



n\(s - 1)! 



The reciprocal of this quantity will be indicated by the letter C. Thus 



C 21 n{n, rii, W2, • • • fis^i, hj) (4) 



represents the number of reactions per second due to the transfer of 

 Ikj quanta from the kth. to the jth oscillator. The specific rate for this 

 distribution can then be written as 



rik 



k(n,ni, n2, ■■■ n._i)i = <^ 2] £ n(.n, 7li, 112, ' ' ' ^^s-l, kj) (5) 



k lki = nj* — nj 



where 22 sums over the s — 1 oscillators which can feed energy into the 



k 



reacting oscillator j. This method of expressing the rate omits the 

 possibility that the I quanta might come from two or more different 

 oscillators into the jth one. Such occurrences will be neglected. For a 

 given n the total rate of decomposition at the ^'th oscillator will be 



rik 



knj = C J2J2 2 nin, ni, 7i2, • • • Ws_i, kj) (6) 



Tlr k IkJ = Itj*— llj 



where ^ is the summation over all sets of n's consistent with the con- 

 servation of energy, ^ rir = n, and the condition that no oscillator have 



r 



enough quanta to dissociate them, that is, Ur < rir*, where iir* is the 

 number of quanta required for dissociation at the rth oscillator. We 

 may define an average 7 such that 



^ (w-nfc-ny + s-3)!_ 



2^ y{n, 7ii, 712, •'•ris-i, hj) = — rrr 7(^1, %, rij, hj) 



(jl - Uk - 7lj)l{s - 3)\ 



where the summation includes all ways of distributing n quanta in the 

 molecule such that the j and k degrees of freedom have the fixed values 

 Uk and 7ij. The rate then becomes 



