C. H. WADDINGTON 



exploration of the simpler varieties of these to give a rather more definite picture 

 of the kind of system with which we are confronted. 



Let us consider, at first, two substances P and Q,, which are being formed out of 

 the raw materials A, B and C, for the supplies of which they compete. To give the 

 simplest possible picture of such a competition, suppose that P is formed from A 

 and B, while Q, is formed from B and C. Again for the sake of simplicity, let the 

 reaction constants be the same for the two syntheses, as shown in Figure i ; and let us 



\ 



B< 



C * 



k 2 



ki 



y ^_ 



■&*- 



Figure i. 



suppose that A, B and C diffuse into the system at rates proportional to the difference 

 in their concentration inside {A, B, C) and outside (a, b, c), while P and Q, are removed 

 at rates k 3 . Then for the rates of change of the various components of the system we 

 shall have a set of equations : 



4 = k{a-A)-k 1 AB+k 2 P 

 at 



^ =k{b-B)- k x AB+k,P- k x BC+ k 2 Q 

 at 



= k{c-C)-k 1 BC+k 2 Q 



dC 

 of 



~ =k 1 AB-k 2 P-k 3 P 



dt 



d Q' = k 1 BC-k 2 (l-k z Cl 

 at 



114 



