386 PROCEEDINGS OF THE AMERICAN ACADEMY. 



But how is it possible to reconcile this complex reaction with the 

 simple mathematical expression — which was found to hold approxi- 

 mately for moderate dilutions? If we represent hj fa* the concentra- 

 tion of the active bromine, by b the total concentration of the hydrobromic 

 acid, and by c the total bromine, the requirement of " mass law" would 

 be at least as complicated as 



(fa) n [ b -'^^ {c -/«)] «> = k (c-fa) «".. 



This is on the assumption that the law holds exactly, and that the hydro- 

 gen tribromide is ionized to the same extent as the hydrobromic acid. 

 Qualitatively this equation holds true ; for an increase in c actually 

 causes an increase in a, as the equation demands. If all the n values 

 are assumed to be unity, it is clear that /a must grow in greater propor- 

 tion than c —fa with increasing c and constant b. Moreover, c must 

 grow faster tlian c — fee ; and it is not at all impossible that for mod- 

 erate concentrations the relation mi^ht be such that" — —k, — the 



^ c 



observed approximate fact. 



lu view of the many-sided relationships shown by the reaction dia- 

 gram, incomplete as it is, and the inaccuracy of the " law of mass- 

 action " when applied to electrolytes, it is hardly worth while to attempt 

 to construct any more precise mathematical relationship. That which 

 has been pointed out, taken in connection with facts concerning other 

 reactions and the known existence of polybromides, seems to indicate 

 that it is not necessary to class the action of hydrobromic acid among 

 catalytic phenomena ; the reaction indicated on this page seems a more 

 probable explanation. 



Summary. 



The following points may be relocated as the chief outcome of the 

 present investigation : — 



* a signifies the rate of change ; the active bromine may be assumed as a 

 function of this rate. 



