TRANSACTIONS OF SECTION B. 397 



ture. C- can, of conrae, be kept constant and hence we obtain on taking logs and 

 differentiating : — 



d log feobserved ^ ^ 



dT kT'' 



But k = - where E is the gas constant per gram molecule. 



Hence ^ log feobserved ^ NTu; 



dT UT' ■ ■ W 



The term N/ir is independent of temperature at least for a very wide range and 

 hence equation (4) may be written ^^^g^obBeived ^ '^onstant^ ^^^^^ .^ _,.^pjy ^^^ 



dT- KT- 



Arrhenius equation, and has been shown to be in very good agreement with experi- 

 ment. We may also compare equation (4) with that of Marcelin and Bice, namely, 



^ °"'^®"^'' = ., where E is approximately the critical increment, that is the 

 di KT" 



quantity of energy which one gram molecule must absorb to make it react. Equating 



the two terms E and N/ic it follows that E/N = hv. But E/N denotes the amount 



of energy whicli must be added to a single molecule to make it reactive and this by 



the above relation is just one quantum of the radiation of the absorbable type i>. 



This is simply a statement of Einstein's law of the photochemical equivalent, and the 



fact that under certain simplifying assumptions we have obtained tliis relation along 



with an expression for the temperature coefficient which is in agreement with the 



Marcelin-Kice equation and that of Arrhenius may be taken as some evidence for the 



general correctness of the ideas underlying the deduction. 



Of course, one realises that more than one approximation has been made in the 



above, and, under certain conditions, therefore, one may expect to find discrepancies 



between experiment and theory. There is not time to enter into any of these in 



detail. One may summarise the results which have been further obtained : — 



(1) Instead of regarding the refractive index n as a constant, it is more correct to 

 allow for its variation with temperature. Making use of the available data 

 it may be shown that the effect of this variation is to slightly diminish the 

 value of N/tj'. 



("2) The index n also is a function of the concentration of the catalyst. When 

 the catalyst is a positive one it can be shown that an increase in its concen- 

 tration diminishes the temperature coefficient. When the catalyst is a 

 negative one it can be shown that increase in concentration increases the 

 temperature coefficient. The experiments of Von Halban and others on mixed 

 solvents support this conclusion. 



(3) In the case of a reaction which reaches an equilibrium it can be shown that 

 the heat of the reaction is simply the difference of the characteristic vibration 

 frequencies of reactants and resultants multiplied by h. This relation has 

 already been deduced as a rather special case by Haber. 



Mr. J. EiCR. — In a series of papers in the Comptes Bendus, Marcelin has discussed 

 reaction-velocity, by considering that only those molecules react which reach a 

 ' critical ' condition, in which they acquire a certain energy considerably in excess of 

 the average energy per molecule of the system. Marcelin's analysis is very general, 

 and his results can be somewhat extended by some limiting assumptions, which define 

 the ' critical ' condition a little more closely. 



Consider a simple case of dissociation or combination of two molecules ; consider- 

 able forces hold the molecules together when near to each other, but the law of force 

 must be such that this attraction weakens and changes to repulsion or non-interaction 

 at some ' critical ' distance. This implies that the potential energy of the two 

 molecules is a maximum at this ' critical ' distance apart. 



In the general case, a certain group of molecules enter into reaction to produce a 

 group of different molecules. We can describe, from a mechanical point of view, the 

 course of the reaction by choosing n generalised coordinates q, g., . . . q,, for a 

 molecular group, and stating the changes which occur in q, q., . . . q,,, and in the 

 velocity coordinates (/, j, ■ . . (/„ during the reaction. We can choose g, q., . . . q„, 

 so that the kinetic energy, E, of a molecular group equals the sum of squares, 

 (} " + (ji" + . . . qii'. If we assume also that it is possible to choose the coordinates 



