R. E. BUCHANAN 55 



rates resemble the effects upon rates of chemical reactions. It is commonly found that 

 chemical reactions are accelerated by rise in temperature, and in ranges of o°-ioo° C. 

 frequently doubled or trebled in rate by each increase of io°. This tendency to double 

 or treble the rate has come to be termed the "R.G.T." {Reaktionsgeschwindigkeit 

 Temperatur) rule. Studies upon rates of bacterial growth in certain ranges have 

 shown values of Qw frequently equal to two or three. 



It has been shown that in chemical reactions the value of Qw tends to decrease 

 with rise in temperature. This relationship has been developed by van't Hoff and 

 Arrhenius into the generalization : The rate of change in the logarithm of the velocity 

 coefficient of a chemical reaction with temperature is inversely proportional to the 

 square of the absolute temperature, i.e., 



dink _ A . , 



It was also shown that the constant^ may be substituted by-^ , in which ju is a con- 



K 



stant characteristic of the reaction (thermal increment) and R the gas constant 



(numerically equal to 2). Integration of equation (22) yields 



lnk = -j,+C (23) 



Conformity of a reaction to the relationship of equation (23) may be determined by 

 plotting the values of In k against the reciprocal of the absolute temperature; agree- 

 ment is manifest by the development of a straight line, with slope - . 



It is of interest to determine whether growth rates (and growth curves) of micro- 

 organisms are similarly related to temperature. The work of Crozier ef al.^ indicates 

 that results of value may be secured by studies of the values of thermal increments 

 (m). It is contended that growth rates are controlled by rates of chemical reactions, 

 and changes in the latter due to temperature changes should produce corresponding 

 changes in the former. Since the growth is probably the resultant, in many cases at 

 least, of a catenary series of reactions, the rate of growth would be controlled by the 

 slowest rate. Changes in temperature may therefore modify the rate of growth in the 

 same manner as they modify the rate of the slowest reaction. 



From equation (23) the following relations are evident: 



k. H-ffi) 



Q,o=eT'T. (25) 



in which ^2 and kj represent the velocity coefficients at the higher and lower tempera- 

 tures (absolute) T2 and Ti, respectively. 



' Crozier, W. J., el al.: J. General Physiol., 7, i8g. 1924. 



