1 78 GROWTH 



catalytic reaction is one in which one of the products of dis- 

 sociation of the original material acts as a catalyst on the 

 material which is obviously decreased in amount as the reaction 

 proceeds. Thus a solution of methyl acetate undergoes auto- 

 dissociation into methyl alcohol and acetic acid ; of these 

 products the acetic acid catalyses the methyl acetate so that 

 the rapidity of the reaction is continually accelerated, owing 

 to the diminishing amount of methyl acetate and the increas- 

 ing amount of acetic acid, until the whole of the substrate is 

 dissociated. 



From his study of the growth of various organisms, Robert- 

 son * concludes that in any particular growth cycle, either of 

 an organism or of a member of an organism, the maximum 

 increase in volume or in weight in a unit of time occurs when 

 the total growth due to the cycle is half completed. Such a 

 cycle of growth conforms to the formula 



where x is the amount of growth in weight or volume which 

 has been attained in time t. A is the total amount of growth 

 attained during the cycle, K is a constant and / is the time at 

 which growth is half completed. These relations are such as 

 would be expected to hold good were growth the expression 

 of an autocatalytic chemical reaction, and the growth of 

 the organism should, from the hypothesis, remain constant, 

 having once attained its maximum. But the contrary obtains, 

 in senescence a loss of weight occurs ; this is supposed to be 

 due to the action of secondary factors which are imposed on 

 the phenomena of growth itself. 



An inspection of Robertson's figures, for example those 

 given for the oat,f or for Cucurbita, shows differences between 

 the observed and calculated growth values of varying magni- 

 tude, and these differences when expressed in percentages 

 sometimes appear too large to support the thesis ; but when 

 the observed and the calculated values are expressed in the 



* Robertson : " Arch. Entwicklungsmech. Org.," 1908, 25, 581. 

 t Id., 26, 108. 



