LAW OF COMPOUND INTEREST 113 



of which depends on the initial capital, the rate of interest 

 and the time the money is accumulating ; the dry weight of an 

 annual plant depends upon the dry weight of the food reserves 

 in the seed, the percentage increase in the dry weight over the 

 selected period, and the time during which the plant is in- 

 creasing in weight. This may be represented by the equation 



Where W l is the final weight, W the initial weight, r the 

 average rate of interest, t time, and e the base of natural 

 logarithms. 



The rate of interest is obviously of first rate importance 

 and if constant the final weight will vary directly as the initial 

 weight, wherefore a large seed, with more initial capital, will 

 give a much larger plant than a small seed, with a relatively 

 smaller initial capital. 



From considerations such as these Blackman arrives at the 

 conception that the rate of increase observed in the plant is 

 the index of efficiency of the plant, a conception which gives 

 a useful basis for comparison but which is not a constant 

 since it is the average of a number of rates which may show 

 variations through a wide range, for it is affected by the external 

 conditions. The rate of increase is highest in the early stages 

 of growth and falls with the inception of the reproductive 

 period. 



The laws governing autocatalytic reactions are the logical 

 outcome of the laws of monomolecular reactions.* An auto- 

 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 

 diminishing amount of methyl acetate, and the increasing 

 amount of acetic acid, until the whole of the substrate is dis- 

 sociated. 



From his study of the growth of various organisms, 



*Vol. I., p. 363. 

 VOL. II. 8 



