COMPOUND INTEREST LAW 177 



tional to the quantity itself. This is the law of compound 

 interest ; money left to accumulate at compound interest 

 increases to an amount the magnitude 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 increasing in 

 weight. This may be represented by the equation 



W, = W e« 



where W x 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 rela- 

 tively 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 ex- 

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

 stages of growth and falls with the inception of the repro- 

 ductive period. 



The laws governing autocatalytic reactions are the logical 

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



* This equation is perhaps the simplest suggested for a mathematical 

 expression of growth ; but simple or complex, the objection may be justly 

 raised that in view of the impossibility of evaluating many of the factors 

 governing the rate of growth, more particularly environmental and internal 

 factors, all formulae, even at their best, are mere approximations and there- 

 fore of but little scientific value. However this may be, many authors 

 give a mathematical consideration of their measurements, which, with 

 one exception, are excluded from the following pages. In some instances, 

 such expressions have become polemical (see, for example, Briggs : " Ann. 

 Bot.," 1925, 39, 475 ; " Proc. Roy. Soc," B, 1928, 102, 280; Gregory: 

 " Ann. Bot.," 1926, 40, 1 ; 1928, 42, 531). 



t Vol. I., p. 469. 

 VOL. II. — 12 



