440 THE BIOLOGY OF FLOWERING PLANTS 



The actively assimilating plant in normal conditions 

 grows in a well-defined fashion. After assimilation has 

 become active the power of the young plant to add to itself 

 is proportional to the amount of matter, or, better, to the 

 amount of active protoplasm, already present, and, as this 

 increases momentarily with assimilation and the growth of 

 the assimilating surface, the power of adding new substance 

 also increases constantly. It works, asV. H. Blackman (1919) 

 has pointed out, like money accumulating at compound 

 interest. The interest for a number of periods is reckoned, 

 not on the amount of the original capital, but, for each period, 

 on that capital plus the interest already accrued to the 

 beginning of that period. In the case of the plant there is 

 this diiference, that the interest is added to the capital not 

 at the end of each year, or week, or day, but from moment 

 to moment. The grand total, the final dry weight sum, is 

 expressed by the formula 



W = Woe'"' 



where r is the rate of interest expressed as a fraction, t the 

 time, W and Wg are the final and initial weights and e = 

 the base of natural logarithms, 2718. The rate of in- 

 terest, which may be taken to represent the efficiency of 

 the particular plant to add to its original capital, the organic 

 material in the seed, is an abstraction with no actual 

 existence ; it changes during the period of growth, besides 

 altering with external conditions. The formula is an ex- 

 pression of the way in which growth takes place early in 

 development, and the rate of interest gives a summarised 

 idea of the efficiency of the plant's constructive capacity. 

 It may be seen that if dry weight is plotted against time 

 the resulting graph will be a logarithmic curve. 



Quite early in development a change takes place. The 

 rate of increase, relative to the dry weight present at any 

 moment, slows down, and the graph connecting growth 

 and time becomes a straight line. The cause of this is 

 partly that, as time goes on, an increasing proportion of the 

 newly formed matter goes to form mechanical tissue which 



