384 SCIENCE PROGRESS 



of an autocatalytic reaction : the growth-rate for the entire 

 season conformed to that of a reaction consisting of two mono- 

 molecular reactions, one of which at first accelerates and sub- 

 sequently retards the other. The same author (" The Nature 

 of the Growth-rate," Journ. Gen. Physiol., ii, 1920, p. 545) 

 measured the rate of increase in height of walnut-trees. The 

 young trees showed distinct growth-cycles in a single season, 

 but in each cycle growth proceeded at a rate corresponding to 

 that of an autocatalytic reaction. In two subsequent papers 

 Reed (" Slow and Rapid Growth," Amer. Journ. of Bot., vii, 

 1920, p. 327 ; also " Correlation and Growth in the Branches 

 of Young Pear-trees," Journ. Agric. Res., xxi, No. 11, 1921, 

 p. 849) emphasises the relationship between the rate of growth 

 and the final size of the plant organ — length of shoots of apricot 

 and pear-trees respectively. The amount of growth " yet to 

 be made " appears to be an exponential function of the final 

 size. The rate may be affected by (i ) a variation in the activity 

 of the catalyst, or by (2) a variation in the supply of potential 

 growth material. 



The suggestion that the rate of growth of a plant organism 

 is similar to an autocatalytic reaction has received the support 

 of Rippel (" Die Wachstumskurve der Pflanzen und ihre 

 mathematische Behandlung durch Robertson und Mitscherlich," 

 Fuhling's Landw. Ztg., Ixviii, Heft 11-12, 1919, p. 201 ; also 

 " Die Wachstumskurve," Ber. d. deutsch. bot. Gesellsch., xxxvii, 

 Heft 3, 1919, p. 169). 



It has been suggested by V. H. Blackman (" The Compound 

 Interest Law and Plant-growth," Ann. Bot., xxxiii, 19 19, 

 p. 357) that the dry-weight of an annual plant, at least in its 

 early stages, increases at continuous compound interest. This 

 can be expressed mathematically by the formula W^ = Woe^\ 

 where PFj = the dry-weight of the plant at the end of time t, 

 Wo = the initial weight of the seed or seedling, e = the base 

 of the natural logarithms, and r = the rate of interest. The 

 value r was termed by the author the " efficienc}^ index" of 

 the plant as a producer of new material, and was regarded as 

 an important physiological constant, but it has since been 

 shown by Kidd, West, and Briggs (" What is the Significance 

 of the Efficiency Index of Plant Growth ? " New Phyt., xix, 

 1920, p. 88) that r is not constant at all, and consequently 

 can be of no value in comparing the efficiency of different plants, 

 except over strictly comparable times and phases of develop- 

 ment. L. R. Waldron (" Rate of Culm Formation in Bromus 

 inerrnis," Journ. Agric. Res., xxi, No. 11, 1921, p. 803), who 

 studied the rate of culm-formation in Bromus inerrnis, showed 

 that the rate of increase is not fixed, but takes place at an 

 accelerating rate. The Compound Interest Law has no real 



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