798 PLANT GROWTH lO 



active, so that in the half-grown leaf the continued enlargement is mainly from 

 the middle and lower parts, particularly along the margins ("marginal meristem") 

 where cell division continues until very late. 



The change of form from a strap-shaped or finger-nail-shaped primordium to 

 the elliptical or ovate leaf has been dealt with geometrically by D'Arcy Thompson 

 and later by Huxley (see Jones, 1957), essentially on the basis that the rate of 

 growth in width is an exponential function of the rate of growth in length, so that, 

 if width hey and length x: 



y = ax^ 



where a and b are constants, the latter usually having a value between i and i .5 

 (see Chapter 2; cf. Avery, 1933). Cast in the form: 



log J ^ b log X + K 



the equation shows that a plot of log (width) against log (length) should give a 

 straight line. In many cases it does (see Whaley and Whaley, 1942, for a good 

 example). The slope of the line is of course different for closely related species 

 (Delisle, 1938) and even for different leaves on the same plant (Jones, 1957). 

 Deeply indented or compound leaves obviously cannot be treated in this way, and 

 besides, their complexity often increases with successive nodes on the plant, or 

 with changed external conditions. 



The measurement of growth in area is experimentally more troublesome than 

 that of length or breadth. Measurements have been made on a few leaves of rela- 

 tively simple geometry, notably by Gregory ( 192 1 ) on cucumber leaves, who found 

 that their enlargement follows a symetrically S-shaped autocatalytic curve. Similar 

 curves were given by the cotyledons when grown at low temperatures, but as the 

 temperature increased their growth curves became more and more asymmetrical 

 and finally lost their S-shape altogether. The significance of an autocatalytic type 

 of curve for growth of any organ is not quite clear. It coidd, of course, be said that 

 any group of cells, each of which continuously divides into two, exhibits a kind of 

 autocatalysis, but the increase in area is primarily due to cell enlargement ; division 

 is responsible only for creating cells which can subsequently enlarge. Furthermore, 

 since cell division and enlargement are unevenly distributed in different parts of 

 the growing leaf one can hardly hope that such mathematical analysis will yield 

 much enlightenment as to the mechanism of the growth process. 



One important point emerges from the general considerations of leaf enlarge- 

 ment, namely that the leaf primordium in dicotyledons must become physiologi- 

 cally differentiated very early, since expansion of the lamina is wholly dependent 

 on light, while elongation of the petiole is not (see especially Gregory, 1957). 

 Dicotyledonous plants grown in complete darkness have virtually no leaf area. This 

 effect of light seems not to be directly due to photosynthesis, for its temperature 

 relations are different from those of photosynthesis, and besides, it exhibits an 

 action spectrum somewhat different from that for photosynthesis and more nearly 

 resembling that for the induction of flowering (Parker et al., 1949), though the 

 spectrum is not sharp enough to draw firm conclusions. However, Williams (1957) 

 has suggested that the action of light is exerted by promoting protein synthesis, a 



