Ill] THE RATE OF GROWTH 281 



Summary and Conclusion 



For the main features which appear to be common to all curves 

 of growth we may hope to have, some day, a simple explanation. 

 In particular we should like to know the plain meaning of that point 

 of inflection, or abrupt change from an increasing to a decreasing 

 velocity of growth, which all our curves, and especially our accelera- 

 tion curves, demonstrate the existence of, provided only that they 

 include the initial- stages of the whole phenomenon: just as we 

 should also hke to have a full physical or physiological explanation 

 of the gradually diminishing velocity of growth which follows, and 

 which (though subject to temporary interruption or abeyance) is 

 on the whole characteristic of growth in all cases whatsoever. In 

 short, the characteristic form of the curve of growth in length (or 

 any other linear dimension) is a phenomenon which we are at 

 present little able to explain, but which presents us with a definite 

 and attractive problem for future solution. It would look as 

 though the abrupt change in velocity must be due, either to a change 

 in that pressure outwards from within by which the "forces of 

 growth" make themselves manifest, or to a change in the resistances 

 against which they act, that is to say the tension of the surface; 

 and this latter force we do not by any means limit to "surface- 

 tension" proper, but may extend to the development of a more or 

 less resistant membrane or "skin," or even to the resistance of fibres 

 or other histological elements binding the boundary layers to the 

 parts within*. I take it that the sudden arrest of velocity is much 

 more likely to be due to a sudden increase of resistance than to a 

 sudden diminution of internal energies: in other words, I suspect 

 that it is coincident with some notable event of histological 

 differentiation, such as the rapid formation of a comparatively firm 

 skin ; and that the dwindling of velocities, or the negative accelera- 

 tion, which follows, is the resultant or composite effect of waning 

 forces of growth on the one hand, and increasing superficial resistance 



* It is natural to suppose the cell-wall less rigid, or more plastic, in the growing 

 tissue than in the full-grown or resting cell. It has been suggested that this plasticity- 

 is due to, or is increased by, auxins, whether in the course of nature, or in our 

 stimulation of growth by the use of these bodies. Cf. H. Soding, Jahrb. d. wiss. Bot. 

 Lxxiv, p. 127; 1931. 



