54 ■ THE RATE OF GROWTH [ch. 



Every growing organism, and every part of such a growing 

 organism, has its own specific rate of growth, referred to a particular 

 direction. It is the ratio between the rates of growth in various 

 directions by which we must account for the external forms of 

 all, save certain very minute, organisms. This ratio between 

 rates of growth in various directions may sometimes be of a 

 simple kind, as when it results in the mathematically definable 

 outline of a shell, or in the smooth curve of the margin of a leaf. 

 It may sometimes be a very constant one, in which case the 

 organism, w^hile growing in bulk, suffers little or no perceptible 

 change in form; but such equilibrium seldom endures for more 

 than a season, and when the ratio tends to alter, then we have 

 the phenomenon of morphological "development," or steady and 

 persistent change of form. 



This elementary concept of Form, as determined by varying 

 rates of Growth, w^as clearly apprehended by the mathematical 

 mind of Haller, — who had learned his mathematics of the great 

 John BernoulH, as the latter in turn had learned his physiology 

 from the writings of Borelli. Indeed it was this very point, the 

 apparently unlimited extent to which, in the development of the 

 chick, inequalities of growth could and did produce changes of 

 form and changes of anatomical "structure,'' that led Haller to 

 surmise that the process was actually without limits, and that all 

 development was but an unfolding, or "evolutio,'' in which no 

 part came into being which had not essentially existed before *. 

 In short the celebrated doctrine of "preformation" implied on the 

 one hand a clear recognition of what, throughout the later stages 

 of development, growth can do, by hastening the increase in size 

 of one part, hindering that of another, changing their relative 

 magnitudes and positions, and altering their forms ; while on the 

 other hand it betrayed a failure (inevitable in those days) to 

 recognise the essential difference between these movements of 

 masses and the molecular processes which precede and accompany 



* Cf. (e.g.) Elem. Physiol, ed. 1766, viii, p. 114, '•Ducimur autem ad evolu- 

 tionem potissimum, quando a perfecto animale retrorsum progredimur, et incre- 

 mentorum atque nautationum seriem relegimus. Ita inveniemus perfectum illud 

 animal fuisse imperfectius, alterius figurae et fabricae, et denique rude et informe : 

 et tamen idem semper animal sub iis diversis phasibus fuisse, quae absque uUo 

 saltu perpetuos parvosque per gradus cohaereant." 



