Ill] A PASSAGE IN DARWIN 59 



with all their parts in proper proportion, as soon as any part 

 became visible." It would seem to me that even the most 

 elementary attention to form in its relation to growth would have 

 removed most of Darwin's difficulties in regard to the particular 

 phenomena which he is here considering. For these phenomena 

 are phenomena of form, and therefore of relative magnitude ; 

 and the magnitudes in question are attained by growth, proceeding 

 with certain specific velocities, and lasting for certain long periods 

 of time. And it is accordingly obvious that in any two related 

 individuals (whether specifically identical or not) the differences 

 between them must manifest themselves gradually, and be but 

 little apparent in the young. It is for the same simple reason 

 that animals which are of very dift'erent sizes when adult, differ 

 less and less in size (as well as in form) as we trace them back- 

 wards through the foetal stages. 



Though we study the visible effects of varying rates of growth 

 throughout wellnigh all the problems of morphology, it is not very 

 often that we can directly measure the velocities concerned. 

 But owing to the obvious underlying importance which the 

 phenomenon has to the morphologist we must make shift to study 

 it where we can, even though our illustrative cases may seem to 

 have little immediate bearing on the morphological problem*. 



In a very simple organism, of spherical symmetry, such as the 

 single spherical cell of Protococcus or of Orbulina, growth is 

 reduced to its simplest terms, and indeed it becomes so simple 

 in its outward manifestations that it is no longer of special interest 

 to the morphologist. The rate of growth is measured by the rate 

 of change in length of a radius, i.e. V = {R' — R)/T, and from 

 this we may calculate, as already indicated, the rate of growth in 

 terms of surface and of volume'. The growing body remains of 

 constant form, owing to the symmetry of the system; because, 

 that is to say, on the one hand the pressure exerted by the growing 

 protoplasm is exerted equally in all directions, after the manner 

 of a hydrostatic pressure, which indeed it actually is : while on 

 the other hand, the "skin" or surface layer of the cell is sufficiently 



* '"In omni rerum naturalium historia utile est mensuras definiri et numeros," 

 Haller, Elem. Physiol, ii, p. 258, 1760. Cf. Hales, Vegetable Staficks, Introduction. 



