88 THE RATE OF GROWTH [ch. 



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 importance of the phenomenon to the morpho- 

 logist we must make shift to study it where we can, even though 

 our illustrative cases may seem sometimes to have little bearing 

 on the morphological problem*. 



In a simple spherical organism, such as the single spherical cell of 

 Protococcus or of Orbulina, growth is reduced to its simplest terms, 

 and indeed becomes so simple in its outward manifestations that it 

 loses interest to the morphologist. The rate of growth is measured 

 by the rate of change in length of a radius, i.e. F = {R' — R)IT, and 

 from this we may calculate, as already indicated, the rate in terms 

 of surface and of volume. The growing body remains of constant 

 form, by 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 homogeneous to exert 

 an approximately uniform resistance. Under these simple conditions, 

 then, the rate of growth is uniform in all directions, and does not 

 affect the form of the organism." 



But in a larger or a more complex organism the study of growth, 

 and of the rate of growth, presents us with a variety of problems, 

 and the whole phenomenon (apart from its physiological interest) 

 becomes a factor of great morphological importance. We no longer 

 find that growth tends to be uniform in all directions, nor have we 

 any reason to expect it should. The resistances which it meets with 

 are no longer uniform. In one direction but not in others it will 

 be opposed by the important resistance of gravity; within the 

 growing system itself all manner of structural differences come into 

 play, and set up unequal resistances to growth in one direction or 

 another. At the same time the actual sources of growth, the 

 chemical and osmotic forces which lead to the intussusception of 

 new matter, are not uniformly distributed; one tissue or one organ 

 may well increase while another does not; a set of bones, their 

 intervening cartilages and their surrounding muscles, may all be 



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

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



