RHYTHMICAL IRREGULARITIES 203 



hydrostatic pressure causes palmate leaves to become not 

 only smaller, but more dissected and with relatively smaller 

 basal lobes. However, as growth in plants clearly follows 

 very different laws from growth in animals, we will not 

 attempt to enter into any detail. 



§ 8. Rhythmical Irregularities of Growth-ratio 



Finally, we must just mention a curious but possibly im- 

 portant fact, namely the tendency of structures to grow by 

 abnormally high growth first in one dimension of space, then , 

 in another, so that the growth-ratio for breadth on length does 

 not remain constant, but fluctuates more or less rhythmically 

 round a mean. Przibram (1902) has pointed this out in regard 

 to the carapace of crabs. In these he followed individuals 

 through several moults, so he could be certain of the fluctua- 

 tion in proportions. 



I. W. Wilder (1924) finds a similar alternation, of periods 

 of filling out and periods of rapid length-growth with drop 

 in the body-build index, in the larval growth of the salamander 

 Eurycea bilineata, and the same phenomenon is stressed for 

 human children by various authors, notably Bean (1924), 

 Harris (1931 A and b), and with all the apparatus of biometrical 

 method by Berkson (1929) 1 . Thiel (1926), as the result of 

 careful measurements on the skull of the bivalve mollusc 

 Sphaerium, finds an alternation of periods of increased intensity 

 of growth in height and decreased intensity of growth in 

 breadth with periods where the reverse relation holds. Cog- 

 hill (1928) finds evidences of the same sort of thing for definite 

 centres within the embryonic nervous system of amphibia. 

 (He also finds evidence that this periodicity alternates in 

 closely adjacent centres.) And various authors have empha- 

 sized that the same phenomenon occurs in regard to the post- 

 natal length- and breadth-growth of the human cranium. 

 Thus the phenomenon would appear to be general. This 

 again emphasizes the need for large bodies of observations 

 on proportionate growth ; but its physiological basis is at 

 present quite unexplained. 



This chapter, as I pointed out in the introduction to it, has 

 inevitably been both discursive and inconclusive. However, 

 the facts and ideas set forth in it may serve to point the way 

 to more crucial and more radical methods of analysing the 

 problem. 



1 See also" the recent paper of Davenport (1931), Proc. Amer. Philos. 

 Soc, 70, 381. 



