224 



PROBLEMS OF RELATIVE GROWTH 



have if it remained approximately cylindrical. This is summar- 

 ized in the following table, abridged from Bower's Table I. 



Diameter of stele, mm. 



Surface-volume ratio of tracheidal 

 tract 



Surface-volume ratio of equiva- 

 lent cylinder 



075 



3-00 



o-8i 



i.e. the actual surface : volume ratio diminishes to about 

 30 per cent of its initial value : but if the conducting tissue had 

 remained cylindrical in form the ratio would have decreased 

 to about 13 per cent. Changes precisely similar in principle 

 occur in phylogenetic series with increase of size : see e.g. 

 Bower's Table X. 



§ 4. Heterogony and Comparative Physiology 



Disproportionate change of relative size with change of 

 absolute size may have important results in studies in com- 

 parative physiology. (See also Murr, p. 260.) 



This is well brought out by Klatt in an interesting paper 

 (1919). He finds the relation of heart-weight to body- weight 

 in vertebrates to follow our familiar formula for constant 

 growth-partition, the (mean) coefficient, or as he calls it, the 

 ' heart-exponent ', being 0-83 : i.e. heart-weight = constant 

 X body- weight °' 83 . It is interesting to find that the value 

 appears to be very similar whether the size-differences con- 

 sidered are intra- or inter-specific ; this result differs from 

 that of Dubois, etc. (1. c), on the brain, a difference which may 

 presumably be correlated with the prompt functional regula- 

 tion of the size of the heart to the work it is called upon 

 to do. 



In passing, it may be noted that the heart as a whole appears 

 to have a different growth-coefficient from the right ventricle 

 and the auricles. These latter, according to Hasebrock (1927), 

 have a coefficient close to 2/3, which would indicate their 

 functional dependence upon surface-area, or upon general 

 metabolism, which in warm-blooded forms is nearly propor- 

 tional to surface-area ; while the left ventricle has a much 

 higher coefficient, nearly in direct proportion to body-weight. 



But from the point of view of comparative physiology, 



