CONCLUSION 147 



extension-factor m into what he styles his relative extension- 

 factor r, which alone makes comparison possible between 

 different species. It is clear, however, that if his general 

 argument is correct, the two factors here recorded will serve 

 to give a complete description of the facts concerning the 

 relative growth of an organ from its first inception. 



We see, for instance, that the brains of chick and duck 

 start of nearly the same relative size, but that that of the 

 duck then grows relatively more rapidly. The gizzard is laid 

 down of larger size in the duck than in the chick, but then 

 grows much more slowly, so that it ends up considerably 

 smaller. Similarly, the sand-martin, which in the adult is 

 characterized by very small hind-limbs, has large hind-limb 

 rudiments which then proceed to grow very slowly. It is 

 interesting to find that the growth-quotient of the hind-limbs 

 is in all species investigated higher than that of the fore-limbs. 



I feel that some of the formulae advanced by Schmalhausen 

 are open to criticism and will need some further corroboration. 

 However, his method for arriving at the true corrected growth- 

 coefficient for embryonic organs is of real value, and if possibly 

 not always fully accurate, is undoubtedly the only way at 

 present available by which we can arrive at a good first 

 approximation. (See also the work of Ford, p. 260.) 



§ 8. Conclusion 



The chief points in this chapter may be briefly summarized 

 as follows : D'Arcy Thompson's method of employing Car- 

 tesian co-ordinates to effect the geometrical transformation 

 of an organism or organ gives evidence of the existence of 

 orderly growth-changes within the body. These may be of 

 complex nature, but can be analysed into a series of growth- 

 gradients. Confirmation of this is provided by quantitative 

 analysis of various organisms during their growth. A curious 

 effect is noted by which the presence of a centre of high growth- 

 intensity intercalated in a main growth-gradient is correlated 

 with minor changes in the growth-intensity of neighbouring 

 parts. Those immediately posterior are somewhat increased 

 in size, those immediately anterior appear to be somewhat 

 decreased in size : i.e. the main growth-gradient is deformed 

 in a regular way by the presence of the subsidiary growth- 

 gradient. Finally, it is pointed out that constant growth- 

 coefficients of parts and regular growth-gradients within organs 

 and the body as a whole, such as here described, appear to be 



