38 PROBLEMS OF RELATIVE GROWTH 



in the adult female of which the abdominal margins far over- 

 lap the leg-bases. 



Then we have the quite different case of Inachus (Fig. 23) 

 which resembles that of the male gnathopod in Gammarus, 

 only here all the marked heterogony appears to be achieved 

 in a single moult-period. And finally we have the fact first 

 discovered by Geoffrey Smith (1906A), that parasitization of 

 Inachus with Sacculina, while reducing or abolishing the 

 heterogony of the male chela, actually increases the growth- 

 ratio of the female abdomen, to remind us that the differential 

 growth-ratios are only constant in certain conditions. 



Similar relations would doubtless be found for other organs, 

 but these are the best analysed. They show that the dif- 

 ferential growth-coefficient of an organ, though it may remain 

 constant throughout post-larval or post-embryonic life, may 

 equally well be confined to the beginning, the end, or the 

 middle (and here sometimes to a very small period) of the 

 life-history, or may change its value slightly but definitely. 

 Since, however, it is justifiable to regard isogony as a special 

 case of heterogony, with growth-coefficiency unity, it remains 

 true that in all cases the growth-coefficients of parts or organs 

 remain constant over definite periods, and that these periods 

 are in the great majority of cases few in number and long in time. 

 (See Hecht, 1916, on the proportions of fishes for a case of 

 long-continued isogony in all measured dimensions : Fig. 24.) 1 



§ 4. Inconstancy of Form and Constancy of 



Form-change 



In concluding this chapter, it may be pointed out that the 

 constancy of growth-ratio over considerable periods of the 

 life-history in spite of environmental fluctuation, is of very 

 considerable importance for analytical morphology. Where- 

 ever it obtains, it implies that the form of an animal, as given 

 by the proportions of its parts, depends (naturally within the 



1 Even here, the isogony is not permanent. Up to a length of 30 cm. 

 — i.e. about a year old — Kearney (reference in Robbins, Brody et al., 

 1928, p. 123) shows that there is heterogony. Hecht further points 

 out that so far as known, all vertebrates with determinate growth 

 change their proportions continuously up to the adult phase. It is 

 only in forms with indeterminate growth like fishes that there exists 

 a long-continued period with no change in external proportions (though 

 even here the relative size of the viscera changes). The work of Keys 

 (p. 259), however, indicates that Hecht's conclusions are riot strictly 

 accurate. Compare also Olmsted and Baumberger (p. 261). 



