CONSTANT DIFFERENTIAL GROWTH-RATIOS 17 



PaJaemon 

 malcomsoni 



2 6 



2 4 



2 2 



2 



(Huxley, 1926, 1927, 193 1), and the horns, mandibles, etc., 

 of various holometabolous insects (Huxley, 1927 — see Chapter 

 II). It is probable that any other changes of proportion which 

 have not yet been analysed from this point of view will turn 

 out to obey the same law, e.g. 

 the progressive increase of rela- 

 tive tail-length in the salamander 

 Eurycea (Wilder, 1924), or that 

 of wing-rudiments in dragonflies 

 (Balfour-Browne, 1909). See also 

 p. 258 (Daphnia), p. 263 (rat). 



Most of the organs thus far 

 cited are positively heterogonic, 

 increasing in relative size with 

 growth ; others, however, de- 

 crease in relative size with 

 increase in absolute size, and 

 are accordingly negatively hetero- 

 gonic. Such of these cases as 

 have been analysed also appear 

 to obey the rule of constant 

 differential growth-ratios : e.g. 

 nucleus in oocytes of Hydractina 

 (Teissier, 1927) ; brain in vari- 

 ous mammals (Lapicque, 1907 ; 

 Dubois, 1914, 1918) ; the number 

 of nerve-fibres and /or neurones 

 in mammals (Lapicque and 

 Giroud, 1923 ; Dubois, 1918) ; 

 heart in many vertebrates (Klatt, 



1919 ; Clark, 1927, for references) ; limbs in post-natal sheep 

 (Hammond, 1927, 1929) ; certain limbs in Hermit-crabs (Bush, 

 I 93°) '> pereiopods in the racing-crab Ocypoda (Cott, 1929) ; 

 legs in Orthoptera (Przibram, 1930) ; Gammarus eyes (p. 260). 



Some of the facts are graphically illustrated in Figs. 4, 5 

 (plant organs) ; 6, 7, 22, 23 (crab abdomen) ; 8, 21, 32, 55, 

 77 (Crustacean chelae) ; 9, 10 (mammalian cranium) ; 11 

 (mouse tail-length) ; 12 (facet-number, Drosophila eye) ; 13-15 

 (various organs of crabs) ; 16-20 (chemical substances in insect- 

 larvae) ; 71 (head-length, whales) ; 25, 27 (deer antlers) ; 

 33-35, 40, 91, 92 (organs of holometabolous insects). 



We may give some tables and figures in support of these 

 statements. 



log body length, mm. 



Fig. 8. — Relative growth of the 

 chela in the prawn, Palaemon mal- 

 comsoni : logarithmic plotting. 



(From the data of Kemp, and Henderson and 

 Mathai.) 



