530 



ON INCREASE IN SIZE 



[PT. Ill 



where jy is the time necessary to accompHsh a given amount of e.g. 

 embryonic development at the temperature x and a and b are 

 constants. Thus log. time/log. temperature gives a straight line. The 

 constant a varies according to the unit of time used, but the constant b 

 is independent of the time-unit and the actual velocity for it repre- 

 sents acceleration. If ^ = i then y = ajx, which is the equation for 

 a rectangular hyperbola, and covers the work of Peairs on insect 

 development as a special case of the general law. Again, the straight- 

 line relation of Krogh and others is another special case, for, ac- 

 cording to it, V ^ kx where v is the velocity and x the temperature 

 and, as jv = ijv and k = i/a, we get y = a/x, which is the original 

 equation once more. As b is usually greater than i, Q^^o usually 

 declines with rise of temperature. Belehradek regards the constant b 

 as a true temperature coefficient, for it does not change with tem- 

 perature, and he has calculated it for various systems which are 

 relevant here. Thus he gets for the embryonic development of 



Copepod Cyclops fuscus (Ziegelmayer) ... 



Fruit-fly Drosophila melanogaster (Loeb & Northrop) ... 



Frog Rana virescens (Lillie & Knowlton) 



Hen Callus domesticus (Fere) 



and for the early segmentation of 



Sea-urchin Strongylocentrotus lividus (Loeb) 

 Roundworm Ascaris megalocephalus (Faure-Fremiet) 



It would appear that b increases with age, for 



Fruit-fly Drosophila melanogaster (Loeb & Northrop) : 

 Larva 

 Pupa 



b 

 i-i6 



2-IO 

 2-36 

 4-10 



I St 



0-99 

 2-50 



2nd 

 I-I3 



and 



and 



and 



Water-beetle Dytiscus semisulcatus (Blunk) : 

 Embryo 



Larva (ist instar) ... 

 Larva (2nd instar) 

 Larva (3rd instar) 

 Prepupa 

 Pupa 



Frog Ranafusca (Krogh) : 

 FertiHsation to ist cleavage 

 End of 1st cleavage to closure of neural fold 

 Closure of neural fold to appearance of external gills 

 Appearance of external gills to 3-branched gills 

 3-branched gills to 7 mm. embryo ... • ... 



7 mm. embryo to 7-8 mm. embryo 



Typographic beetle Tomicus typographus (Hennings) : 

 Embryo 

 Larva 



210 

 2-28 



i-io 

 1-14 

 1-26 

 1-38 

 1-48 

 I -60 



I -20 

 1-64 

 1-76 

 1-92 

 1-69 

 2-52 



2 -02 

 3-52 



