Ill] OF BROOKS'S LAW 165 



interest rate in the growth and metamorphosis of insects is known 

 as Dyar's, sometimes as Brooks's, law. According to Przibram, an 

 insect moults as soon (roughly speaking) as cell-division has doubled 

 the number of cells throughout the larval body. That being so, each 

 stage or instar should weigh twice as much as the one before, and 

 each linear dimension should increase by ^2, or 1-26 times — a 

 Ineasure identical, to all intents and purposes, with Brooks's first 

 estimate. As sl first rough approximation the rule has a certain value. 

 According to Duarte's measurements the locust's total weight in- 

 creases from moult to moult by 2-31, 2-16, 242, 2-35, 2-21, or a 

 mean increase of 2-29, the cube-root of which is 1-32. Each phase 

 is doubled and more than doubled, in passing to the next*, but 

 Przibram's estimate is not far departed from. 



Whatever truth Przibram's law may have in insects, or (as Fowler 

 asserted) in the Ostracods, it would seem to have none in the 

 Cladocera : and this for the sufficient reason that the shell (on which 

 the form of the creature depends) goes on growing all through post- 

 embryonic life without further division or multiphcation of its cells, 

 but only by their individual, and therefore collective, enlargementf. 



Shells are easily weighed and measured and their various dimen- 

 sions have been often studied; only in oysters, pearl-oysters and 

 the Hke, have they been so kept under observation that their actual 

 age is known. The oyster-shell grows for a few weeks in spring just 

 before spawning time, and again in autumn when spawning is over ; 

 its growth is imperceptible at other times J. 



* Cf. H. Przibram and F. Megusar, Wachstummessungen an Sphodromantis, 

 Arch. f. Entw. Mech. xxxiv, pp. 680-741, 1912; etc. How the discrepancy is 

 accounted for, by Bodenheimer and others, need not concern us here. But cf. 

 P.* P. Calvert, On rates of growth among. . .the Odonata, Proc. Amer. Phil. Soc. 

 Lxviii, pp. 227-274, 1929, who finds growth faster in nine cases out of ten than 

 Przibram's rule lays down. 



Millet asserts, in support of Przibram's law, that in spiders mitotic cell-division 

 is confined to the epoch of the moult, and is then manifested throughout most of 

 the tissues (Bull, de Biologie {SuppL), viii, p. 1, 1926). On the other hand, the 

 rule is rejected by R. Gurney, Rate, of growth in Copepoda, Int. Rev. Hydrohiol. 

 XXI, pp. 189-27, 1929; Nobumasa Kagi, Growth-curves* of insect-larvae, Mem. 

 Coll. Agric. Kyoto, No. 1, 1926; and others. 



t Cf. W. Rammer, Ueber die Giiltigkeit des Brooksschen Wachsturasgesetzes 

 bei den Cladoceren, Arch. f. Entw. Mech. cxxi, pp. 111-127, 1930. 



X Cf. J. H. Orton, Rhythmic periods... in Ostrea, Jonrn. Mar. Biol. Assoc. 

 XV, pp. 365^27, 1928; Nature, March 2, 1935, p. 340. 



