288 
STATISTICS: PEARL AND REED 
Proc. N. a. S. 
Curtis, M. R., 1914, "A Biometrical Study of Egg Production in the Domestic Fowl. 
IV. Factors Influencing the Size, Shape, and Physical Constitution of Eggs," Arch. 
Entwicklungsmech. Organ., B. 39, Heft 2/3, pp. 217-327. 
Pearl, R., 1909, "Studies on the Physiology of Reproduction in the Domestic Fowl. 
I. Regulation in the Morphogenetic Activity of the Oviduct," J. Exp. Zool., 6, No. 3, 
pp. 339-359. 
Pearl, R., 1914, "On the Law Relating Milk Flow to Age in Dairy Cattle," Proc. 
Soc. Expt. Biol. Med., 12, No. 1, pp. 18-19. 
7 Donaldson, H. H., 1908, "A Comparison of the Albino Rat with Man in Respect 
to the Growth of the Brain and of the Spinal Cord," /. Compar. Neurol. Psych., 18, 
No. 4, pp. 345-389. 
Donaldson, H. H., 1909, "On the Relation of the Body Length to the Body Weight 
and to the Weight of the Brain and of the Spinal Cord in the Albino Rat {Mus nor- 
vegicMS var. albus)," Ibid., 19, No. 2, pp. 155-167. 
Donaldson, H. H., 1910, "On the Percentage of Water in the Brain and in the Spinal 
Cord of the Albino Rat," Ibid., 20, No. 3, pp. 119-144. 
Donaldson, H. H., 1911, "On the Regular Seasonal Changes in the Relative Weight 
of the Central Nervous System of the Leopard Frog," /. Morph., 22, pp. 663-694. 
Donaldson and Hatai, Shinkishi, 1911, "A Comparison of the Norway Rat with the 
Albino Rat in Respect to Body Length, Brain Weight, Spinal Cord Weight, and the 
Percentage of Water in Both the Brain and the Spinal Cord," /. Compar. Neurol. 
Psych., 21, pp. 417-458. 
Hatai, Shinkishi, 1909, "Note on the Formulas Used for Calculating the Weight 
of the Brain in the Albino Rats," Ibid., 19, No. 2, pp. 169-173. 
Hatai, Shinkishi, 1911, "A Formula for Determining the Total Length of the Leopard 
Frog {R. pipiens) for a Given Body Weight," Anat. Rec, 5, No. 6, pp. 309-312. 
Hatai, Shinkishi, 1911, "An Interpretation of Growth Curves from a Dynamical 
Standpoint," Ibid., 5, No. 8, pp. 373-382. 
s Always, be it clearly understood, on the assumption that the average standard of 
living, method of agricultural production, etc., either do not further change at all in the 
period between the end of historical past record of fact and the time when dy/dx be- 
comes negligibly small as the asymptote is approached, or that the net effective magni- 
tude of any such changes as do occur will be relatively so small as to be negligible in 
comparison with the effect of such factors as reproduction and immigration in deter- 
mining the relation between population and time in an area of fixed limits. In any math- 
ematical treatment of the subject these factors of standard of living, methods of agri- 
culture, etc., represent essentially constant (and hence omitted) parameters of any 
assumed functional relation between population and time. 
^ Omitting 000 here and in the subsequent calculations till the end. 
10 Cf. Pearl, R., The Nation's Food, Philadelphia (W. B. Saunders Company), 1920 
(247). 
11 Pearl, R., loc. cit., p. 76. 
12 As a matter of fact East, in his able presidential address on "Population," before 
the American Society of Naturalists has shown that the United States has already 
entered upon the era of diminishing returns in agriculture in this country. 
13 Robertson, T. Brailsford, "On the Normal Rate of Growth of an Individual and 
Its Biochemical Significance," Arch. Entwickmech. Organ., 25, pp. 581-614. 
Robertson, T. Brailsford, "Further Remarks on the Normal Rate of Growth of an 
Individual, and Its Biochemical Significance," Ibid., 26, pp. 108-118. 
