SAMUEL BRODY 433 



any chosen time t, anywhere along the reaction curve, on either side 

 of the maximum, rather than that h is negative. Equation (4) may 

 be still further simplified by writing it 



log -^ K (t- h) (5) 



A — X 



where K is written for KiA. Equation (5), used by Robertson^ in 

 the study of growth, may now be applied to the study of data on 

 ovulation. 



A large amount of data on ovulation of the domestic fowl is found 

 in the work of the several Agricultural Experiment stations in this 

 country. The best known published records are undoubtedly those 

 prepared by PearP on the weighted mean monthly egg production of 

 barred Plymouth Rock pullets representing 4,210 birds covering the 

 records kept from 1899 to 1907 at the Maine Agricultural Station, 

 and the results of the international egg laying contests conducted by 

 the Storrs Experiment Station.^ The average monthly production 

 of 1 ,000 White Leghorn pullets during the seventh international con- 

 test^ will be taken as the second example for computation. 



It might be well before applying equation (5) to these data to rede- 

 fine them in terms of ovulation during the pullet year, x = number 

 of eggs laid from November 1 of the pullet year up to the end of any 

 month, t. A = total number of eggs laid in the natural laying season 

 which lasts very nearly 1 year, November 1 of pullet year to Novem- 

 1 of the succeeding year. Some eggs may be, and in fact are, laid 

 outside this arbitrarily defined limit of 1 year. However, all pub- 

 lished records adhere to this arbitrary year, and hence A is tenta- 

 tively defined as eggs laid from November 1 to November 1 of the 

 succeeding year, ti = time in month when x = A — x = time 

 required to lay half of the total number of eggs laid in 1 year = time 

 when the monthly rate of laying is at its maximum. K = velocity, 

 constant found by substituting values for x, A, t, and h, and solving 

 for K. Substituting the values of A, K, t, and h, and solving for x, 

 we obtain the following calculated values for the two examples chosen, 



5 Pearl, R., U. S. Bureau Animal Industry, Bull. 110, 1910, pt. 2. 

 ^ Card, L. E., and Kirkpatrick, W. F., Storrs Agric. Exp. Station, Bull. 100, 

 1919, pt. 2, 35. 



