230 



SCIENCE 



[Vol. LVI, No. 1443 



In the preface to his "Easy Mathematics," 

 1906, Sir Oliver Lodge stated that "the mathe- 

 matical ignorance of the average educated per- 

 son has always been complete and shameless." 

 One cause of this ignorance has been the lack 

 of popular and reliable books dealing with 

 serious mathematical subjects. By the pub- 

 lication of the present volume Professor 

 Keyser has rendered a very notable service 

 towards the supply of such popular books. He 

 has introduced into the book at various places 

 somewhat serious doses of mathematics but 

 these places are probably sufficiently separated 

 by non-mathematical material to hold the 

 reader who would not be interested in a book 

 restricted to real mathematics. 



G. A. Miller 



University or Illinois 



SPECIAL ARTICLES 

 THE "WINTER CYCLE" IN THE FOWL 



The idea of the superimposition of a Men- 

 delian factor or factors determining the egg 

 production of the "winter cycle" upon the 

 factors determining the egg production of the 



1 Harris, 3. Arthur ; ' ' The Value of Inter- 

 annual Correlations," Amer. Nat., Vol. 49, 707- 

 712, 1915. 



2 An exhaustive series of correlations for the 

 egg records of the individual months of the first 

 and second year was determined some months ago 

 and is now in press in Genetics. The correlations 

 for the total productions of the "cycles" have 

 been only recently determined, because of the diffi- 

 culty of dealing with the moments of such large 

 numbers without grouping. 



normal or "reproductive cycle" has become 

 widely familiar as an explanation of the phe- 

 nomenon of the inheritance of fecundity in the 

 domestic fowl. 



In recent years there has been much skep- 

 ticism among geneticists concerning the validity 

 of this hypothesis. Crucial evidence for or 

 against it is difficult to obtain. 



Some light may be thrown upon the problem 

 by the determination of the coiTelations be- 

 tween the egg records of the various "cycles" in 

 the first and second laying year. If the birds 

 of a flock differ fundamentally among them- 

 selves by reason of the presence in or absence 

 from the zygotes from which they developed of 

 Mendelian genes or factors determining their 

 winter egg production, it would be logical to 

 expect that the highest inter-annual correla- 

 tion"^ would be that of the winter period. This 

 must be considered true under the theory stated 

 unless the further assumption be made that 

 genes of factors which determine egg produc- 

 tion during the "winter cycle" of the first lay- 

 ing year have no influence in determining pro- 

 duction during the "winter cycle" of the second 

 laying year. 



We have, therefore, determined all possible 

 correlations between the total egg records of 

 the "cycles" of the first and of the second year 

 for a series of 443 White Leghorn birds, for 

 which complete records for the first two laying 

 years are available.^ 



The correlations appear in the accompanying 

 table. These show that for all four periods 

 considered there is a higher correlation between 

 the records of homologous periods than be- 



3 The conventional limits of these "cycles" are as follows: Winter, November to February; 

 spring, March to May ; summer, June to August ; autumn, September to October. 



4 Ratio of correl.Ttion coefficient to its probable error. 



