270 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD 



the years 1911 to 1917. The prediction equations have been tested upon 

 415 birds whose records were obtained during the year extending from 

 November 1, 1917, to October 31, 1918. 



The justification for the course followed is found in the general principle 

 that a theory should not be tested against the observations upon which 

 it is based. 



For practical reasons this paper is limited to a test of the accuracy with 

 which the egg record of a series of 415 birds trap-nested at Storrs during 

 1917-1918 can be predicted by a series of linear equations based on the 

 experience of the six preceding years, 1911-1917, at the same place. It 

 may be urged that conditions at Storrs are not representative of those 

 prevailing in different parts of the country. Recognizing, for the sake ol 

 argument at least, the validity of this objection we have been glad to avai 

 ourselves of records taken elsewhere. These are now being used to tesi 

 the accuracy with which the production of birds in any locality may b( 

 predicted by means of equations based primarily upon experience in anothe: 

 place or with another series of birds. The results of these studies wil 

 eventually be published. 



NOTATION AND THEORY EMPLOYED 



We shall find it convenient to have a simple and rigid notation. Le 

 e represent the recorded egg production of a bird in any month, 2 denot 

 a summation of monthly egg records for a given bird, 1, 2, 3, ... 1. 

 denote the twelve successive months of the pullet year, i.e., the Novembe 

 of the year in which the bird was hatched until and including the followin, 

 October. Then ei, e 2 , e 3 , . . ., e^ represent the November, Decembei 

 January, . . ., October egg record of a bird with an annual record c 



12 



E = 2 (e) eggs. Further, E n denotes the total number of eggs laid i 

 i 



any month or group of months subsequent to any given month or grou 

 of months used as a basis of prediction, i.e., 



12 12 



-En = E - ei = 2 (e), Eio =E - ei - e 2 = 20), . . ., EI = e n . 



2 3 



In the present paper we have used only the linear prediction equatior 

 derived from the means, standard deviations and product-moment coeff 

 cients of correlation between the periods, or groups of periods, of egg pr&amp;lt; 

 duction, i.e., with equations of the type 



E = (E - r. 



\ VE 



p ) - r e E e p 

 I P &amp;lt;r f 



