35 J. ARTHUR HARRIS 



RECAPITULATION 



In many instances the biologist has to consider the relationship be 

 tween a measurement and some of its logical subdivisions or components. 

 The first has been called an independent and the second, which is always 

 some fraction of the first, a dependent variable. 



For the analysis of such relationships two coefficients are required, 

 the correlation between the variable and the dependent variable and the 

 correlation between the variable and the deviation of the dependent var 

 iable from its probable value on the assumption that the relative mag 

 nitude of the dependent variable is independent of the magnitude of 

 the variable. 



This paper gives (a) the supplementary formulae which are required 

 in certain cases in which the correlation between a variable and the 

 deviation of a dependent variable from its probable value is to be com 

 puted, and (b) a series of illustrations of the applicability of this co 

 efficient, drawn from a wide range of biological phenomena. 



The method has been most extensively applied to the problems of the 

 physiology of seed production in plants. The relationship of the number 

 of ovaries which develop to maturity to the total number of ovaries 

 formed, and the relationship of the number of seeds which mature to 

 the total number of ovules laid down, have been determined in a consid 

 erable number of plant forms. That it may be useful in the study of 

 the relationship of seed viability to the number of seed formed is shown 

 by analysis of meagre data for carnation crosses. 



The formulae have been applied to the problem of sex by an investi 

 gation of the relative proportion of macrosporophylls and microsporo- 

 phylls in data for Arisarum, Ficaria and Homogyne, and for the rela 

 tive numbers of males and females in litters of swine. 



Under certain conditions the method may be of use in testing the 

 assumption of the existence of a differential viability in Mendelian 

 dominants and recessives. 



The usefulness of the method in morphology has been illustrated by 

 its application to the problem of the relationship between total length 

 and anterior length in Paramecium, to that of the relative size of the 

 head in developing trout, to that of the relative frequency of abnormal 

 pedicels in the inflorescence of Spiraea, and to that of the relationship of 

 the numbers of cotyledons and primordial leaves to the total number of 

 leaf homologs in a highly variable race of Phaseolus. Such studies have 

 not merely an independent morphological value, but have their bearing 



