57° 



Journal of Agricultural Research 



Vol. XX, No. 7 



Assuming that the diagrams in figures 7, 8, and 9 accurately represent 

 the causal relations, it appears that birth weight is determined to a very 

 much greater extent by variations in the rate of growth of the foetuses 



than by variations in the length of 

 the gestation period (^ x -q == °-74» 

 d x . P = o.ii). Size of litter has much 

 more effect on birth weight by re- 

 ducing the rate of growth of the 

 foetuses than by causing early partu- 

 rition (d x . Q . L = 0.26, </ x .p.l = o.02). The 

 difference in birth weight caused 

 by a difference of a day in gestation 

 period can be calculated from the path 

 coefficient and the standard deviations 



Fig. 8. — Path coefficients measuring the rela- 

 tions between birth rate (AT), rated growth 

 (Q), gestation period (P), size of litter (L), 

 and other causes (.4 , C). 



by the formula for path regression, p. regx-p = px.r--^' The result, 3.34 



Ox 



0p 



gm. per day, should measure the average rate of growth just preceding 

 parturition. The actual regression, 5.66 gm. per day of delay in parturi- 

 tion, is larger because a long gestation period means not merely a longer 

 time for growth but also, in general, a smaller litter and hence more 

 rapid growth. 



On introducing other data the analysis can be carried much farther. 

 There are other paths of influence which should be recognized, positive 

 paths connecting A, C, and L, representing the favorable effects of good 

 health in the dam on rate of growth, gestation period, and size of litter, 

 and a negative path from Q to P 

 to represent the tendency of rapid 

 growth to induce early parturition. 

 The relations between the observed 

 interval between litters and the ac- 

 tual gestation period should also be 

 considered. The results presented 

 here are thus intended merely to fur- 

 nish a Simple illustration Of the Fig. 9.— Coefficients of determination. Symbols 



method. A more complete analysis as in figure 7 ' 



of the relations among the factors which affect birth weight and later 



growth will be presented in a later paper. 



DETERMINATION IN TERMS OF CORRELATION 



Having obtained a formula for correlation in terms of determination, 

 the question arises whether the converse is possible. For a special class 

 of cases such a formula is easily obtained. 



