30 



Scientific Proceedings (55). 



3. The correlation between these two characters, as measured 

 by the coefficient r, is surprisingly low. This result certainly 

 cannot be said to furnish particularly strong evidence that natural 

 selection has had anything to do with fixing the relationship 

 between number of mammae and size of litter. 



Turning next to the regressions it is found that the regression 

 of size of litter on mamma number is sensibly linear. The more 

 interesting and significant regression of number of mammae of 

 dam on size of litter is non-linear, as is shown by the following 

 constants 1 



V = 7714. 

 f = .2426, 



.67449 



Vi Vf = 3412. 



The determination of the precise form of the regression equa- 

 tion here cost a good deal of labor. It was finally found to be 

 logarithmic. The following equation expresses the relation be- 

 tween the number of young at birth and the mean number of 

 mammae of the dam, the constants having been determined by 

 graduation of the first five means of arrays. Beyond that point 

 resort is had to extrapolation, since the number of observations 

 is too small to give reliable results. 



y (probable mean number of mammae of dam) = 3.9616 — .3512* 

 (number of young in litter) -f- 8.6208 log x. 



For the linear regression of size of litter on mamma number 

 we have 



x (probable number of young per birth) = .5566V 

 (number of mammae of dam) + .5331. 



1 Cf. Blakeman, Biomelrika, Vol. IV, pp. 332-351, 1905. 



