158 H. H. NEWMAN 



small for accurate work or one or more of the fetuses had under- 

 gone degeneration. Such cases were also ruled out. Finally, all 

 cases in which either mother or offspring showed any atypical band 

 arrangements, such as fusions or splittings, the whole set was put 

 aside for special treatment in a subsequent paper. There remain 

 then only 115 sets that are normal and perfect in every way, of 

 which 56 are males and 59 females. The scute totals of these, 

 together with that of their mothers, are given in table 1, A and B. 

 The method of calculating the coefficient of correlation is that 

 devised by Pearson for such cases as this. The general formula 

 used is: 



ax- + ay'- - 0-^2 



' XV 



2 (ax ay) 



Without going into details of calculation the results may be 

 given as follows: 



a. Coefficient of correlation between 56 sets of male quadruplets 

 and their mothers (data from table 1, A) 



Mean of mothers (x) = 559 ± 1.26 scutes 



Mean of offspring (y) = 558.62 ± 0.65 scutes 



Standard deviation of mothers (ax) = 14.02 ± 0.89 scutes; 



ax^- = 196.64 

 Standard deviation of offspring {ay) = 15.36 ± 0.48 scutes; 



ay' = 236.18 

 Square of the average difference between mothers and offspring 



(aV^) = 195 



Substituting for the general formula we get : 



^ 196.64 + 236.18-195 ^ ^^^^^2 ^ 0.0625 

 2(14.02 X 15.36) 



6. Coefficient of correlation between 59 sets of female quadruplets 

 and their mothers (data from table 1 , B) 



Mean of mothers {x) = 559.8 ± 1.34 scutes 

 Mean of offspring (y) = 559.05 ± 0.57 scutes 

 ax of mothers = 15.34 ± 0.95 scutes; ax~ = 235.37 

 ay of offspring = 13.03 ± 0.41 scutes; ay- = 169.95 

 ar- of mothers and offspring = 180.29 



