PEOFESSOR PEAKSO^'S CONTRIBUTIONS TO OSTEOLOGY. 467 



and with the theory for two organs as a special case of this. 

 He gives, as the best vahie of the correlation coefficient (r), 

 for 11 pairs of organs, 



where x and y are the deviations of the two organs from their 

 respective means, and S (xi/) = sura of the products of corre- 

 sponding deviations. The probable error of the coefficient of 

 correlation is 



•674506 , ^~^' ' 



(3) Heredity. — Professor Pearson defines ' Heredity ' as 

 follows: "Given any organ in a parent, and the same or any 

 other organ in its offspring, the mathematical measure of 

 heredity is the correlation of these organs for pairs of parents 

 and offspring. ... If the organs are not those of parent and 

 offspring, but of any two individuals with a given degree of 

 blood relationship, the correlation of the two organs will still 

 be the proper measure of the strength of heredity for the given 

 degree of relationship." 



(4) Beyression.— The word 'degression' was formerly only 

 used to denote the relative degree of abnormality of parents 

 and offspring. Professor Pearson proceeds to give the term a 

 more general significance, which includes the former as a special 

 case. He says: "Let A and B be two correlated organs 

 (variables or measurable characteristics) in the same or different 

 individuals, and let the sub-group of organs B, corresponding to 

 a sub-group of A, with a definite value a, be extracted. Let the 

 first of these sub-groups be called an array and the second a 

 type. Then we define the coefficient of regression of the array 

 on the type to be the ratio of the mean deviation of the array 

 from the mean B-organ to the deviation of the type a from the 

 mean A-organ." Or, to use our former notation, 



Coefficient of regression = —• 

 *= X 



Where the frequency is normal this is constant for all types of 



