22 C. C. Engberg 



3. The coefficient of correction p. Correlated variability is such 

 a relation between the magnitudes of two characters that any abmo- 

 dality of the one is accompanied by a corresponding abmodality of 

 the other. This coefficient varies evidently between the limits ± 1. 

 If two characters are perfectly correlated the value of p is evidently 

 1, while o indicates no correlation. A negative value of p shows 

 that while one character increases the other decreases. The mathe- 

 matical formula is 



Sum of products of (deviation of subj. class X deviation 



_2 f xy of each assoc. rel. class X number of cases in both) 



7i<j x u y total no. of individ. X S. D. of subj. X S. D. of rel. 



In this paper Duncker's short method of computing the corre- 

 lation is used. He puts the above formula into the following 

 form : 



._ai(/yr)-a 1 (/Y)-a 1 (/y)+s 1 (/)-s a (/K)-s i (/Y)-;/^ 



where X and Y are the integral parts of the deviations from the 

 means of subject and relative respectively, £ and 77 are the comple- 

 ments of the fractional parts of these means, f stands for the num- 

 ber of cases, and the numbers indicating the summation refer to 

 the quadrants as shown in the correlation table. 



EXPLANATION OF THE TABLES 



These tables were compiled by Mr. E. C. Stevenson from the 

 data obtained by him. 



Table I gives the measurements of the hooks of 28 worms of 

 the species Taenia serrata. The measurements of the large and 

 small hooks of the same head are given on the same line, thus 

 making possible a comparison of the dimensions of the two kinds 

 of hooks. 



Table II gives the same measurements similarly arranged for 

 the hooks of 15 worms of the species Taenia serial is. 



Table III is a correlation table, for characters a and b of the 

 small hooks of Taenia serrata. It is divided into 4 quadrants by 

 lines drawn through the zero points, i. e., the means. The column 



212 



