THE AMERICAN NATURALIST [Vol. XLIV 



The best illustration I have is from Apstein's 14 work on Musis. 



Table IV shows the body length in millimeters and the number 

 of eggs and embryos for a series of 52 individuals taken Feb- 

 ruary, 1904, and Table V the same characters for a series of 24 

 taken at all other times in 1904 and 1905. 



TABLE IV TABLE V 



The range of both characters is large. If one were to prepare 

 a regular correlation table (omitting all unnecessary columns 

 and rows) he would have tables of 341 and 222 compartments 

 for the 52 and 24 observations ! 



Multiplying out with the help of the first two pages of Bar- 

 tow's tables for the higher squares, we find for the first series: 

 S(x') =946; S{x' ) =17,516; S(y') =1,623; S(y") =67,089; 

 8(xY) =31,432; # = 52 whence 



r—iS(xy)N— la 1923 X 31 21 15]/ (2. 4261 X 17.7768) = .85. 

 For the second series S(x') =424; S(xf) = 7,672 ; S(y') =665; 

 S{in =24,149; flf(a>y) =12,018; V = 24, whence 



r=[S{x'y')/y- 17.6667 X 27.7083]/ (2.7487 X 15.4420 = .26. 

 The professional statistician will note that mathematically 

 there is nothing novel in the methods suggested. But I have 



