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THE AMERICAN NATURALIST [Vol. XLV 



The original data appear seriated by individual plants in 

 Table I. From this we derive the symmetrical intra-individual 

 correlation surface, Table II. 



Working- by the conventional product moment method, but 

 taking all moments around as suggested elsewhere in these 

 pages, 8 we get : 



S(aO= 2,179,781, v / = 10.0524 = 4, 



2(x' 2 ) =24,578,235, „ 2 ' = 113.346284, 



S(asyj = 22,438,814, ^ = 12.205679 = a 2 , 



N= 216,842. 2(x'y')/N— 103.480018. 



The y moments are of course the same as the x, and we have : 



r = fl(sy) = 8{x' y')/N — v x 'v y ' _ 



Or we may use a short formula for the difference method. 9 



Where <r, is the standard deviation of the difference between 



Where the number of individuals in an array is very small 

 the method presents no very marked advantages, but when the 

 arrays are large it may be very useful and its range of applica- 

 bility very wide. 



For instance, one of the tests of the genotype theory of in- 

 heritance is to compare the correlation between parents and off- 

 spring with that between the parents co-fraternity and the off- 

 spring in a population of self fertilizing or vegetatively 



