154 



THE AMERICAN NATURALIST [Vol. LI 



purposes, a sort of result whicli is familiar to any one 

 who has had any considerable experience with the method 

 of moments. 



To return now to the series we find, using 10-place 

 logarithms in the intermediate computations and the 

 Forsyth approximation, 



log Co = 72.3493814 -100. 



We have now to calculate the successive terms of the 

 series. If this were done for the whole range it would in- 

 volve a literally colossal amount of labor. Fortunately 

 this is not necessary. We need only take that part of the 

 range which includes appreciable frequencies. By a few 

 trials we find that this part of the range begins with 

 r = 36. In Table II are given the frequencies for the 

 several terms in the series between r= 36 and r = 147 in- 

 clusive, the total area being taken as unity. To reduce 

 these frequencies to the actual numbers for the second 

 sample we have only to multiply in every case by 9017. 

 We have calculated Cse by (vii) and used the Forsyth Co. 



From this table we easily deduce 



Median = 83.5331, 

 Lower quartile = 75.6104 (ix) 

 Upper quartile = 91.8218. 



Now, remembering that if the same law holds for the 

 second Mendelian distribution as for the first we should 

 expect the x class in that distribution to be 0.582 times the 

 value of the same class in the first distribution, we have 



Expected mean value of x class in 





second distribution 



= 49.14 



Expected modal value of x class in 





second distribution 



= 48 



Expected lower quartile value in 





second distribution : 



= M.01 



Expected upper quartile value in 





second distribution: 



= 53.44 



