No. 527] SHORTER ARTICLES AND DISCUSSION 



point or origin to the true means, I have found the following 

 method to result in a material saving of time and energy. 



If for y arrays of integral variates 8 we take instead of the 

 grade thought to be nearest the mean as the origin, we at once 

 obtain the total for the array by simmiin^ the products of the 

 frequencies by their grades. By multiplying up by the grade of 

 x character we at once obtain S(x'y'). 



I illustrate by a table showing the relationship between the 

 number of ovules formed and the number of seeds developing 

 per locule for a series of pods of Hibiscus Syriacus taken in the 

 Missouri Botanical Garden in the autumn of 1907. Table I gives 

 the data. 



TABLE I 



127 146 153 



350 450 525 635 690 714 

 208 300 244 326 368 395 



i ,129 I 1,839 2,319 | 2,535 | 2,986 | 2,975 | 2,324 j 



The total number of seeds developing for each ovule-class is 

 found with great ease and rapidity by multiplying the frequen- 

 cies by the number of seeds per locule and summing at the same 

 time on the machine. 8 This gives Table II. By multiplying the 



totals of seeds by 

 they were produc< 



