Variation and Correlation of Oats — Part II 85 



auger hole in a board, the hole being 5.5 centimeters in diameter. A tiny- 

 bucket was then suspended from the middle point of the piece of straw 

 by means of a hook made from wire about one millimeter in diameter. 

 Shot was then poured into the bucket at a uniform rate until the straw 

 broke. A very fine shot, about No. 12, was used. The combined weight 

 of the bucket and the shot required in order to break the straw was 

 considered as the breaking strength of the straw. 



Yield 



Total yield of plant. — This was determined by weighing, in milligrams, 

 the grain produced by the plant, or by adding together the yields de- 

 termined for individual culms of the plant. 



Total yield of culm. — This was determined in some series by weighing 

 the grain produced by each culm. 



Average yield of culm per plant. — This was obtained by dividing the 

 total yield of the plant by the number of culms per plant. 



mathematical methods 



In determining the mathematical results herein reported, calculations 

 were made to the fifth decimal place. If the fifth place exceeded five 

 in value the fourth place was increased by one, otherwise the fifth number 

 was dropped. With the exception of the coefficient of variability, the 

 constants are reported with three decimal places, the fourth place, deter- 

 mined as above, being dealt with as was the fifth place above. When the 

 constants reported in this paper were used in the determination of other 

 constants, as the coefficient of variability, they were used as herein reported; 

 that is, with three decimal places. 



Rietz and Smith (1910:304), following Pearson, make the following 

 statement regarding the significance of the probable errors: 



" In the comparison of two statistical results, the difference between 

 the two results compared to its probable error is of great value. In 

 general, we may take the probable error in a difference to be the square 

 root of the sum of the squares of the probable errors of the two results. 

 If the difference does not exceed two or three times the probable error 

 thus obtained, the difference may reasonably be attributed to random 

 sampling. If the difference between the two results is as much as five 

 to ten times the probable error, the probability of such differences in ran- 

 dom sampling is so small that we are justified in saying that the differ- 



