1910.] PUBLIC DOCUMENT — No. 31. 201 



At the other extreme stands the lot from West Virginia, with 

 an index of 1.2272 ± .0035. The average apple grown under 

 exactly those conditions under which these apples grew has a 

 cross diameter about 1.2272 times larger than the longitudinal 

 diameter, and we know that the chances are even that this figure 

 is not more than .0035 of the transverse diameter out of the 

 way. Stating this last in another way, it means that the chances 

 are even that the true index of form is not less than 1.2257 nor 

 more than 1.2307. 



The third column of Table 3 gives the standard deviation 

 with its probable error, which gives a measure of variability for 

 each lot. This is affected by the selection or want of selection, 

 as the case might be, of the person sending the apples, some 

 growers sending the apples just as they came from the trees and 

 some selecting them more or less, and doubtless throwing out 

 many specimens which were off type, thus reducing the amount 

 of variation in that lot. Several tests showed that the amount 

 of variability among the larger apples and smaller apples of a 

 given lot was about the same, and this was also true of the mean 

 index of form. It is believed, however, that this selection has 

 not greatly modified the figures, and that the mean indexes of 

 form are scarcely affected at all. 



The fourth column gives the coefiicient of variability and its 

 probable error. This is an abstract number giving, in per- 

 centages of the means, the variability of each lot of apples, and 

 enables one to compare the variability in form with that of any 

 other character of the apples, or any character which can be 

 measured and expressed by this method. 



The variation in form is showui graphically in the diagrams in 

 plates I. to V. These are based on the same measurements as 

 the mathematical calculations, each lot being reduced to the basis 

 of 200 apples for the sake of uniformity. Many of them are 

 somewhat irregular, owing to the small numbers of specimens 

 measured. The ordinate representing the index of form of 

 1.1300 is in each case made heavier in order to furnish a stand- 

 ard for comparison, this ordinate being near the average of all 

 apples measured. The shape and relative position of these dia- 

 grams show strikingly the differences in variability and in mean 

 index of form of the various lots of apples. 



