Dec, 19I5-] Harris: The Beetle Bruchus. 245 



parent exception : In the Golden Wax series the incidence of insects 

 in pods with the lowest number of ovules here recorded is slightly 

 higher than in the next higher ovule grade. The result is probably 

 quite accidental and attributable to the fact that in these two classes 

 relatively few pods and seeds were available. This point will be 

 taken up below. 



While the ratio of injured seeds to total seeds formed is the most 

 logical basis of comparison, it has seemed desirable to test the results 

 in another way. I have therefore taken the ratio 



Total Infested Seeds 



Total Seeds Weighed^ 



for each class of pods. This purely arbitrary but useful ratio is 

 shown in the final column of the tables. The results fully substanti- 

 ate the conclusions to be drawn from the preceding method. 



The trustworthiness of any percentage frequency of course de- 

 pends upon its numerical magnitude and upon the number of observa- 

 tions upon which it is based. To determine whether the deviations 

 from the general percentage found in the case of pods with various 

 numbers of ovules are statistically trustworthy one may calculate the 

 extreme range in percentage of infested seeds which one might reason- 

 ably expect to occur as a result of random drawings of samples as 

 large as these actually considered for the particular class of pods from 

 a series of seeds showing the percentage incidence observed in the 

 whole material. If the observed percentages for the several classes 

 of pods fall well outside these limits, it is clear that the deviations 

 may be looked upon as significant. 



Let A^ be the total number of seeds examined, Nzu the total number 

 infested by weevils. Then Nzv/N = p, the proportion of the injured 

 seeds. The proportion of seeds not infested by weevils is i — P = q- 

 Assuming that our general series of seeds is large enough to give 

 trustworthy values to p and q the standard deviation of any class of 

 seeds may be taken to be \/mpq, or the standard deviation of the per- 

 centage ratio ioo\/mpq/ni, where ni is the number of seeds examined 

 in the class. 



In the graphs the limits of twice the standard deviation above and 



1 Numbers of seeds from each of these series were weighed individually 

 for breeding purposes. These were drawn quite at random. 



