268 D. F. JONES. 



selves convincing as in these the numbers are large, the differen- 

 tiation of the seeds in both groups is precise and the deviations 

 clearly show the superiority of self-pollination. 



The data from pollen mixture number I have been published 

 previously (Jones, 1918) although at that time plants had not 

 been grown to test the error in separating the seeds. The greatest 

 number of mistakes of classification of any of the mixtures were 

 made in this lot and the deviation is now well within the limits 

 of random sampling. The data are included here to make this 

 report complete. In the previous publication the probable error 

 used was the familiar formula used for Mendelian ratios. The 

 determinations applied to each half of the proportion alone. 

 Since the ratio on each of the paired plants is dependent upon 

 the ratio on the other, it seems to the writer now that the use 

 of this method of calculating the probable error in connection 

 with this particular problem is wrong. 



The method of calculating the significance of the figures as 

 used here is that proposed by Elderton (1901) and is in general 

 use in presenting genetic data. It is obtained in the following 

 manner. The deviations of the terms in the actual proportion 

 found from the closest perfect proportion as calculated are 

 squared and divided by the terms of the perfect proportion. Their 

 sum gives a value % 2 > which by use of convenient tables calculated 

 by Elderton, gives a probability value varying from o to I 

 proportional to the goodness of fit. 



The calculations must be based on the actual numbers of seeds 

 obtained and not on the percentages. To obtain a perfect pro- 

 portion from which the deviations of the numbers found will be 

 the smallest in the four terms it is necessary to balance the 

 figures so that the same number of individuals are represented on 

 the A and B plants. This is done by reducing the number of 

 seeds of the greater and increasing the lesser keeping the ratios 

 the same, of course. The deviations of the proportions, balanced 

 in this way, from the closest perfect proportions are then used to 

 obtain the probability value in the way described above. The 

 same result is obtained more quickly by calculating the value of 

 X 2 from the percentages and multiplying this figure by one half 

 the total number of seeds. 



