SELECTIVE FERTILIZATION IN POLLEN MIXTURES. 269 



With four terms the values of x 2 greater than 18 have no 

 probability out to three decimal places. Since very much 

 greater numbers were secured in most cases, as shown in Table 

 II., the deviations are clearly not due to the differences of random 

 sampling alone if the application of this method of calculation 

 is justifiable. The writer is not perfectly sure that it is because 

 it should be noted that the theoretical proportion is calculated 

 directly from the results found, that is, there is no possible way 

 of knowing the real amounts of the two kinds of functional pollen 

 contained in the mixtures. Moreover the probable error does 

 not take into consideration the corrections which are made for 

 the mistakes of classification found in a sample drawn from each 

 lot. 



There may be a selective action when the pollen is applied to 

 one plant but not to the other or the action may be reversed. 

 All that is measured is the combined effect if both are in the 

 same direction or the excess of one over the other if in opposite 

 directions. It seems reasonable to suppose, however, that the 

 selective fertilization is approximately the same on both members 

 of the pair as a large number of mixed pollinations are avai able 

 made with many different types of plants and the majority 

 give the same result. If this were always true, however, the 

 ratio obtained by out-crossing the mixture onto a distinct strain 

 should not deviate from the ratio of the closest perfect proportion 

 calculated from the figures of the reciprocal crosses beyond allow- 

 able limits. That is, the ratio obtained from the out-crossed 

 seeds is supposed to represent very nearly the actual ratio of 

 effective pollen in the mixture since both kinds are more nearly 

 on the same footing. In the three experiments, Nos. I, 19 and 

 20 in which such out-crossed seeds were obtained, the deviation 

 is even greater in two cases than that from the reciprocal applica- 

 tions. In pollen mixture number I all the deviations are small 

 and probably without significance. 



Since the results are convincing when considered without a 

 probable error, it is not necessary to lay much stress on the 

 method of its calculation at this time. Considering the data 

 altogether, magnifying the actual experimental error to its fullest 

 extent, and taking a common-sense view of the allowances to be 



