4 Harris, Observations on fche Physiology of Seed Development in Staphylea. 



to attach inuch weight to these constants if he had any regard to 

 tlieir probable errors. 



Taking next Vns, we find that eighteen out of twenty differ 

 from zero by less tbaD . 100, and that the two others only slightly 

 exceed this limit. 



Of the values for Tnf, fourteen fall below our limit of trust- 

 worthiness, five exceed it by not more than .063, and a Single 

 individual, again plant 28, shows a more substantial correlation. i) 



Xotwithstanding the low values of the coefficients with regard 

 to their probable errors, there may still be some significance in 

 these constants. Suppose the real relationship between the char- 

 acters to be 0; we would then not expect to find correlations of 

 when we calculated the coefficients upon the basis of three hundred 

 locules, but results falling above or below this value by an amount 

 due to the probable error of random sampling. This is precisely 

 the condition observed; some have the positive and some the ne- 

 gative sign. Xow by comparing the number of cases in which the 

 values fall abovc and below 0, we may be able to get some idea 

 of the sign, at least, of the correlation in a population of individuals. 



For rno nine of the coefficients have the positive and eleven 

 the negative sign. In a series of only twenty individuals one 

 could not expect a more nearly even division. The positive con- 

 stants average . 1305 while the negative ones give a mean cor- 

 relation of —.0718. If we omit the high value for plant 28, the 

 positive values average . 1022. The mean for the twenty series, 

 having regard to signs, is + . 0192. But the Standard deviation 

 of the coefficients =.1226, about, and .67449 a,. =|/2Ü"= . 0185. 

 The mean is, therefore, Ar -.01^2 + .0185, and we conclude that 

 so far as our data go there is no evidence in favor of any re- 

 lationship between the number of fruits per inflorescence and the 

 number of ovules per locule. 



Consider Vns. Of the twenty, four are positive as compared 

 with sixteen negative, while if actually ;■ = and the results were 

 due to random sampling, we should expect 10 and 10. Observation 

 differs from theory by six cases. For the probable error, we 

 have . 6745 ]/ 20 x . 5 x . 5 = 1.51, and 6 + 1.51 is perhaps significant. 

 The mean of the four positive coefficients is . 0399 and that for 

 the sixteen negative — .0598; for the whole twenty individuals 

 A = —.03987. By the brüte force method, o,. = . 0530 and 

 Ea = . 00799. Now an average correlation of - -.0399 + . 0080 

 may be significant, but with such low values throughout any cautious 

 statistician would hcsitatc in attaching much significance to them. 



The constants for Vnf need not be discussed in detail. Since 

 the constants for Vno are about equally divided between positive 

 and negative while those for Vns are preponderatingly negative. 



1) ISTaturally the Suggestion of an arithmetical blander in the case of this 

 individual will occur to the reader, but I have been unable to find any slip in 

 the work. 



