APPLICABILITY OF A COEFFICIENT OF CORRELATION 337 



It follows, therefore, that in the larger heads the purely pistillate flow 

 ers are relatively less, and the hermaphrodite flowers relatively more, 

 numerous. 



Illustration 4. Fertility of capsules and viability of seed in 

 carnation crosses 



STUART (1912) has recorded the number of seeds obtained and the 

 number germinated, planted into the field, and producing flowers in 

 various carnation crosses. Our problem is to determine whether the 

 seeds which come from capsules producing a large number of seeds are 

 relatively more (or less) viable than those from capsules producing 

 small numbers. . 



Using his two larger tables of data, tables 3 and 6, 3 and confining at 

 tention to the relationship between number of seeds per capsule, and 

 the number which germinated, I find 



For commercial X commercial, STUART S table 3, N = 23, 

 r sg = -775 -056, r sa = -.072 .141 



For single flower X double flower, STUART S table 6, N = 32, 

 r g(J = .649 .069, r s ~ = .118 .118. 



The signs are both negative, indicating a relatively higher failure to 

 germinate among the seeds which are produced many in a capsule. With 

 regard to their probable errors, the constants are untrustworthy. Be 

 cause so few observations are available, no biological significance is at 

 tached to these two series, which serve merely as another illustration 

 of the kind of problems to which the method may be applied. 



Illustration 5. Relationship between the total number of pedicels and 

 the number of abnormal pedicels in Spiraea Vanhonttei 



In Spiraea Vanhouttei the pedicels of the umbel-like raceme normally 

 produce but a single flower each. An abnormal condition in which one 

 or more pedicels may bear a relatively large number of flowers is fre 

 quently observed (HARRIS 1917 d). 



Let x be the total pedicels in an inflorescence and a the number which 

 are abnormal. Then if abnormality be distributed purely at random 

 among the pedicels one would expect material values of r xa . The cor 

 relation r xs meets our requirements since it shows whether inflorescences 

 with a large number of rays have relatively more or fewer of their rays 

 abnormal than those with a small number. 



3 In table 6 the cases in which the seeds are not normally developed are omitted. 

 GENETICS 3: Jl 1918 



