308 Prof. K. Pearson. Mathematical Contributions [Jan. 20. 



Table VII— Whorls, 3rd, 4th, and 5th only. 



Number of Branches to 1st Whorl of Pair. 





7. 



8. 



9. 



10. 



11. 



12. 



13. 



Totals. 



7 



28 



8 



8 



1 



1 











46 



8 



8 



28 



19 



3 









58 



9 



8 



19 



146 



26 



6 





1 



206 



10 



1 



3 



26 



196 



35 



1 





262 



11 



1 





6 



35 



110 



9 



1 



162 



12 







1 





9 



10 





20 



13 • 









1 



1 







2 



Totals 



46 



58 



206 



262 



162 



20 



2 



756 



pq 



Now let us consider how to handle the material, allowing for the 

 differentiation of the whorls. To begin with, our formula requires 

 the use of the same number of homologous parts for each organism, 

 and it is, on account of the value of the probable error of the random 

 sample, undesirable to use fewer than 100 individuals. This leads to 

 our cutting off Table V at the 10th whorl. In this way we get rid 

 also of the forking, which certainly begins in many individuals at the 

 11th or 12th whorl. Table VIII gives us the data of Table V recon- 

 stituted for 110 plants, with ten whorls apiece. The only serious 

 difficulty now remaining is that which I have referred to as arising 

 from heterogenity in the first whorl. A glance at the mean and 

 standard deviation of the branches in the first whorl given in Table V 



Diagram 2. 



> — 





















































J 



-a 



> — - 



























































c 



> 





































































\ 









































( 



\ 















































\ 









































> 







































r 







































) 







































to 



■§ 



V. 

 0) 



Position of WhorL. ^.Origin. 

 £qudltion : y= 9-451,443 - -549,4302 3Z--1 79, 983/ OC z - -008,4206 O0 3 . 



; Regression curve. —Whorl branches and position. 



