Researchey iiitu the tlieory of pmljability. 



19 



Third Example. Distribution of frcqiimcii in the /reigJif of hroivn heans. 



Johannsen lias made a very important investigation ') into the weiglit and other 

 qualities of brown beans (Fhaseolus vulgaris), wliich lie has studied in many genera- 

 tions. What is specially characteristic in his researches is the self-fertilisation of 

 the plants used in his experiments, so that it is possible for him to study the effect 

 of heredity in its purest form. From the material published by him I take out his 

 results respecting the weight of the beans in the third generation (1902). All the 

 beans here considered derive in direct line from 19 grandmother-beans (1900), each 

 constituting a line distinct from the other ones. 



We have here to do with graduated variâtes (Davenport) that are capable of 

 assuming all possible values within certain limits. In the first 2 examples the 

 x-coordinates that measure the character in question, could assume only integer 

 values. The graduated variâtes must be taken together in classes. The class range 

 I take as by Johannsen to 50 mg. The provisional origin is for all lines taken 

 to 475 mg. Hence class 1 has a mean weight of 525 mg, class 2 of 575 mg and 

 so forth. The numbers given by Johannsen for the weight of the beans are con- 

 tained in the following table. 



TABLE IV. Frequency tahle of hroirn beans (.Johannsen). 



Middle of 

 the class 



125 



175 



225 



275 



325 



375 



425 



475 



525 



.575 



625 



675 



725 



775 



825 



875 



V 



Class 



—7 



—6 



—5 



-4 



—3 



2 



—1 



0 



+1 





+3 



+i 



+5 



+6 



+7 



+8 





Line A 













2 



5 



9 



14 



21 



22 



24 



23 



17 



6 



2 



145 



B 









1 



6 



19 



32 



66 



88 



100 



90 



50 



19 



1 



3 





475 



„ C 













5 



14 



50 



76 



58 



44 



29 



5 



1 







282 



D 









5 



2 



9 



21 



38 



68 



77 



62 



22 



3 









307 



„ E 









4 



1 



12 



29 



62 



65 



57 



19 



6 











255 



„ F 









2 



8 



21 



46 



74 



•46 



28 



14 



1 



1 









241 



„ G 







3 



9 



28 



51 



111 



174 



101 



44 



6 





1 



5 







533 



„ H 







1 



(3 



20 



60 



106 



114 



75 



33 



3 













418 



„ J 





1 



2 



14 



38 



104 



172 



179 



140 



53 



9 













712 



„ K 







1 



2 



6 



31 



55 



55 



28 



6 



4 













188 



„ L 







1 



5 



15 



37 



88 



76 



, 33 



13 



4 



1 











273 



„ M 







4 



9 



26 



56 



82 



76 



32 



9 



1 













295 



„ N 



1 



3 



11 



22 



29 



72 



120 



69 



23 



5 



2 













357 



„ 0 



4 



4 



5 



19 



69 



69 



44 



5 



















219 



„ P 









3 



1 



18 



35 



27 



13 



3 



4 



2 











106 



„ Q 







1 



2 



7 



16 



44 



93 



80 



52 



10 













305 



„ R 









2 



3 



12 



17 



27 



19 



3 















83 



„ S 







1 



2 



3 



8 



27 



47 



37 



30 



4 













159 



„ ï 











1 



6 



20 



37 



39 



30 



8 













141 



Each line was treated according to the before given scheme. The corrections 

 of Sheppard for the moments were not applied. The results were duly controlled. 

 The values of the parameters for the different lines are contained in the follow- 

 ing table. 



') »Ueber Erblichkeit in Populationen und in reinen Linien-, Jena 1903 (Fischer), 



