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XXXVI. 



SIMPLIFIED SOLUTIONS OF CERTAIN MENDELIAN 

 PROBLEMS IN WHICH FACTORS HAVE INSEPARABLE 

 EFFECTS. 



By JAMES WILSON, M.A., B.Sc, 



Professor of Agriculture in tiie Royal College of Science, Dubliu. 



[Read March 23. Published April 12, 1915.] 



In a paper entitled "Unsound Mendelian Developments, especially as 

 regards the Presence and Absence Theory," published in the Proceedings 

 of this Society in December, 1912, it was shown tliat, when the effects of 

 different factors are inseparable, the results obtained from two or more 

 crosses in which the same pair of factors is operating can be combined and 

 the relations between factors which are not operating together determined. 

 For the proof then given a simpler can now be substituted. The fol- 

 lowing are the necessary observations and deductions from Mendel's work, 

 which hold so long as the characters dealt with are related to each other as 

 dominants and recessives and each pair is distributed independently of the 

 others : — 



(1) If the original parents differ in n pairs of characters, then 2" gives 

 the number of groups into which their hybrids' progeny can be divided, 

 and (3 + 1)" tlie ratio in which the groups stand to each other numerically. 



(2) Conversely, if their hybrids' progeny consist of 2, 4, 8, 16 . . . 2" 

 groups, the numbers in which are numerically in the ratio (3 + 1)", then the 

 original parents differed in n pairs of characters. 



(3) If the original parents differ in 1, 2, 3 . . . n pairs of ciiaracters, tlien 

 the characters borne by, and the proportionate numbers in, the groups in their 

 hybrids' progeny are : — 



When the parents differ 



In one In two 



pair. pairs. 



3 X 9 X r 



\ X '6 X 11 



3 X Y 



\ X IJ 



SCIENT. PKOC. E.D.S., VOL. XIV., NO. XXXVI. 



