482 Scientific Proceedings, Royal Dublin Society. 



(4) The same results follow whether one parent carries all the dominants 

 and the other all tlie recessives ; or the dominants and reeessives are carried 

 some by one parent, some by the other. For instance, tlie same kind of 

 hybrid is produced whether the parents carry the characters XY and 

 xy, or Xy and xY. 



(5) The hybrids carry all the dominants of the pairs in which tiieir 

 parents differed. 



(6) In tlie hybrids' progeny the numerically largest group carries all the 

 dominants ; the groups next in size carry one dominant less ; those next in 

 size again still one less; and so on down to the smallest group which carries 

 all the recessives but no dominants. 



(7) In the hybrids' progeny the largest group differs from the smallest in 

 n pairs of characters, each differs from the groups next them in one pair less, 

 and so on. At the same time, the intermediate groups differ among them- 

 selves in definite numbers of pairs of characters, which can be ascertained 

 by examining any typical set. For instance, in the two-pair set of four 

 groups 



9 X Y 



'6 X y 



3 X Y 



I X y 



the first and last groups differ from eacli other in two pairs of characters, and 

 each differs from the two middle groups in one pair. At the same time, the 

 middle groups differ from each other in two pairs. 



(8) Each character in which the parents differ appears in half the groups 

 of their liybrids' progeny precisely. In tlie two-pair set of four groups, 

 X appears in two groups, and, in the three-pair set of eight groups, X appears 

 in four groups. Thus, if any character be carried by more tlian half the 

 groups in a set, it must be carried by all. If, for instance, the tliird group in 

 tlie two-pair set 



Si X Y Z 



2> X y Z 



'6 X Y 



1 X y Z 



did not carry Z, it would differ from tiie fii'st and last groups in more pairs 

 than one and from the other middle group in more pairs than two. 



(9) If one or more of the groups in a set of hybrids' progeny carry any 

 character outside those producing the set, that character is common to all the 

 groups iu the set. If, for instance, the last group in the following set 

 carried Z and the other three groups did not, then the last group would 



