4:02 Scientific Proceedings, Royal Dublin Society. 



must be either familiar or readily imagined, we shall take them from domestic 



animals rather than from plants. 



Take first the formula for one pair of characters, viz., 



X:x= 3:1. 



A set of second-cross cattle may be divided into two groups by reason of 

 their colours, which are black and red, in the ratio 3:1. The formula tells us 

 that, in this case, there is one pair of differentiating characters, namely, black 

 and red, and that these colours are an alternative pair with black dominant 

 and red recessive. It tells us that the grandparents of the second crosses were 

 black on the one side and red on the other. It can be inferred readily that a 

 factor whose function is to produce blackness produces the black character, 

 and another whose function is to produce redness produces the red. 



Take nest the formula for two pairs of characters, viz., 



T:y:T:y 

 9:3 : 3 : 1 



Another set of second-cross cattle may be divided into four groups by 

 reason of their colour and their horns. The groups .are — black and liornless, 9; 

 black and horned, 3 ; red and hornless, 3 ; red and horned, 1. The formula 

 tells that there are two pairs of characters concerned, that both dominants 

 are shown by the group of nine, one dominant and the remaining recessive 

 by each group of three, and both recessives by the group of one. Thus the 

 two alternative pairs are blackness and redness on the one hand, and horn- 

 lessness and homedness on the other : the first-named being dominant in 

 each case. The formula cannot tell whether the grandparents were similar to 

 the two end or to the two middle groups, since tlie same result could come 

 from either mating. As in the previous case, the characters and the factors 

 which produce them are obvious. 



Take nest the formula for three pairs of characters, viz., 



X:X:x:X:X:x:x:x 



Y:Y:Y: y : y:Y:y:y 



Z -.z -.Z-.Z-.z -.z -.Z-.z 



27 : 9 : 9 : 9 : 3 : 3 : 3 : 1 



Still another set of second-cross cattle may be divided into eight groups 

 by reason of their colour, their horns, and their faces. The difterentiating 

 characters in the groups and the numbers of individuals in each are — black, 

 hornless, and white-faced, 27 ; black, hornless, and black-faced, 9 ; red, 



