Wilson — Unsound Mendelian Developments. 



401 



foi-king lines from X and x downwards, we see that these eight groups bear 

 the following characters, while the numbers in each are shown by the figures 



attached, viz., 27 XTZ, 9 XFs, % XyZ, 2, Xi,z, 9 xTZ, 3 wYz, ^ syZ> 

 1 xy%. 



The following table shows how the groups and the numbers of individuals 

 in each expand up to the case in which ten pairs of characters are 

 considered : — 



NUJrBER OF GrKOUPS. 



Number of 



indlTiduals in 



each group. 



1 



3 



9 



27 



81 



243 



729 



2187 



6561 



19683 



59049 



Total number of 

 groups = 



16 



64 



128 256 512 1024 



Reading from tlie top of the columns of figures downwards, the top groups 

 (always containing one individual) carry every recessive operating in the 

 case ; the next groups (of three individuals) carry n - \ of the recessives 

 and one dominant ; the next groups (of nine individuals) carry n - 2 

 recessives and two dominants, and so on. Reading from the bottom upwards 

 the same rule holds, if dominants be substituted for recessives and recessives 

 for dominants. 



Tlie table will indicate hov/ difficult it is to deal, experimentally or 

 otherwise, with cases in which more than three or four pairs of characters 

 are considered. 



The chief uses of the foregoing formulae are three, viz., (1) to tell how 

 many groups are formed, witli the proportionate numbers of individuals in 

 eacli, by the second crosses from two individuals differing in one or more 

 pairs of alternative characters; (2) conversely, to tell, from the numbers 

 of groups of second crosses and the proportionate numbers in each, in how 

 manj' pairs of alternative characters the original parents differed; and (3] to 

 indicate which characters are alternatives and how the two characters in a 

 pair stand to eacli other as regards dominance and reeessiveness. 



Let us consider several examples, by way of illustration; and, since they 



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