September 17, 1915] 



SCIENCE 



385 



ferably numerical, designation of each one of 

 these possible types, each such designation to 

 be of course unique and permanent. 



Table I. gives such a general solution of the 

 problem of simply designating pedigree types, 

 through the matings of F^ to produce Fj. Be- 

 yond that it is not practical to go. A word 

 should be said in explanation of the table. 

 Letters denote individuals or groups of indi- 

 viduals which are brothers and sisters. Solid 

 lines, with circles in their course, connecting 

 letters, denote matings of the kinds of indi- 

 viduals indicated by the connected letters. 

 Dotted lines lead from the mating to the kind 

 of individual produced. Arrow heads indi- 

 cate the direction of the mating, the arrow 

 being supposed always to pass from the male 

 to the female. Separate numbers are not 

 given to reciprocal matings after the matings 

 of the P generation to produce Fj. To desig- 

 nate separately reciprocal matings after that 

 point would greatly complicate the system 

 without any significant gain from a practical 

 point of view. In the later generations, re- 

 ciprocals may be indicated if desired, by affix- 

 ing a sub-figure 1 to the designation of the 

 mating. 



The numbers within the circles are the des- 

 ignations (or names) of the matings, and 

 from the very nature of the case, these num- 

 bers designate not alone the particular mating 

 but also, in F^ and later generations, the na- 

 ture of the pedigree of each of the individuals 

 entering that mating. This will be clear as we 

 proceed. 



This table is to be read in the following 

 manner: Individual Xc? is mated with Y2 to 

 produce Fj individuals Z, and this mating is 

 designated 0. Individual Fc? is mated with 

 X2 and produces F^ individual P, and the 

 mating is 1. The Fj individuals, mated in all 

 possible ways inter se and with the parents X 

 and Y, as indicated in matings designated 2 

 to 8 inclusive, produce seven kinds^ of F^ in- 

 dividuals, A to G. These seven sorts of Fj, 

 individuals bred in all possible ways inter se 

 and with their parents and grandparents pro- 



2 ' ' Kinds ' ' referring here only to the manner in 

 ■which the individuals have been bred. 



duce 56 sorts of F, individuals, as indicated 

 in the lower half of Table I. As already noted, 

 separate account of reciprocals is not taken. 

 The use of the table may be indicated by 

 some examples. Suppose one wishes to mate 

 in an experiment the two birds called M and 

 N in an earlier paragraph of this paper. He 

 will wish to indicate in some way in his notes 

 the previous breeding history of each of these 

 birds. If he does this verbally — and hitherto 

 this appears to have been the only way of 

 reaching such end — he must say of individ- 

 ual N, for example, something like the fol- 

 lowing : " This Fj bird was produced by the 

 mating of an F^ male with an Fj female pro- 

 duced by mating a Barred Plymouth Eock 

 male with a Houdan female. The F„ male 

 was himself produced by the mating of an F, 

 male, out of the cross Houdan male by Barred 

 Eock female, on a pure Houdan female." 

 Quite apart from the amount of space involved 

 in such a setting forth of the facts, it is very 

 difficult to form quickly a clear mental picture 

 of the bird's pedigree from this tedious verbal 

 exposition. Suppose we are using the system 

 of pedigree designation discussed in this paper 

 we could then cover all the facts set forth 

 above about bird N by merely writing in our 

 notes 



"Bird N (5S) BPR-Houdan series," 

 and to describe completely the mating of M 

 with N we have merely to write 



"F,(iM {22)X FSN {58) BPR-Houdan series." 



The figure 58 in the case of N means that 

 she was produced from a mating of the type 

 indicated in the table as E y^Z, and the des- 



DIAGRAM II 



Houdan c? X BPR 9 

 (F) (T) (X) 



/ 

 Fid' X Houdan 9 



iP) [i) {Y) 



/ 



Fjcf X Fi 9 from reciprocal cross 



(£) (58) (Z) 



