36 



breeder's judgment and experience would be less wanted, but 

 his time, the time of the station, now wasted in breeding use- 

 less varieties, might be saved, and instead of its taking thirty 

 years to bring a flock or a brand to perfection it might be 

 that ten years or loss would suffice. 



My object therefore is to examine, if I can, this said system 

 of in-and-in breeding, this breeding like witli like, and by 

 symbolising the relations that arise amongst sheep on those 

 stations, where in-and-in breeding is observed, I hope to 

 suggest a method by which to classify and arrange the various 

 degrees of affinity into groups, as a preparatory step towards 

 those experiments, which will I believe, if made by competent 

 persons, and on a sufficient scale, enable us to lay down and 

 define the laws governing the art of selection. 



I know that my method is crude and deficient in many 

 respects, wanting in the accuracy so necessary to scientific 

 research. I regard it entirely as the suggestion of an un- 

 scientific person to men more capable, who may be able to 

 discern the truth, if there be any in it, and who in that case 

 may give precision to the symbolisation I propose to use. 



My proposal is to regard the organisation of the individual, 

 its race, its blood, or whatever is understood by these 

 generalisations, as a quantitative equality, and to treat it 

 quantitatively. 



Thus if I call the ram A, and the ewe B, I term the product 

 of their union AB for the male issue, and BA for the female. 

 If I marry A the father with BA the daughter, I call 

 their issue A^ B if a ram lamb, and BA^ if a ewe lamb. If, 

 again, I marry AB the son with his mother, I call the progeny 

 AB^ if male, and B-A if female. If I marrv AB the son with 

 BA the daughter, I call the issue A2 B2 if male, B2 A2 if 

 female. 



By this method I hope to make the changes in the shades of 

 affinity apparent and tangible. 



In the sketches of pedigrees appended to the paper, and 

 which I now lay before you, I assume that the ewes produce 

 100 per cent., and an equal proportion of sexes. This for 

 convenience. 



Pedigrees No. 1 and No. 4 show the breeding of a ram with 

 his daughters, grand, and great granddaughters, and if we 

 examine the practice of every station where in-and-in pre- 

 vails, it will be found that the results of this plan of breed- 

 ing, and the strain it produces, must be the prevailing strain, 

 and the action in that direction progressively increasing in 

 force. 



It is true that the stud rams are each year recruited with 

 a small accession from their sons. But the number of sons 



