^98 REPORT— 1898. 



as at least approximately true, it will be found most serviceable in show- 

 ing tlie relative importance and range of the data which breeders must 

 take into account, if they pursue their art with thoroughness. The law is 

 that, on the average, the two parents contribute between them one-half of 

 the total heritage of the offspring, that the four grandparents contribute 

 between them one-quarter, the eight great-grandparents one-eighth, and 

 so on. Consequently, since ^ + :^-j-^-|--iJ^ + &c.=l, the whole of the heri- 

 tage is accounted for. The same law may be stated in another form, 

 namely, that each parent contributes on the average one-quarter, each 

 grandparent one-sixteentli, each great-grandparent one sixty-fourth, and 

 .so on. It is a property of the first series of fractions that each term is 

 equal to the sum of all those that follow (| being equal to \ + ^ + ^(; + kc. ; 

 ^ to |--fy',; -f »tc.), therefore it results that if genealogical knowledge should 

 ■cease with the grandparents, inasmuch as they contributed one-quarter, 

 another quarter of the heritage will remain indetermined ; if it ceases 

 Avith the great-grandparents one-eighth will remain indetermined ; if 

 with the next ascending grade, one-sixteenth, &c. 



[It must be understood that the law is intended to apply only to what 

 may be called plain heredity, that is to cases where qualities are capable 

 of blending freely, or, if they refuse to blend, where they present them- 

 selves as alternative possibilities. The necessary modifications have yet 

 to be investigated when it has to be applied to hybrid heredity, and to 

 those partial forms of hybridism which occur in cross-breeding, especially 

 in plants, where two parental qualities seem to produce a third and dif- 

 ferent quality in the ofTspring. Again, it takes no notice of prepotency, 

 because it considers prepotency as likely to occur with equal frequency in 

 each and all of the ancestral places, but when the prepotencies of par- 

 ticular ancestors are known or suspected it is easy to take them into 

 account. Similarly the law takes no cognisance of the prepotency of one 

 sex over the other, which must be allowed for in those particular races and 

 qualities where it is known to exist. Lastly, as it relates to averages, its 

 predictions will be truer for the mean of many offspring than for any one 

 of them in particular. However, as we know that fraternal variation 

 admits of being defined with mathematical precision for any measurable 

 quality in any race, the diminution in trustworthiness when a predic- 

 tion relating to a fraternity is applied to a single member of it, is easily 

 calculated.] 



The ancestral law specifies the number, the grades, and the relative 

 importance of the ancestors whom breeders must take into account, in 

 order to predict with any given degree of certainty the most probable 

 character of the future produce. It clearly shows the necessity of a much 

 more comprehensive system of records than now exists. A breeder ought 

 to be in a position to compare the records of at least the four parents of 

 the animals he proposes to mate together, in respect to the qualities in 

 which he is interested. More e.specially he ought to have access to photo- 

 graphs which indicate form and general attitude far more vividly than 

 verbal descriptions. But the information in stud and herd books is too 

 meagre for the requirements 'of the breeder, while the photographs pub- 

 lished in newspapers and elsewhere are inadequate for making complete 

 genealogical collections. 



Utilisation of the Records. — My principal suggestion is that a system 

 of collecting photographs should be established, which would be serviceable 



