236 



NA TURE 



[July 8, 1897 



cases, there is strong reason for its acceptance, as applicable 

 generally to all qualities in all the higher (bisexual) animals. 

 When it is applied to individual cases, minor corrections should 

 of course be made in respect to sexual limitations, prepotencies 

 of particular ancestors, and the like. 



The law shows the proportion of the heritage that is contri- 

 buted on the average by each parent, grandparent, great-grand- 

 parent, and so on. There must be an average contribution, 

 drawn from each ancestral place independently of all the rest, 

 because cases are familiar to observers in which a peculiarity 

 found in some single ancestor has appeared in one or more of 

 the oftspring ; the present law expresses its amount. 



The general considerations upon which the law was originally 

 founded, are four in number but not equally cogent ; there is 

 only one solution that satisfies them all. ( i ) The consequence 

 of limitation in space on particulate germinal matter, which 

 necessitates the loss of one-half of the total germinal material con- 

 tributed by the two parents. This is confirmed by the commonly 

 (though not universally) accepted fact of observation in the life- 

 history of the germ. (2) The remark already made, that any 

 ancestor however remote may contribute his peculiarity 

 independently of the rest. (3) The contribution of the two 

 parents to the child, being analogous to that of the 4 grand- 

 parents to the 2 parents, of the 8 great-grandparents to the 4 

 grandparents, and so on, make it probable that the latent links 

 of the chain of ancestral contributions form a geometric series 

 of terms, diminishing as we proceed from the ancestor down- 

 wards. (4) The sum of the contributed heritages must be 

 equal to i. 



These four conditions are satisfied by the series ^ + i + s + 

 iV + &c. In other words by the supposition that the two 

 parents contribute between them \ of the total heritage of the 

 child ; the four grandparents, \ : the eight great-grandparents, 

 \, &c. Or again, that a single parent contributes \ ; a single 

 grandparent, -^-^ ; and a single ancestor in the «th generation. 

 i/22«. A noteworthy consequence of this is that all the 16 great- 

 great-grandparents taken together, are no more efiicient than a 

 single grandparent, and only one quarter as efficient as a single 

 parent. 



This supposition does not run counter to the commonly 

 accepted view that the true line of descent stretches from germ 

 to germ, and not (except in, perhaps, a small degree) from 

 person to person ; the person must on the average be a fair 

 average representative of the germ, consequently statistical 

 averages which are true of the one, would be true of the other, 

 also. 



The verification of the above theory is the object of Mr. 

 Gallon's memoir. Appropriate materials for the purpose were 

 at last found in the registered colours of the pedigree stock of 

 Basset hounds. This stock was started some twenty years ago by 

 Sir Everett Millais, who purchased on the continent 93 selected 

 hounds for the purpose, and has subsequently interbred their 

 most valuable descendants. A Basset Club has long been 

 established, which publishes an occasional stud-book (the latest 

 was in 1896) containing the registered name, parentage, date 

 of birth, and breeder of each hound. The colours are not printed 

 in it, but they are always entered on the form sent by the 

 breeders to the Club, and Sir E. Millais kindly had them 

 copied for his use. Now there are two, and only two, recognised 

 varieties of these colours : the one technically known as lemon 

 and white (the word " lemon " standing for any shade between 

 yellow and reddish-brown), and the other known as tricolour, 

 from its containing black as well. So there are only two alterna- 

 tive conditions to be considered : " with black " and " without 

 l)lack " ; or " Tricolour," and " Non-tricolour"— say for brevity, 

 T. or N. It is asserted that intermediate and doubtful cases 

 between T. and N. hardly exist. 



The result is a collection (i) of 817 hounds of registered 

 colours, T. or N., descended from parents whose colours are 

 also known. (2) Of these, in 567 cases, the colours of all four 

 grandparents are known ; again (3) of these, in 188 cases, the 

 colours of all eight great-grandparents are known. These three 

 sets form the material that is tabulated and discussed, and 

 supplies the requisite means for comparing calculated results 

 with observed ones. 



There are numerous points dealt with in the memoir, and 

 explained away, to which there is not space to speak of here ; 

 one only need be mentioned, namely the question whether 

 either the sire or the dam is so prepotent in transmitting colour, 

 as to make it necessary to treat the sexes apart. It proves that 



the dam is prepotent over the sire in this respect, but only in 

 the proportion of 6 to 5 ; also that the neglect of sex made no 

 sensible difference in a test case. Consequently all ancestral 

 places in the same generation are treated as of equal average 

 efficiency. In short, if n be the order of any given generation 

 (counting « = i for parents, = 2 for grandparents, &c.), there 

 are 2" ancestral places in the «th order, and these contribute 

 between them 1/2" of the total heritage ; consequently each 

 ancestral place contributes 1/2^" of it. If the same hound fills 

 more than one ancestral place, he has to be rated separately for 

 each of them. 



The contributions from the unknown ancestry are reckoned as 

 follows. It was found that 79 per cent, of the parents of T. 

 hounds are T. also, and that 56 per cent of the parents of N. 

 hounds are T. ; consequently the unknown grandparents, great- 

 grandparents, &c., of the T. hounds would have probably (79 )^ 

 (79)^. &c., of T., and those of the N. hounds would have 

 (■56)^ (■56)'', &c., of T. A simple calculation shows that the 

 sum of the T. contributions to the offspring of the unknown 

 ancestry of each T. grandparent would be 00408, and that of 

 each N. grandparent would be 0*0243 5 these values are used 

 in discussing the set (2). In set (3) the great-grandparents 

 are known, ignorance beginning above that stage ; in this case, 

 the pre-ancestral contribution of T. through each T. great- 

 grandparent, is found to be 0'0I02, and that through each N. 

 great-grandparent is o'oo6i. There is no need here to allude to 

 minor corrections, noticed in the memoir, whose effect is too 

 small to be worth regarding. 



It thus becomes a very simple matter to determine the con- 

 tribution from each several known ancestor as well as that from 

 the unknown ancestry of each of them, and, by adding these 

 together, to obtain a coefficient appropriate to any given group 

 of similar cases, such as when multiplied into the total number 

 of offspring, shall give the "calculated" number that are T. 



The test of the truth of the theory lies in the accordance 

 between these calculated numbers and the observed number. 



Owing to the large proportion of T. hounds and to selective 

 breeding in favour of T., the different possible matings are by 

 no means equally common, those in which the known ancestry 

 are all (or nearly all) N. being non-existent. The results for such 

 as occurred, are summarised below (excluding seven cases, falling 

 into three groups, that lay outside the limits of the Table for 

 set 3). The coefficients are added to show the degree of variety 

 in the test conditions. Fuller information is to be found in 

 the Tables published in the memoir, out of which these figures 

 are extracted. 



Calculated and Observed Values Compared. 

 Set 2. 



NO. 1445. VOL. 56] 



Comparing the totals of each of the two sets, we see that the 

 calculated results are practically identical with the observed 

 ones, 391 with 387 ; 180 with 181 ; grand total, 571 with 568. 

 There is therefore no constant error, the errors in individual 



