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Mr. S. M. Jacob. Inbreeding in a [Mar. 18, 



not known with any degree of certainty, various determinations which have 

 been given ranging in value from as much as 1 to 8 per cent, of the total 

 number of marriages. It is beyond the scope of this paper to consider 

 the accuracy of these determinations, and they do not claim to be more than 

 approximations. 



So far as can be judged, however, a first cousin marriage rate of 5 per 

 cent., such as may occur perhaps among the peerage, is not likely to be 

 exceeded in any considerable group of the population, though it may 

 apparently be as small as 1\ or 1^- per cent, for parts of the community of 

 low social status. Accordingly, in what follows the determinations have 

 been made on the basis of percentage rates of first cousin marriage from 

 1 to 5. 



For the moment, only first cousin marriages are dealt with, all other 

 marriages being assumed to be non-consanguineous. 



Let A.i be the percentage of first cousin marriages. Let e\ be the 

 proportion of the offspring of first cousin marriages which has the allogenic 

 constitution {act). The value of c x is given by the preceding analysis. 



Let e and E be the proportions of allogenic constituent in the offspring of 

 non-related couples, and in the population at large. As a rule, E will be the 

 datum available from statistics. 



Then, clearly, the total proportion of allogenic element in the whole 

 population can be expressed in two ways, which together give rise to the 

 equation 



X^ + ClOO-^-Oe = 100E. 

 Now, if we put pjq = z, we have 

 _ l+/7i~ 



Where ^ = 4(1673i) • 



Thus (1 + ,?) 2 100E = \ 1 (l+£is) + 100-\ 1 . 



and , 2 + ( 2 _^L), + l_l = . (12) 



This is a quadratic which determines z, and thus the values of e± and e can 

 at once be obtained. The percentage of the allogenic population which is 

 the offspring of first cousin marriage is then given by X^i/E. The value of 

 this function has been calculated for frequencies of occurrence of the 

 allogenic constituent at chosen intervals from 25 per cent, of the whole 

 population to one case in a million. The results are given in Table II. 



Here, again, we observe that, when the recessive element is a very rare 



