several Ancestor' to the total Heritage of the Offspring. 407 



V and VI, between calculation and observation, proves that the law 

 is correct in the present instance, and that the principle by which 

 the unknown ancestry was apportioned, is practically exact also. It 

 is not so strictly exact as it might have been, because the whole of 

 the available knowledge has not been utilised. The 079 applied to 

 A4, &c, requires some small correction according to the known 

 colours of the offspring of A 3 . If they had been all tricolour the 0*79 

 would have to be increased; if all non-tricolour, it would have to be 

 diminished. Having insufficient data to check a theoretical emenda- 

 tion, I note its omission, but shall not discuss the matter further. 



It will be easily understood from these remarks how collateral data 

 are to be brought into calculation, for if the collaterals were more 

 tricolour than the average of hounds, the 0*79 would have to be 

 somewhat increased (but not beyond the limiting value of l'OO); if 

 less tricolour than the average, the 0*79 would have to be diminished. 

 The knowledge of collaterals would be superfluous, if that of the 

 direct ancestry were complete, but this important prolongation of the 

 present subject must not be considered further on this occasion. 



There are three stages in Tables V and VI at which comparisons 

 may be made between calculated results and observed facts. 



(1) Th.e Grand Totals. — In Table V the sum of all the calculated 

 values amounts to 391 ; that of all the observed ones to 387, which 

 are closely alike. In Table VI they amount to 180 and 181 re- 

 spectively, which is a still closer resemblance. Consequently the 

 calculations are practically exact on the ivhole, and the error occasioned 

 by neglect of sex, &c, is insignificant. 



(2) The Subordinate Pairs of Totals. — These are entered at the 

 sides of the tables, and are nine in number, namely, 236, 239 ; 149, 

 139 ; 6, 9 ; 53, 56 ; 52, 56 : 9, 9 ; 8, 6 ; 49, 46 ; 9, 8. The coincidences 

 are striking, in comparison with such results as statisticians have 

 usually to be contented with ; the second pair, 149, 139, is the least 

 good, and will be considered in the next paragraph. 



(3) Individual Pairs of Entries. — There are 32 of these ; here also 

 calculation compares excellently well with observation, excepting in 

 tjie line that furnishes the " subordinate totals " of 149, 139, where 

 the " all cases " of 37, 158, 60 yield the tricolour contingents of 20, 

 79, 36. Dividing each tricolour by the corresponding " all cases," 

 we obtain what may be called " Coefficients from Observation," to 

 compare with the calculated coefficients. They are as follows : — 







Biff. 





Diff. 





Coefficients from observation . . t <, 



54 



(-4) 



50 



( + 10) 



60 



„ calculation .... 



66 



(-8) 



58 



( -n 



51 



The great irregularity of the entries in the upper line shows 

 that the observed values cannot be accepted as true representa- 



2 f 2 



