PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 289 
Still one or two remarkable general principles may be noticed. Let us suppose, what 
is not improbable, that there is a first organ, say in the father, which has no sensible 
correlation with a second organ in the offspring, but that the latter organ in the 
mother is closely correlated by assortative mating with the first organ in the father. 
The formula for regression in the offspring of parents having the deviations h. 2 and A, 
in the two organs (or characteristics) will now be 
er. 
h, + 
This shows us that the possession in any exceptional degree of the first organ by 
the father will actually reduce the amount of the second organ which the offspring 
inherits from the mother. Let a special example be used to illustrate this. Suppose 
the problem to be the inheritance of artistic sense from the mother and (/q, h 3 ) be 
measures of the deviations of this sense in son and mother from the normal. Suppose 
further that h 2 be a measure of the father’s physique, say his girth of chest. Now it is 
conceivable that artistic sense in the mother may be closely correlated with physique in 
father. If now we deal with artistic sense of the son as related to physique in father 
and artistic sense in mother, we conclude that exceptional physique in the father will 
reduce the exceptional artistic sense which the son inherits from his mother. Simi¬ 
larly, the exceptional physique which the son would inherit from his father would be 
reduced by exceptional artistic sense in his mother. It will be noted that these 
results have no relation whatever to the coexistence or not of artistic sense with 
physique in the father or the mother. They depend entirely on the influence of 
assortative mating. It is remarkable that, given mothers of high artistic sense, then 
this will be handed down in a greater degree to those offspring whose fathers have a 
physique below the average, than to those of fathers who have a physique above the 
average. 
The above example is not to be taken as a demonstrated truth, but as an illustration 
of the effect of assortative mating on cross-heredity. Innumerable similar statements 
can be made, but it seems desirable to await the collection of definite statistics before 
discussing them at length. 
The only statistics which are at present at my disposal for the consideration of 
bi-parental inheritance are Mr. Galton’s “ Family Records,” and to these I now turn. 
2 P 
MDCCCXCVT.— 
