266 
PROFESSOR KARL PEARSOX. MATHEMATICAL 
But 
thus : 
Thus we deduce : 
or ; 
r'cr'j 'cr'i ~ rcr^/cr, 
changed, the coefficient of regression is unchanged hi/ weighting fertility, or by 
reproductive selection. 
This important conclusion is only an illustration of a very interesting theorem, 
which has been referred to in another memoir^ and will be proved generally in a 
memoir on directed selection, written but not yet published, be., that in a wide range 
of cases selection, whether random or directed (natural and artificial) changes 
correlation but not regression. 
Before proceeding further a general remark will enable us to considerably simplify 
the otherwise lengthy algebra. Namely, the relation of M"i, M'b, cr"i, a'o, r" to M'j, 
Mb, cr'i, o-b, r' is pi’ecisely the same as that of M',, Mb, <j\, crb, r themselves to Mj, 
Mo, (Ti, cTo, r. Consequently an interchange of symbols in results already found will 
lead us to the remainino’ formulm needful. 
o 
As an illustration of this, let us verify the result we have found for M'b- By an 
interchange in (v.) : 
hence using (v.), (i.) and (xiii.), we find : 
* Contributions to the Theory of Evolution.—V. On the Reconstruction of Stature,” ‘ Phil. Trans.,’ 
A, vol. 192, p. 177. 
