V.] NORMAL VARIABILITY. 57

am satisfied to claim that the Normal Curve is a fair average representation of the Observed Curves during nine-tenths of their course ; that is, for so much of them as lies between the grades of 5° and 95°. In particular, the agreement of the Curve of Stature with the Normal Curve is very fair, and forms a mainstay of my inquiry into the laws of Natural Inheritance.

It has already been said that mathematicians laboured at the law of Error for one set of purposes, and we are entering into the fruits of their labours for another. Hence there is no ground for surprise that their Nomenclature is often cumbrous and out of place, when applied to problems in heredity. This is especially the case with regard to their term of " Probable Error," by which they mean the value that one half of the Errors exceed and the other half fall short of. This is practically the same as our Q.1 It is strictly the same whenever the two halves of the Scheme of Deviations to which it applies are symmetrically disposed about their common axis.

The term Probable Error, in its plain English interpretation of the most Probable Error, is quite misleading, for it is not that. The most Probable Error (as Dr. Venn has pointed out, in his Logic of Chance)

1 The following little Table may be of service Values of the different Constants when the Prob. Error is taken as unity, and

their corresponding Grades.

Prob. Error 1.000 ; corresponding Grades 25°•0, 75°•0

Modulus 2.097 ; |
7°•9, |
92°•1 | |

Mean Error 1.183 ; |
21°•2, |
78°•8 | |

Error of Mean Squares 1.483 ; |
,, ff |
16°•0, |
84°•0 |