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relation between the major and minor axis of the ellipses was changed 3 per cent. ; and their inclination to one another was changed less than 2°.1

It is obvious from this close accord of calculation with observation, that the law of Error holds throughout with sufficient precision to be of real service, and that the various results of my statistics are not casual and disconnected determinations, but strictly interdependent.

I trust it will have become clear even to the most non-mathematical reader, that the law of Regression in Stature refers primarily to Deviations, that is, to measurements made from the level of mediocrity to the

1 The following is a more detailed comparison between the calculated and the observed results. The latter are enclosed in brackets. The letters refer to Fig. 11 :


The" Probable Error" of each system of Mid-Parentages = 1.22 inch. (This was an earlier determination of its value ; as already said, the second decimal is to be considered only as approximate.)

Ratio of mean filial regression = f.

"Prob. Error" of each Co-Fraternity = 1.50 inch.

Sections of surface of frequency parallel to XY are true ellipses. (Obs.-Apparently true ellipses.) MX : YO = 6 : 17 -5, or nearly 1 : 3.

(Obs.-1 : 3.)

Major axes to minor axes   7 : 1 2 = 10:5.35. (Obs.-10 : 5.1.)

Inclination of major axes to OX = 26° 36'. (Ohs. 25°.)

Section of surface parallel to XZ is a true. Curve of Frequency. (Obs.-Apparently so.)

" Prob. Error ", the Q of that curve, = 1.07 inch. (Obs.-.1.00, or a little more.)