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X. Contributions to the Mathematical Theory of Evolution.—Il. Skew Variation in 
Homogeneous Material. 
By Kart Pearson, University College, London. 
Communicated by Professor HENRICI, ERS. 
Received December 19, 1894,—Read January 24, 1895. 
Puates 7-16. 
CONTENTS. 
Part I.—THEORETICAL. 
Page. 
Section 1.—Classification of asymmetrical frequency curves in general. -Types actually 
occurring . . > 9 Be BlnG see Oi 344 
Sections 2-5 —Fitting of point Ginomuale be methods of quadvatio nad eats cae vee le wo ee 345 
Section 6.—TI]lustrations in cases of barometric heights and crab measurements . . . . 351 
Section 7.—Fundamental geometrical relation between symmetrical binomial and normal 
frequency curve. . . 6 . 6 : By a coke et ae 855 
Section 8.—Extension of this Heaisa to the deatenon of a Eee eqnenoy curve from 
the asymmetrical binomial. . . . : ket cbs el liGuG 356 
Sections 9-10.—General remarks on the defects of the ‘seal fy equency curve as applied to 
actual statistics. Skewness and limited range. The five types of theoretical curves . . 357 
Section 11—The hypergeometrical series as replacing the point-binomial. Curves related to 
the hypergeometrical series in the same manner as the normal curve to the ae ae 
point-binomial . . . 360 
Sections. 12-13.—Equations i the paasible feoueney curves deaiteoa sot ine yer 
geometrical series . . cA OR aaeaes tegen 4 ee tcuct its Sp eB) | Bynes hic 362 
Section 14.—Curve of Type L Fics eric with range limited in both dizeations Criterion 
for the existence of this type and method of fitting . ......4.4.2.422.4. +, 367 
Section) 15:—special case of range being/piven 2. a OO 
Section 16.—Special case of one end of range being given. . . : ee 371 
Section 17.—Curve of Type II. Symmetrical with range limited! in ibottl directions! This 
curve better than the normal curve, if observations vary on the side of a point-binomial 
from normality... . EEE TO OS Oho Ban Db \ a. ew OS ome one OMS 372 
Section 18-18 bis.—Curve of Troe. UT. ane and range limited in one direction only. 
Criterion and method of fitting . . 373 
Sections 19-20.—Curve of Type IV. Ranes anlinntedle in hoth disedtions, eit siudwtibas! 
Criterion and method of fitting. Discussion of the G-integral . . . . ... .- 374 
16.7.95, 
