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ITT, Contributions to the Mathematical Theory of Evolution. 
By Karl Pearson, University College, London. 
Communicated by Professor Henrici, F.R.S. 
Received October 18,—Read November 16, 1893. 
[Plates 1—5.] 
Contents. 
Page. 
I.—On tbe Di.ssection of Asymmetrical Frequency-Curves. General Theor}-, §§ 1-8. 71-85 
Example: Professor Weldox's measurements of the “ Forebcad ” of Crabs. 
§§9-10 :. 85-90 
II.—On the Dissection of Sjunmetrical Frequency-Curves. General Theory, §§ 11-12 
Application. Crabs “No. 4,” §§ 13-15.. 90-100 
III.-—Investigation of an Asymmetrical Frequency-Curve representing Mr. H. Thomson’s 
measurements of the Carapace of Prawns. §§ 16-18.. . 100-106 
Table I. First Six Powers of First Thirty Natural Numbers. 106 
Table II, Ordinates of Normal Frequency-Curve. 107 
Note added February 10, 1894 . 107-110 
l.~On the Dissection of Asymmetrical Frequency-Curves. 
(1.) If measurements be made of tbe same part or organ in several hundred or 
thousand specimens of the same type or family, and a curve be constructed of which 
the abscissa x represents the size of the organ and the ordinate y the number of speci¬ 
mens falling within a definite small range hx of organ, this curve may be termed a 
frequency-curve. The centre or origin for measurement of the organ may, if we 
please, be taken at the mean of all the specimens measured. In this case the 
frequency-curve may be looked upon as one in which the frequency—per thousand or 
per ten thousand, as the case-may be—of a given small range of deviations from the 
mean, is plotted up to the mean of that range. Such frequency-curves play a large 
part in the mathematical theory of evolution, and have been dealt with by 
Mr. F. Galton, Professor Weldon, and others. In most cases, as in the case of 
errors of observation, they have a fairly definite symmetrical shape* and one that 
* Symraetrical shapes may of course occur which are not of the normal or eiTor-curve form. See 
Part II., § 11 of this paper. 
9.5.94 
