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XI. Mathematical Contributions to the Theory of Evolution. —X. Supplement 
to a }[enioir on. Skew Variation."^ 
By Kael Peaesox, F.R.S., University Collcye, Lcnidon. 
Received May 22, —Read, June 20, 1901. 
(1.) lx a memoir on Skew Variation published in the ‘Phil. Trans.,’ A, vol. 186, 
1895, a series of frequency curves are discussed which are integrals of the differential 
equation 
1 d// 
y d.r Cj d- + cyr 
(See p. 381 of the memoir.) 
The discussion of four main types is given in detail, and a l)rief reference is made 
to various suh-tvpes which may occur. The types considered in that memoir covered 
at the time all the frecpiency series, and they were fairly numerous, that I had liad 
occasion to deal with. In the course of tlie last few years, hov^ever, I liave been 
somewhat })uzzled bv frequency distributions for which the criterion 
(see p. 378) was positive, and therefore d priori a curve of the type 
1 
was to be expected, but which on calculation gave v imaginary. The frequency 
distributions in question arosef occasionally in sociological statistics, but also in 
* ‘Pliil. Trans.,’ A, a'oI. 186, p. 343. 
t Some other frequency distributions, which on first investigation fell under Types V. and VI. of the 
present paper, were found with improved values for the moments to fall unrler types already discussed. 
Mr. tv. F. SHEPrAEu’s values for the moments (‘ Lond. Math. Soc.,’ vol. 29, p. 369, formula 30) should 
certaiidy be used in preference to those given by me (‘Phil. Trans.,’ A, vol. 186, p. 350) whenever we are 
calculating the moments of a curve from areas and not from true ordinates. I hope shortly to publish a 
paper on this point, which is one really of quadrature formula?. INleanwhile for every true frequency 
curve wifh high contact at both termincds we ought to use 
instead of the values given on p. 350, remaining unchanged. 
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