PKOFESSOK Pearson's contributions to osteology. 463 

 the probable error of its determinatiou is 



±•67449^==' 



The probable error of the standard deviation is 



±•67449 /^=. 



Asymmetrical Frequency. — Many frequency polygons occur 

 in biological statistics which are not symmetrical about the 

 maximum ordinate. These consequently cannot be 'fitted' 

 with a normal frequency curve. The asymmetry, or skewness, 

 may be due to one of two sets of causes. 



(«) The material dealt with may be heterogeneous, and 

 consist of a mixture of two or more homogeneous 

 materials. 



{h) The material may be homogeneous, but tend to deviate 

 more to one side of the mean than to the other. 



These two sets of conditions have been dealt with by 

 Professor Pearson in two memoirs in the Phil. Trans., viz., 

 " Contributions to the Mathematical Theory of Evolution " 

 {Phil. Trcms., vol. 185), and " Contributions to the Mathematical 

 Theory of Evolution — II. Skew Variation in Homogeneous 

 Material " (Phil. Trans., vol. 186). 



In the first paper the dissection of an abnormal frequency 

 curve into n normal curves is discussed. The problem is solved 

 for the case where n = 2. The analytical difficulties for higher 

 values of n are such as would render a more general treatment 

 impracticable. Fortunately, as Professor Pearson points out, 

 the resolution into two is of special importance. " A family," 

 he says, " probably breaks up first into two species, rather than 

 three or more, owing to the pressure at any given time of some 

 particular form of natural selection ; in attempting to procure 

 an absolutely homogeneous material, we are less likely to have 

 got a mixture of three or more heterogeneous groups than of 

 two only. Lastly, even where the heterogeneity is threefold or 

 more, the dissection into two is likely to give us, at any rate, 

 an approximation to the two chief groups." The method is, 

 moreover, of great value from the purely qualitative point of 



vol. XXXV. (N.S. vol. XV.) — JULY 1901. 2 I 



