MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 279 



As a result of Articles (15) and (16), it is possible to use the frequency curve of 

 type y = y\ (1 + a5/ct) p fi~ wl> with as much certainty as to the nature and magnitude 

 of the errors made in the constants as has hitherto been possible in the case of the 



normal distribution y = - -.- e-" 7 '-*"'. The method has been exemplified numerically 



in twenty-three cases in a memoir on the " Variation of Barometric Frequency " (see 

 'Phil. Trans./ A, vol. 190, p. 423). It may not, however, be amiss to illustrate it 

 further in a special case having closer bearings on the theory of evolution. 



(18.) Numerical Illustration Incidence of Enteric Fever. 



In a memoir in the 'Phil. Trans.,' A, vol. 186, p. 391. it is shown that the curve 

 y = 1894-57 (l + 3 .^ J'^V-- 



closely represents the distribution with age of 8,689 cases of enteric fever received 

 into the Metropolitan Asylums Board Fever Hospitals. The unit of x is five years, 

 and the origin is the mode at 14 '3025 years. The criterion is not very nearly zero, 

 although small, but the curve is graphically a good fit (see Plate 12, fig. 9). 

 The following are the numerical values of all the constants : 



Mean = 18'9691 years. d = mean-mode. 

 Mode = 14-3025 years. = '933,313 unit. 



Sk = skewness '462,594. 



7=1-071,453. /> = 3-673,042. 



= 3-428,094. 



y = modal frequency = 1894*57. 



y l = mean frequency = 1687'80. 



o- = standard deviation = 2*01756 units = 10'087 years. 



From these the numerical values of the probable errors and of the correlations 

 between the errors of the constants were found by the processes indicated and the 

 formulae given above. 



We found 



T = -022,525, S = -044,735, 



whence 



of the distribution. It is, however, clear from their tables and plate that no selection could be made of 

 the absolute number of glands without altering tire variability of the gland distribution and the 

 correlation between different systems of glands. 



