282 PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



We see at once from the above table that if the mean age of incidence of enteric 

 fever in any group were raised, the disease would be concentrated in fewer years, the 

 modal and mean incidence would be brought closer together, and the incidence in the 

 modal year of frequency would be heavier. The changes here are very sensible. 

 Thus, if we raised the mean age of attack to that of phthisis, or about nine years, the 

 modal frequency would be increased about 41 per cent., the concentration of the 

 incidence of the fever increased about 40 per cent., while the distance between mode 

 and mean would be reduced to nearly 2/5 of its original value. The skewness would 

 not be changed. Much less marked effects would arise from a selection of modal 

 frequency. Any increase of modal frequency tends to slightly raise the mean age of 

 attack, to increase slightly the concentration, to draw the mode towards the mean 

 and reduce the skewness. 



The changes produced by closer concentration of the attacks of the disease, i.e., the 

 limitation of its incidence to fewer years, would be of a more marked character, they 

 would raise the mean age of attack and the modal frequency, they would decrease the 

 interval between mode and mean, and reduce the skewness. Concentration of the 

 disease would thus tend to render its distribution more normal. 



To increase the interval between mean and mode lowers the mean age of attack, 

 reduces the modal frequency, increases the period of liability to incidence, and much 

 increases the skewness. 



Finally, increase of skewness decreases the modal frequency, increases the period 

 of liability and the interval between mean and mode. 



These statements with regard to the manner in which enteric fever would affect 

 different groups selected at random from the general population seem of considerable 

 interest, for there is reason to believe that what is thus stated for enteric fever in 

 different groups may be applied to different fevers in one and the same group. For 

 example, the lower the mean age of attack of any fever, the greater its concentration ; 

 the less the concentration, the more nearly normal is its distribution, &c., &c. 



(19.) Probable Errors and Error Correlations of the Constants of the Generalised 



X \"'i / 3C V' 1 * 



1 + -- ) 1 1 -- ) . 



Transfer the origin to one end of the range, and the equation to the curve becomes 



n T (m. + m t + 2) / x V'" / a \ 



T r (Wl + 1) r ( Wl TT) (T) ( l ' ' T) < ]xxv ->' 



where n is the number of observations and b is the range. 



The following values are given in 'Phil. Trans./ A, vol. 186, pp. 368-9, where 

 r = m, + w, -j- 2 : 



