MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 399 
Returning now to the curve and statistics, we have the following comparative 




results :— 
Number of 1000’s of houses. 
Value. 
Theory. Statistics. 
U aaah 
nder 10 | 3580 3175 ‘ 
10-20 | 1045 \ ez 1451 \ oze 
20-30 452 4.42 
30-40 253 260 
40-50 153 151 | 
| 50-60 97 90 
60-80 102 104 
80-100 46 47 
Above 100 66 110 





The general accordance here is very marked, the chief divergences being accounted 
for by the special causes to which we have referred above, 2.e. (i) the crowding of 
houses just below the limit of taxation, and (11) the divergent character of the causes 
at work determining the frequency of low and high class house property. 
The results are depicted, Plate 14, fig. 13. 
It will be observed that so far as the observations can be plotted to the theoretical 
curve, it leaves little to be desired. The histogram* shows, however, the amount of 
deviation at the extremes of the curve. 
(81.) Example XI.—Frequency curves of the type considered in Example X. are 
so common that it is needful to make a few further remarks with regard to them, 
and illustrate them by further examples. Such curves occur in many economical 
instances (income tax, house valuation, probate duty), in vital statistics (infantile 
mortality), and not uncommonly in botanical statistics of the frequency of variations 
in the petals or other characteristics of flowers. 
As we have noted, the method of moments developed in this memoir cannot be 
directly applied, or only applied to obtain a first approximation to the constants 
required. This first approximation, however, will often assist us to obtain with 
quite sufficient accuracy the value of the moments of portions of the area, especially 
if the position of the initial or asymptotic ordinate is known. 
For example, consider the curve of limited range : 
y= pe? (b— 2) 
where p lies between 0 and 1. Then if « be its area, aw”, = the s** moment about 
the asymptotic ordinate of the area up to «: 
* Introduced by the writer in his lectures on siatistics as a term for a common form of graphical 
representation, 7.e., by columns marking as areas the frequency corresponding to the range of their base. 
