398 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
very unlikely to be homogeneous. Houses with an annual valuation of over £300 
hardly fall under the same series of causes as the bulk of houses in the kingdom 
which fall under £100. Secondly, when we are told that 3,174,806 houses are valued 
under £10, it can hardly mean that any houses are valued at 0, certainly not the 
maximum number. Hence our frequency curve in theory must not be expected to 
rise from zero, but from some point between 0 and £10, which corresponds to the 
customary minimum at which a cottage can be rented. 
Lastly, there is one special cause at work tending to upset, about the value of £20, 
the general distribution due to a great variety of small causes. This is the value at 
which taxation commences, and we should expect a larger proportion of houses to be 
built just under the taxable value than is given by a chance distribution. 
Notwithstanding the many disadvantages of these results, I determined to obtain 
if possible a skew curve approximating to the main portion of the distribution. I took 
£10 as my unit of value and 1000 houses as my unit of frequency. I started with 
the ordinary method of moments, concentrating each area at its centroid as given by 
the total valuation of the group, also recorded by Mr. GoscHeEn, and found a curve of 
the type 
Yy = you? e-™, 
with 
p= — 65448, y= 2008. 
This was so far satisfactory that it showed even by this rough method that p was 
negative, and between 0 and 1. Thus the theoretical curve gave an infinite ordinate, 
but finite area at its start. 
A laborious method of trial and error was then adopted, and by varying p and y 
slightly, as well as y, and the origin of the curve, I sought to improve the fit given 
by the rough method (in this case) of moments. The fundamental consideration was 
to keep the total areas under £100 value as nearly as possible the same in the 
theoretical curve and the statistics. This portion of the curve I treated as prac- 
tically referring to homogeneous material. Ultimately I found the following curve : 
i 1388°32 gn 690077 Cmeienizs 
with the origin as ‘45 unit from zero. Thus the minimum annual valuation was 
£4 10s., or, to a weekly valuation, of 1s. 7}d. This would connote probably a weekly 
rental of 1s. 8d. to 2s. The total area of this theoretical curve was 5795 in thousands 
of houses ; of these 5729 had a valuation under £100 and 66 over £100; the corres- 
ponding numbers for the statistics themselves are 5720 and 110. The additional 44 
over £100 I assume to be due to the heterogeneity of the statistics—high values 
corresponding to blocks of chambers, large hotels and other buildings hardly falling 
into the same category as the small house under £100 in value. Unfortunately the 
“tail” of the statistics is so defectively recorded that there is no hope of reaching a 
separate distribution for this high class property. 
