MR. K. PEARSON ON THE MATHEMATICAL TH'ORY OF EVOLUTION. 397 
scale to which the curve can be drawn, it tails away indefinitely to the right. This 
justifies us in the assumption that the curve will be fairly approximated to by a form 
of type 
U Vie: OE 
where p would turn out to be a negative quantity lying between 0 and 1. But the 
details given us of the start and finish of the curve are far too scanty to allow us to 
proceed by moments. Jn the first place, to measure an element of area of the 
frequency curve by an element of value into its mid-ordinate is perfectly legitimate 



at such a point as B; it fails entirely, however, at such a point as A, which includes 
the part of the curve which is asymptotic to the ordinate of maximum frequency. 
The area at such a point is much greater than the element into the mid-ordinate, 
and the calculation of moments on the assumption that 3,174,806 houses may be 
concentrated at £5, is purely idle. The ordinate obtained from the area in this 
manner may often differ 30 per cent. from the true ordinate, and yet about three- 
fifths of the total number of houses fall into this first group. 
Further treating the area as ordinate into element of vaiue is also true only if the 
element of value be small. For “elements” such as £150, £200, or even £500, which 
are all that are given in the tail of these statistics, it is perfectly idle to concentrate 
the area at the mid-ordinate. The centroid of a piece of tail such as the accompanying 
figure suggests lies far to the left of the mid-ordinate In other words, to attack the 
problem by the method of moments, we require to have the “tail” as carefully 
recorded as the body of statistics. Unfortunately the practical collectors of statistics 
often neglect this first need of theoretical investigation, and proceed by a method of 
“lumping together ” at the extremes of their statistical series. 
Still three further points in regard to the present series of statistics. First, they are 
