TRANSACTIONS OF SECTION F. 825 
2. On Geometrical Illustrations of the Theory of Rent. 
By Professor J. D. Evererr, 2S. 
If 2 denote outlay, inclusive of interest, and y the return which it brings, then 
y—x will be the surplus which governsrent, Let 2 stand for y—., and let the curve 
whose co-ordinates are wv, z be plotted, also the curve whose co-ordinates are 2, y, 
the axis of a being in both cases horizontal. 
The cultivator aims at making the surplus profit = a maximum. The condition 
for this is ie 0, or Bh ; in other words, that a very small increment (positive 
or negative) of x brings an equal increment of y and leaves z unchanged. For that 
value of 2 which makes z a maximum, the tangent to the 2, < curve is horizontal, 
and the tangent to the z, y curve slopes at 45°. For smaller values the tangent 
to the 2, y curve is steeper, and for larger values less steep than 45°, The received 
theory asserts that the actual rent as settled by competition will be the maximum 
value of s. More precisely, in view of the practical impossibility of foreseeing 
what outlay will in a given year be most remunerative, the rent may be taken to 
be that value of z which makes as near an approach to the maximum as a fairly 
skilful cultivator will usually attain. 
The ordinary mode of graphically illustrating rent is by a curve in which the 
abscissa wv represents outlay, and the ordinate 7 is such that the integral of nda, 
from 2=0 to any specified value of the outlay 2, represents the return for that 
outlay. The rent is represented by that portion of the area which lies above a 
horizontal line drawn through the top of the last ordinate, the last ordinate being 
that which corresponds to the limit of profitable cultivation. This mode of repre- 
sentation is less simple than either of the two above employed. It also invoives 
the inconvenience of assigning a shape to the early part of the curve—a part which 
has no definite shape—and the further drawback of representing two comparable 
things, outlay and return, by two magnitudes which are not comparable, length 
and area, 
3. On the Use of Galtonian and other Curves to represent Statistics. 
By Professor F. Y. EpGrwortu. 
Comparing different modes of representing statistics of frequency, such as the 
returns which specify the number of persons in a country having each amount of 
income, the author gives the preference to those formule which not only fit the 
data, but also are recommended by an a priori reason. Such a reason is commonly 
afforded by the phenomena of organic and social life: where a great number of 
independently varying influences go to the formation of a result, the quantity of 
that result is apt to vary according to the normal law of ‘error’ or frequency. 
The symmetrical curve which is often employed to express that law is but a first 
approximation, the normal curve of frequency is in general somewhat unsymme- 
trical. A very unsymmetrical group, indeed such as that which the frequency of 
incomes of different sizes constitutes, cannot be represented by a normal curve, but 
it may often be connected therewith by the hypothesis that each observation, 
though not identical with or proportional to, is yet dependent on a function of 
some attribute which fluctuates according to the normal law. 
FRIDAY, SEPTEMBER 15. 
The following Papers were read :— 
1. Some Aspects of American Municipal Finance. 
By J. H. Houianper, Ph.D., Johns Hopkins University. 
The fiscal activities of cities of the United States of 50,000 or more inhabitants 
have been characterised in the main by, (1) Progressive expenditure, (2) inelastic 
revenue, (3) increasing funded indebtedness, (4) crude budgetary procedure. 
' Published in the Jowrnal of the Royal Statistical Society, December 1899, 
