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APPENDIX

and that principle is perhaps more clearly expressed in this
symbolic language than in the more cumbrous language of
ordinary intercourse.
We may express these conceptions in a diagrammatic
form. Take a point P, and two lines Oz, Op, at right
angles to each other, to which its position is referred. Draw
PN perpendicular to Ox. Then, if ON=x PN=y, the
position of P expresses at once a value of x and a value of y.
It shows the value of y which corresponds to a given value
of #, or the value of x which corresponds to a given value of
y. The relation between x and y which is expressed in
equation (i) may be
expressed in diagrammatic
 form by stating
that P is always found
on some definite line,
as Dd. If we knew the
form of the function
f(x), we should know
the shape of the curve
Dd. They are two
ways of expressing the
same thing. Clearly,
if we knew the shape of
the curve Dd throughout
 its length, we
should know all about
the state of demand
symbolised by it. What
we do know is that no
vertical line like NP cuts Dd more than once, and that the
line D4 falls as we pass from left to right along it. This is
the geometric expression of what is stated above in algebraic
symbols.
The actual knowledge of the shapes of such curves as
Dd, which are called “ demand curves,” is not detailed or extensive.
 Careful gathering of statistics may afford knowledge
of the shapes of such curves in the immediate neighbourhood
of the points on them which correspond to actual prices and
supplies. Not much is, or is likely to be, known of their
shapes at parts far removed from these points.
The two kinds of change in demand, referred to on p. 29,
can be distinguished with great clearness by means of our
diagram. Thus, a fall of price from that represented by PN

Fig. (1)