188 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK
Evidently, in exact analogy with equations (3) and (4),
namely:

p2/ ps3
Ss o G2/ Pr and Ws R:/R;3
Si R:/Rs WwW, F/F,
Fy/F,

we may obtain also

ps/ ps
Ss _ ¢4/¢s and Ws _ Ry/Rs
Ss R4/Rs Ws = F./Fs
F,/F,

Multiplying these together vertically, and remembering that
F1=F3, R3—=R; and R,—R,, that is, that the scale of prices of
the same food and the same rent in the same market are the
same to different families, we obtain

Eh

(7)

(8)

Multiplying (7) and (8), and cancelling, we have

These results come each from multiplying two equations.
Similarly, by threefold multiplication we can obtain > and n,
1 1
by fourfold multiplication, = and >, etc., indefinitely. The
1 I
values of Si, Ss, Ss, Sz, So, etc., can thus be calculated and will
successively increase (or successively decrease, as the case may
be) indefinitely, while W., W3, Ws, W1, Wy, etc., will do the
opposite.
We can thus (if suitable statistics are at hand) locate any
number of points on the curve in Figure I connecting income and
the marginal want for money, instead of only the two which were
plotted. Unfortunately, as yet, we do not have many statistics