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