384 NATURE OF CAPITAL AND INCOME 
In order to show that this is a correct representation let us 
first take the case of semi-annual income. RR" represents one 
year ; Rr represents half a year. Draw the ordinate rh. From 
h draw vertically upward hq to represent a half-year’s install- 
ment of income, that is, half of Rs. To avoid complicating the 
figure, hq is omitted; were it drawn, q would lie on the line 0Q". 
Then, according to our previous representation, the capital- 
value will follow the curve Ohg, which forms a “tooth.” The 
line Og is therefore a line drawn through the top points of two 
neighboring teeth. Its direction is a first approximation to 
h 
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Fic. 43. 
the direction OQ of the curve for the continuous case. This 
direction Oq is the diagonal of a parallelogram formed by 
producing Oh to meet the ordinate from R' in H', producing 
0g to Q' and completing the parallelogram. 
Since H'Q' is twice as far from O as hq (ie. RR"=2 (rR) 
by hypothesis), it follows, by similar triangles (i.e. Ohg and 
OH'Q'), that it is also twice as long. But hg represents a 
half year’s installment of income. Hence H'Q' represents two