The nature of capital and income . equal to RS, the rate of income at that time, representsthe other tendency. The resultant, OQ, drawn according tothe principle of the parallelogram of forces, will represent theactual direction in which the curve will be moving at thepoint 0. In other words, a point moving under the influ-ence of two forces, OK and OH, will generate the requiredcurve NO. 384 NATURE OF CAPITAL AND INCOME In order to show that this is a correct representation let usfirst take the case of semi-annual income. RR represents oneyear; Rr represents half a year. Draw the ordinate rh.
The nature of capital and income . equal to RS, the rate of income at that time, representsthe other tendency. The resultant, OQ, drawn according tothe principle of the parallelogram of forces, will represent theactual direction in which the curve will be moving at thepoint 0. In other words, a point moving under the influ-ence of two forces, OK and OH, will generate the requiredcurve NO. 384 NATURE OF CAPITAL AND INCOME In order to show that this is a correct representation let usfirst take the case of semi-annual income. RR represents oneyear; Rr represents half a year. Draw the ordinate rh. Fromh draw vertically upward hq to represent a half-years install-ment of income, that is, half of Rs. To avoid complicating thefigure, 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 Ohq, which forms a tooth. Theline Oq is therefore a line drawn through the top points of twoneighboring teeth. Its direction is a first approximation to. Fig. 43. the direction OQ of the curve for the continuous case. Thisdirection Oq is the diagonal of a parallelogram formed byproducing Oh to meet the ordinate from W in IT, producingOq to Q and completing the parallelogram. Since HQ is twice as far from 0 as hq { RR =2 (rR)by hypothesis), it follows, by similar triangles ( Ohq andOHQ), that it is also twice as long. But hq represents ahalf years installment of income. Hence H^Q represents two APPENDIX TO CHAPTER XIII 385 such installments, or the annual rate of income. ThereforeOK, being of the same length, also represents this annual rateof income. In other words, the direction from O to g lies along a paral-lelogram of which the side OK represents the annual rateof income and the side OIF a chord of the discount curveOP. Now it is evident that if, instead of a semi-annual installment,we assume greater frequency, the same statement will applyexcept that the point h will be nearer 0. By proce
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