CHAPTER XIV

THE THIRD APPROXIMATION UNADAPTED TOMATHEMATICAL FORMULATION

§1. Introduction

The second approximation fails to conform to condi-tions of actual life chiefly with respect to risk. While itis possible to calculate mathematically risks of a certaintype like those in games of chance or in property andlife insurance where the chances are capable of accuratemeasurement, most economic risks are not so readilymeasured. 1

To attempt to formulate mathematically in any use-ful, complete manner the laws determining the rate ofinterest under the sway of chance would be like attempt-ing to express completely the laws which determine thepath of a projectile when affected by random gusts ofwind. Such formulas would need to be either too generalor too empirical to be of much value.

In science, the most useful formulas are those whichapply to the simplest cases. For instance, in the studyof projectiles, the formula of most fundamental impor-tance is that which applies to the path of a projectile ina vacuum. Next comes the formula which applies to thepath of a projectile in still air. Even the mathematiciandeclines to go beyond this and to take into account theeffect of wind currents, still less to write the equations

3 See The Nature oj Capital and Income, Appendix to Chapter XVI.

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