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equally sure to diminish gain. Herein lies the virtue of insur-ance and the vice of gambling. Neither alters (directly) theamount of wealth. But insurance modifies and gambling intensi-fies its fluctuations. Hence the one increases the other decreasesgain.
§ 13 .
Again it may be objected to the foregoing definitions that the useof infinitesimals is inappropriate since an individual does not andcannot reckon infinitesimals. The same apparent objection attachesto any application of the calculus. We test forces by weights butcannot weigh infinitesimal masses nor do they probably exist; yetthe theory of forces begins in infinitesimals. We apply fluxions to thevarying density of the earth, though we know that if we actuallytake the infinitesimal ratio of mass to volume we shall generally getzero since matter is discontinuous. The pressure of a confined gasis due to collisions of its molecules against the containing vessel.As each molecule rebounds the change of momentum divided by theinfinitesimal time is the pressure. Yet at any actual instant thevalue of this fluxion is quite illusory. But these facts do not mil-itate against the use of fluxions for a thinkable theory of forces,density and gaseous pressure. In cases of discontinuity fluxionshave important applications though infinitesimals may not exist.The rate of increase of population at a point in time is an impor-tant idea, but what does it mean ? It is convenient to define it asinfinitesimal increase of population divided by the infinitesimal timeof that increase though we know that'population increases dieeon-tinuously by the birth of whole individuals and not of infinitesimals.
Practically we can find the approximatemarginal utility of a commodity just aswe approximately find the rate of increaseof population by taking small incrementsin place of infinitesimals.
In actual fact inequality of utilities isthe rule and absolutely equal utilities neverexist. Instead of a curve of utility weshould draw a belt (fig. 1) whose limitsare ill-defined and whose width in generaldepends on the amount of antecedent atten-tion which the individual has bestowed on the alternative amountsand modes of consumption.