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adjustment of the breadth of each cistern may be represented by oneinch. That is, if 100 cu. in. of water are put in each A cistern theordinate must be one inch. This applies as well to the utility ofmoney, so that the scale U at the left indicates the number of utilsat which the individual values the last dollar of his income. Itshould, however, be noted that the variation of utils is only valuablein the same register, that is, for the same individual. There is noimportant meaning attached to the ratio of the scale readings U fortwo individuals. If that of I is 1 and of II 2 it means simply thatII values his last dollar twice as much as his 100th ton of A, whileI values his last dollar just as much as his 100th ton of A. It is in-teresting to observe that analogously'the price registers are not tobe compared, for while one indicates price per ton the other indicatesprice per yard, etc. Thus the mechanism is independent of anycommon measure of utility for different individuals and any commonmeasure of prices for different commodities.
§*■
It will be observed that the numbers on the various registers areso connected that the product of the register of A by that of itsprice added to the like products for B, C, etc., will equal the sumof all the income registers.
Moreover if each cistern is provided with a graduation to showmarginal utility, this number will be found to be the product of thenumber for price in its front-and-back row, by that for valuation ofmoney in its right-and-left row.
§8.
The mechanism just described is the physical analogue of theideal economic market. The elements which contribute to thedetermination of prices are represented each with its appropriaterole and open to the scrutiny of the eye. W e are thus enabled notonly to obtain a clear and analytical picture of the interdependenceof the many elements in the causation of prices, but also to employthe mechanism as an instrument of investigation and by it, studysome complicated variations which could scarcely be successfullyfollowed without its aid. Its chief uses may be briefly classified asfollows :
1. Arrange the stoppers I, II, III, etc., so that the money incomesof I, II, III, are all equal. The differences of distribution of thecommodities will depend on individual characteristics, that is, on