in the theory of value and prices. 41 



ordinates of the front row are proportional to those of the row next 

 behind, also of the second row behind and so on. Remembering 

 that each ordinate is a marginal utility we have: 



cVU^ d\J _ dJJ^ d^ _dJ] d^ ___ 



dk^ ' cIB/' ' ' ' ~ dX/' dB/' ' ' ' " dA/' dB'/' ' ' ' ~~ ' ' 



which is the required condition that marginal utilities must be pro- 

 portional (§3). 



Secondly there are the horizontal levers (F34, etc., fig. 10) lying 

 on the surface of the M^ater in the tank. These relate to prices. 

 The sliding pivots 3, 4, etc. are connected with rods RRR, which 

 in turn are connected by vertical pins with the rear walls of the 

 cisterns. A motion of one of these rods causes all back compart- 

 ments in that row to expand or shrink in unison. The pivots 3, 4, 

 etc. ai'e so situated on these rods that if the levers F34, etc. should 

 assume a right-and-left position along the dotted line FF, the back 

 compartment of every cistern would be completely closed. Hence 

 R3 equals the thickness of each back compartment in the A row, 

 R4 the corresponding thickness in the B row and so on. 



By the similar triangles FR3 and F34 in fig. 10, it is clear that 

 the lines R3 and R4, and consequently the rear thickness in the A 

 and B rows are proportional to the distances of the A and B rods 

 R and R from the float F. But we have just seen that the ordinates 

 of lA and IB are proportional to these same distances. Hence the 

 thicknesses of the back compartments of the cisterns are propor- 

 tional to the ordinates of those cisterns, that is to marginal utilities. 

 Hence we are free to call the thickness of each back compartment, 

 the money* price of the commodity to which that cistern relates. 



* Money is here used solely as a measure of value. It is not one of the com- 

 modities in the market. The high or low price of commodities in terms of 

 this money is dependent entirely on the amount of it at which we agree to rate 

 the yearly consumption of the market, that is the amount of liquid originally iit 

 the back cisterns. We are so accustomed to regard money as the medium of 

 exchange and therefore as a commodity that we may not observe that it is per- 

 fectly possible to have a measure of value which is not a commodity at all. Thus 

 we might agree to call the consumption of the United States for a year $10,000,- 

 000,000, and this agreement would immediately fix a measure of value, though the 

 new dollar need have no equality to the gold or silver dollar. It would be easy 

 to translate between such an arbitrary standard and any commodity standard. 

 Thus if statistics showed that the consumption measured in gold dollars was 

 $12,000,000,000, the agreed standard is at 120 compared with gold and by means 

 of this factor we can reduce the prices of all commodities. In the mechanism 

 the aggregate amount of liquid in the back cisterns corresjxnids to the $10,000, 

 000,000. If we take it so nnd if the amount of liquid in tlie I row is given at 

 $1,000, this means that (in whatever standard) the consumption of I is one-ten- 

 millionth in value the aggregate consumption. 



