42 Irving Fisher — Mathematical i7ivestigatio)is 



It is to be observed that the cisterns are free to move only verti- 

 cally^ the rods and rear cistern walls only forward and hackioard^ 

 the wooden floats can shift only sidewise right and left while the 

 levers assume such positions as the mechanism compels. 



Let given quantities of water be introduced into each front-and- 

 back-row of front cisterns and into each right-and-left row of back 

 cisterns. The system will attain a stable equilibrium and the level 

 of water in each cistern will be that of the tank. 



The front cisterns of a front-and-back row must have a uniform 

 level on account of their niutual connection. The back cisterns of 

 a right-and-left row must preserve a uniform level for a similar rea- 

 son. The movable rear walls allow the pressure of the outside 

 water in the tank to keep the back cisterns at the same level as the 

 front. Without taking account of the levers the cisterns would 

 thus all have the same level as the tank. But it would be possible 

 to arrange their vertical positions and their rear thicknesses in many 

 arbitrary ways. The levers simply specify or determine this arrange- 

 ment. 



§6. 



It may be needful to restate carefully the magnitudes, their units 

 and the conditions which determine them. The magnitudes are: 



1. The quantities of each commodity consumed by each individual 

 during the year. These are represented by the quantities of water 

 in each front compartment. 



2. The giveti total quantities of each commodity consumed by the 

 whole market — represented by the fixed amount of water in each 

 front and back row of front comparments and registered on scales* 

 A, B, C, at the rear of the tank. Each commodity-water may have 

 a distinguishing color. 



3. The money paid for each commodity by each individual — rep- 

 resented by the water in each back compartment. 



4. 7%e total, money income of each individual — represented by 

 the fixed amount of water in each right-and-left row of back com- 

 partments, and registered on sccdes\ TJ II, Til, at the right of the 

 tank. 



* The stoppers A B, C regulate this amount of water. The stoppers are each 

 directly connected with the pointers on the scales A, B, C, and so arranged that 

 when the stopper is withdrawn so that the scale reads zero, the water entirely 

 disappears from the cisterns. 



f The stoppers I, II, III are also directly connected with pointers on the scales 

 I, II, III. 



