ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 269 



predecessor and its successor, he brings the first term into relation with 

 the last term. Though the final and initial shapes of the Unit cannot 

 even approximately be superposed, yet its content of utility is preserved 

 constant. It is true that at each step of this process some deviation may 

 occur. At each act of weighing something may fall out of the balance. 

 But something may fall in also. And thus, in the absence of a constant 

 bias towards error in one direction, there is reason to believe that — except 

 for very long deferred payments — the result will be as accurate as that 

 which is attainable under more favourable conditions. 



Professor Marshall's method may thus he illustrated. Let us, with Cournot, 

 represent ratios by logarithms, and logarithms by linear distance. But, unlike 

 Cournot, let us take account, not only of the price, but also of the quantity of each 

 article. Let the distance of the dot a from the abscissa represent the price of 

 the first commodity, and the size of the dot the quantity consumed (per unit of 

 time). Let the abscissa represent time. At tlie initial epoch, corresponding to 

 the origin, the purchasing power of money, the denominator of the sought unit, is 

 represented by 00, where is the centre of gravity of the system initially. Now, 



Fig. 2. 



if, during the interval Tj, only money and prices were affected, other things 

 being constant, the required (numerator of the) Unit would be TjO',, where 0'. is 

 the centre of gravity of the system in its new position. But other things are 

 not constant. There occur variations, not only in the relative positions of the 

 particles, but also in their masses (as shown by the varying size of the dots). 

 Also new particles enter the system {e.g., 7j at the time Tj), and old ones drop 

 out. Thus the true centre of gravity at the time Tj is not C\, but Oj. This 

 point can be found at that time ; but it is not available for our first edition of a 

 tabular standard. The second edition at the time T, is similarly obtained by 



