is to weight the different prices by the number of units of each kind of good sold, namely, T. Thus, in Wilson's illustration, we would define P as [(5c.x10) + (20c.x3) + (35c.x1)]/14 P is then 10-5/14 c., while T is 14. PT is, then, equal to $1.45, which is the total expenditure, or MV + M'V'. Be it noted, here, that P is defined in terms of T, _i. e._, P is defined as a fraction, the denominator of which is T. No other definition of P will serve, if T is to be defined independently. But notice the corollary. P must be differently defined each year, for each new equation, as T changes in total magnitude, and as the elements in T are changed. The equation cannot be kept straight otherwise. Suppose that the prices remain unchanged in the next year, but that one more pound of coffee, and two less pounds of sugar are sold. P, as defined for the equation of the preceding year would no longer fit the equation. P, as previously defined, would be unaltered, since none of the prices in it had changed. P, defined as a weighted average with the weights of the first year, would, then, still be 10-5/14 cents. The T in the new equation is 13. The product of P and T is $1.34-9/14. But the total expenditure, (MV + M'V') is $1.70. The equation is not fulfilled. To fulfill the equation, it is necessary to get a new set of weights for P, in terms of the new T of the new equation. From the standpoint of a _causal_ theory, this is delightful. P is the _problem_. But you are not allowed to _define_ the problem until you know what the _explanation_ is! Then you define the problem as that which the explanation will explain! Fisher, however, appears unaware of this. At all events, he does not mention it. And he ignores it in filling out his equation statistically, for he assigns one set of weights to the particular prices in his P throughout.[148] The causal theory with which the equation of exchange is associated is as follows: P is passive. A change in the equation cannot be initiated by P. If P should change without a prior change in one of the other factors, forces would be set in operation which would force it back to its original magnitude. M and T are independent magnitudes. A change in one does not occasion a change in the other. An increase or decrease in M will not cause a change in V. Therefore, an increase in M must lead to a proportionate increase in P, and a decrease in M to a proportionate decrease in P, if the equation is to be kept straight. Changes in T have opposite proportional effects on P. Before examining the validity of the causal theory, and the arguments by which it is supported, it will be best to state the more complex formula which Professor Fisher advances as expressing the facts of to-day. The original formula ignored credit, and ignored the possibility of resort to barter. It also failed to reckon with certain complications which Fisher deals with as "transitional" rather than "normal."