Of course Professor Fisher himself recognizes that his central problem is, not to state and justify, mathematically, his equation[145]--that is a work of supererogation, and the statistical chapters devoted to it seem to me to be largely wasted labor. Professor Fisher recognizes that his central problem is to establish _causal_ relations among the factors in his equation of exchange. It is from the standpoint of its adaptability as a tool in a theory of causation that I have been considering it. It should be noted that "volume of trade," as frequently used, means not numbers of goods sold, but the money-price of all the goods exchanged, or PT. It is in this sense of "trade" that bank-clearings are supposed to be an index of volume of trade. The sundering of the p's and Q's really is a big assumption of many of the points at issue. Indeed, it is absolutely impossible to sunder PT. It is always the p aspect of the thing that is significant, Fisher himself finally interprets T, statistically, as billions of _dollars_.[146] As a matter of mathematical necessity, either P must be defined in terms of T or T defined in terms of P. The V's and M and M' may be independently defined, and arbitrary numbers may be assigned for them limited only by the necessity that MV + M'V' be a fixed sum.[147] But P and T cannot, with respect to each other, be thus independently defined. The highly artificial character of T has been pointed out by Professor E. B. Wilson, of the Massachusetts Institute of Technology, in his review of Fisher's _Purchasing Power of Money_ in the _Bulletin of the American Mathematical Society_, April, 1914, pp. 377-381. "Various consequences are readily obtained from the equation of exchange, but the determination of the equation itself is not so easy as it might look to a careless thinker. The difficulties lie in the fact that P and T individually are quite indeterminate. An average price-level P means nothing till the rules for obtaining the average are specified, and independent rules for evaluating P and T may not satisfy [the equation.] For instance, suppose sugar is 5c. a pound, bacon 20c. a pound, coffee 35c. a pound. The average price is 20c. If a person buys 10 lbs. of sugar, 3 lbs. of bacon, and 1 lb. of coffee, the total trading is in 14 lbs. of goods. The total expenditure is $1.45; the product of the average price by the total trade is $2.80; the equation is very far from satisfied." Wilson thinks it necessary, to make the matter straight, to define T, arbitrarily as (MV + M'V')/P in which case, the equation is true, but so obviously a truism that no one would see any point in stating it. T no longer has any independent standing. Fisher has, however, an escape from this status for T, but only by reducing P to the same position. He defines P as the _weighted_ average of the p's (27), and fails, I think, to see how completely this ties it up with T. The only method of weighting the p's that will leave the equation straight