For the present, I waive a discussion of the comparative importance of these different methods of conducting exchanges. The situation varies greatly with different countries. Fisher's and Kemmerer's equations are at best plausible when presented as describing American conditions, are much less plausible when applied to Canada and England, and are caricatures when applied to Germany and France. So much for the statement of the equation of exchange, except that it is important to add that the period of time chosen for the equation is one year. Just why a year, rather than a month or two years or a decade should be chosen, may await full discussion till later. I shall venture here the opinion that the yearly period is not the period that should have been chosen from the standpoint of Fisher's causal theory, and that it probably was chosen, if for any conscious reason at all, because of the fact that statistical data which Fisher wished to put into it are commonly presented as annual averages. The question now is, however, as to the use to be made of the equation in the development of a causal theory. CHAPTER IX THE VOLUME OF MONEY AND THE VOLUME OF CREDIT John Stuart Mill, who first among the great figures in economics gives a realistic analysis of modern credit phenomena, thought that credit acts on prices in the same way that money itself does[155] and that this reduces the significance of the quantity theory tendency greatly, and to an indeterminate degree. The quantity theory is largely whittled away in Mill's exposition of the influence of credit. In Fisher we have a much more rigorous doctrine. The quantity of money still governs the price-level, because M governs M'. The volume of bank-deposits depends on the volume of money, and bears a pretty definitely fixed ratio to it. Just how close the relation is, Professor Fisher does not say, but the greater part of his argument, especially in ch. 8,[156] rests on the assumption that the ratio is very constant and definite indeed. At all events, the importance of the theory, as an explanation of concrete price-levels, will vary with the closeness of this connection, and the invariability of this ratio. It is not too much to say _that the book falls with this proposition_, to wit, that M controls M', and that there is a fixed ratio between them. We would expect, therefore, a very careful and full demonstration of the proposition, a care and fullness commensurate with its importance in the scheme. But the reader will search in vain for any proof, and will find only two propositions which purport to be proof. These are: (1) that bank reserves are kept in a more or less definite ratio to bank deposits; (2) that individuals, firms and corporations preserve more or less definite ratios between their cash transactions and their check transactions, and between their cash on hand and their deposit balances.[157]