It is perfectly true, however, that studies running through long periods, which give simply figures for general prices and figures for quantity of money, omitting volume of trade, are not very relevant either for proof or disproof.[377] And the conception underlying the studies of Kemmerer and Fisher, that not merely money and prices, but also volume of bank-credit, volume of trade, velocity of monetary circulation, and velocity of bank-credit, must be measured, undoubtedly represents a big advance in the conception of the statistical problem involved. The mere stating of the problem is an intellectual achievement of no mean order, and the ingenuity and scholarship involved in seeking data for concrete measurement of these highly elusive elements must command the admiration of every student of monetary problems. Volume of trade, velocity of money and velocity of bank-credit had been generally supposed, until these studies were undertaken, to be beyond the reach of the statistician. There can be no doubt at all that the efforts to measure them, or to measure variations in them, by Kemmerer and Fisher, have greatly advanced our general knowledge of the phenomena of money and credit. With great admiration for the magnificence of the problem undertaken, and for the industry, ingenuity and scholarship which have been devoted to its solution, I have nevertheless reached the conclusion that the figures assigned by these writers to the magnitudes of their "equations of exchange" are, with the exceptions of the figures for money and deposits, widely at variance from the real facts in the case, and second, that if they were correct, they could in no sense be said to constitute proof of the quantity theory. In the critical analysis which follows, chief attention will be devoted to Fisher's statistics. His is the later study, and it follows, in main outlines, the methods laid down by Kemmerer. He has employed Kemmerer's statistics in considerable part, amplifying them for later years, using some data not available when Kemmerer wrote, and undertaking a fuller solution of certain problems than Kemmerer did. I shall, however, from time to time make reference to Kemmerer's figures, and show points of difference between the two studies.