In the following chapter, as in most of the preceding chapters, constructive doctrine is aimed at, even though the discussion takes, in considerable part, the form of critical analysis of opposing views. We shall seek to set forth the facts, as far as may be, regarding the relations of banking transactions to trade, the relations of clearings to amounts deposited in banks, the relation of New York City clearings to country clearings, and of New York bank transactions to bank transactions in the rest of the country. We shall seek to ascertain the extent of variability in that highly elusive magnitude, "velocity of circulation," particularly "V'." We shall indicate something of the bearing of index numbers of prices on the theory of the value of money as here presented. In reaching conclusions on these and related matters, we shall build on the investigations of Dean Kinley, on the very interesting statistical studies of Kemmerer and Fisher based on Kinley's figures, on investigations more recently made by the American Bankers' Association regarding the relation of bank transactions and bank clearings, on figures from reports by the Comptroller of the Currency, as well as on other sources. One purpose of the chapter is to criticise the statistics which purport to prove the quantity theory. The bulk of the chapter is given to this. But the work of Fisher and Kemmerer thus criticised yields rich rewards for the study. The conclusions they have drawn from their figures are, in the judgment of the writer, untenable, but the figures themselves are of immense interest and importance. The controversy over the quantity theory has been waged with many weapons. Theory, history, and statistics--to say nothing of invective!--have been freely employed. In large measure, the statistical studies have been concerned with the direct comparison of quantity of money and prices, in their variations from year to year. One of the best of these studies, that of Professor Wesley C. Mitchell, in his _History of the Greenbacks_ (followed by his _Gold, Prices and Wages under the Greenback Standard_), has, to the minds of many students, including the present writer, put it beyond the pale of controversy that the fluctuations in the gold premium, and in the level of prices, in the United States during the Greenback period, both for long periods and for daily changes, were not occasioned by changes in the quantity of money,[373] but rather, primarily, by military and political events, and other things affecting the credit of the Federal Government, together with changes affecting the values of gold and of goods. Professor Mitchell's discussion is so detailed and thorough, that what controversy remains relates, not to his facts, but rather to the possibility of interpreting those facts in harmony with the quantity theory, by repudiating the notion that the direct comparison of gold premiums or of prices with quantity of money gives a valid test.[374]