years, which changes have accounted for the resulting changes in P. The study is similar to that previously made by Professor Kemmerer, but is more detailed and has attained a higher degree of accuracy, due, chiefly, to statistics which have become available since the publication of Professor Kemmerer's valuable book on "Money and Prices." It thus comes about that all of the statistics for the five magnitudes are new. In particular the statistics for the velocity of the circulation of money are entirely new and worked out according to a method explained a year ago in the Journal of the Royal Statistical Society for December, 1909. It is interesting to observe that previously there have been no figures available for M'. The statistics for so-called "individual deposits" are not statistics of deposits subject to check, for they include savings bank deposits, certificates, and other time deposits not subject to check. It is found that the statistics of deposits subject to check are sometimes only two-thirds of the statistics for individual deposits. The statistics for deposits subject to check have been worked out from the monograph by Professor David Kinley on the "Use of Credit Instruments" and from statistics kindly supplied at my suggestion by Dr. A. Piatt Andrew of the National Monetary Commission for the years 1896, 1899, 1906, 1909. For intermediate years the results were obtained by methods of interpolation. As the methods of computing these five magnitudes are completely described in the reprint which has been distributed, it will not be necessary for me to go into details. When these five magnitudes have been computed it becomes possible to reckon what the value of P should be as determined by the equation of exchange, assuming that the theory is correct which ascribes the causation of price levels to these five causes working through the equation of exchange. In other words, it is possible to compute P by the formula The resulting value for P can thus be compared with the actual statistics for the price level as shown by the statistics of the Bureau of Labor, making due allowances for wages and the prices of securities. The comparison between these two results for P as directly observed and as calculated indirectly from the five magnitudes on which it depends may be said to supply a verification, for those who need it, of the quantity theory of money, and for those who do not, a verification of the statistics themselves. The results agree remarkably well as will be seen presently. There are, however, discrepancies and it is therefore necesary to correct the various magnitudes so as to make them harmonize with the equation of exchange. To secure the most probable results these corrections should be made in all six magnitudes. It is found that the correction, or doctoring, in most cases is usually very small-in the majority of cases not being over one per cent and in almost all instances being less than two per cent. The results are shown in the following diagrams. The 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 FIGURE 1. first shows in the continuous lines the values of M and M' as first calculated and in the dotted lines the corrected values. Evidently the dotted line nearly coincides with the continuous line. In the next figure, which shows the corresponding results for V and V', the continuous line gives these as originally calculated and the dotted lines show the slightly different results as finally corrected. The third figure shows T as originally and finally calculated; and the fourth figure shows P in three lines. The upper line gives P as directly computed from statistics; the dotted line shows this value as finally corrected; while the bottom line shows what this value would be if calculated indirectly from the other five magnitudes in the equation of exchange. The parallelism between all three lines is evident. The values of the upper and lower lines, or, in other words, the values directly and indirectly calculated, are very close. The application of Karl Pearson's coefficient of correlation shows a high degree of correspondence between these two curves, a correspondence considerably higher than that found for the somewhat similar curves of Professor Kemmerer. In order to set forth the statistical results which have been given in a manner which will relate together the six magnitudes in the equation of exchange, I have adopted a mechanical picture of the equation of exchange as shown in Figure 5. In this figure 100 FIGURE 5. M, the quantity of money in circulation, is represented by a purse; M', by a bank book, both hanging at certain distances from the fulcrum, the distances corresponding to their respective velocities of circulation. On the right in a tray are hung the things which are exchanged during the year, while the distance from the fulcrum at which this tray is hung represents the price level. This mechanical picture shows that an increase in M, that is in the weight of the purse, other things being equal, will require a readjustment of the point at the right at which the tray hangs. It will need to be pushed farther to the right. If there is an increase in M there will be an increase in P. In like manner P will increase from an increase in M', V, and V', or a decrease in T. In figure 6 are shown the changes during fourteen years in all of the six magnitudes-M, M′, V, V', P, and T. It is shown that the quantity of money in circulation in these years has doubled; the volume of deposits subject to check has about tripled; the velocities of circulation have increased only slightly; and the volume of trade has been doubled. We find that prices rose about two-thirds as a net result of the changes in these five factors, as is shown by the length of the arm at the right. There are interesting variations connected with the panic year 1907. It is interesting to make a quantitative comparison of the various magnitudes with the increase in the quantity of money as the most important factor in raising the price level. While it is true that the volume of deposits subject to check has increased greatly, the major part of the increase has to be ascribed to the increase in the quantity of money. Only so far as the volume of deposits subject to check has increased relatively to the money in circulation, can the increase of deposits be regarded as an independent cause of the rise in prices. We have thus to consider the relative importance of the five causes affecting prices: 1. The quantity of money in circulation (M). 2. The volume of bank deposits subject to check considered M' relatively to money (M) 3. The velocity of the former (V). 4. The velocity of the latter (V′). 5. The volume of trade (T). We may best compare the relative importance of these five magnitudes by answering the question: What would the result have been had any one of these magnitudes remained unchanged during these years, assuming that the other four changed in the same manner that they actually did change. We find (1) that if the money in circulation, M, had not changed, the price level of 1909 would have been 45 per cent lower than it actually M' was; (2) that if the relative deposits, had not changed, the M |