circulate one after the other, and after realising their prices successively, and therefore the sum of those prices, £8, they come to rest at last in the pocket of the distiller. The £2 thus make four moves. This repeated change of place of the same pieces of money corresponds to the double change in form of the commodities, to their motion in opposite directions through two stages of circulation. and to the interlacing of the metamorphoses of different commodities.²⁹ These antithetic and complementary phases, of which the process of metamorphosis consists, are gone through, not simultaneously, but successively. Time is therefore required for the completion of the series. Hence the velocity of the currency of money is measured by the number of moves made by a given piece of money in a given time. Suppose the circulation of the 4 articles takes a day. The sum of the prices to be realised in the day is £8, the number of moves of the two pieces of money is four, and the quantity of money circulating is £2. Hence, for a given interval of time during the process of circulation, we have the following relation: the quantity of money functioning as the circulating medium is equal to the sum of the prices of the commodities divided by the number of moves made by coins of the same denomination. This law holds generally.

The total circulation of commodities in a given country during a given period is made up on the one hand of numerous isolated and simultaneous partial metamorphoses, sales which are at the same time purchases, in which each coin changes its place only once, or makes only one move; on the other hand, of numerous distinct series of metamorphoses partly running side by side, and partly coalescing with each other, in each of which series each coin makes a number of moves, the number being greater or less according to circumstances. The total number of moves made by all the circulating coins of one denomination being given, we can arrive at the average number of moves made by a single coin of that denomination, or at the average velocity of the currency of money. The quantity of money thrown into the circulation at the beginning of each day is of course determined by the sum of the prices of all the commodities circulating simultaneously side by side. But once in circulation, coins are, so to say, made responsible for one another. If the one increase its velocity, the other either retards its own, or altogether falls out of circulation; for the circulation can absorb only such a quantity of gold as when multiplied by the mean number of moves made by one single coin or element, is equal to the sum of the prices to be realised. Hence if the number of moves made by the separate pieces increase, the total number of those pieces in circulation diminishes. If the number of the moves diminish, the total number of pieces increases. Since the quantity of money capable of being absorbed by the circulation is given for a given mean velocity of currency, all that is necessary in order to abstract a given number of sovereigns from the circulation is to throw the same number of one-pound notes into it, a trick well known to all bankers.

Just as the currency of money, generally considered, is but a reflex of the circulation of commodities, or of the antithetical metamorphoses they undergo, so, too, the velocity of that currency reflects the rapidity with which commodities change their forms, the continued interlacing of one series of metamorphoses with another, the hurried social interchange of matter, the rapid disappearance of commodities from the sphere of circulation, and the equally rapid substitution of fresh ones in their places. Hence, in the velocity of the currency we have the fluent unity of the antithetical and complementary phases, the unity of the conversion of the useful aspect of commodities into their value-aspect, and their re-conversion from the latter aspect to the former, or the unity of the two processes of sale and purchase. On the other hand, the retardation of the currency reflects the separation of these two processes into isolated antithetical phases, reflects the stagnation in the change of form, and therefore, in the social interchange of matter. The circulation itself, of course, gives no clue to the origin of this stagnation; it merely puts in evidence the phenomenon itself. The general public, who, simultaneously with the retardation of the currency, see money appear and disappear less frequently at the periphery of circulation, naturally attribute this retardation to a quantitative deficiency in the circulating medium.³⁰

The total quantity of money functioning during a given period as the circulating medium, is determined, on the one hand, by the sum of the prices of the circulating commodities, and on the other hand, by the rapidity with which the antithetical phases of the metamorphoses follow one another. On this rapidity depends what proportion of the sum of the prices can, on the average, be realised by each single coin. But the sum of the prices of the circulating commodities depends on the quantity, as well as on the prices,