Let us begin with the money side. If the number of dollars in a country is 5,000,000, and their velocity of circulation is twenty times per year, then the total amount of money changing hands (for goods) per year is 5,000,000 times twenty, or $100,000,000. This is the _money_ side of the equation of exchange. Since the money side of the equation is $100,000,000, the goods side must be the same. For if $100,000,000 has been spent for goods in the course of the year, then $100,000,000 worth of goods must have been sold in that year. In order to avoid the necessity of writing out the quantities and prices of the innumerable varieties of goods which are actually exchanged, let us assume for the present that there are only three kinds of goods,--bread, coal, and cloth; and that the sales are: 200,000,000 loaves of bread at $ .10 a loaf, 10,000,000 tons of coal at 5.00 a ton, and 30,000,000 yards of cloth at 1.00 a yard. The value of these transactions is evidently $100,000,000, _i. e._, $20,000,000 worth of bread plus $50,000,000 worth of coal plus $30,000,000 worth of cloth. The equation of exchange therefore (remember that the money side consisted of $5,000,000 exchanged 20 times) is as follows: $5,000,000 x 20 times a year = 200,000,000 loaves x $ .10 a loaf + 10,000,000 tons x 5.00 a ton + 30,000,000 yards x 1.00 a yard This equation contains on the money side two magnitudes, viz. (1) the quantity of money and (2) its velocity of circulation; and on the goods side two _groups_ of magnitudes in two columns, viz. (1) the quantities of goods exchanged (loaves, tons, yards), and (2) the prices of these goods. The equation shows that these four sets of magnitudes are mutually related. Because this equation must be fulfilled, the prices must bear a relation to the three other sets of magnitudes--quantity of money, rapidity of circulation, and quantities of goods exchanged. Consequently, these prices must, as a whole, vary proportionally with the quantity of money and with its velocity of circulation, and inversely with the quantities of goods exchanged.