Finally, if there is a simultaneous change in two or all of the three influences, _i. e._, quantity of money, velocity of circulation, and quantities of goods exchanged, the price level will be a compound or resultant of these various influences. If, for example, the quantity of money is doubled, and its velocity of circulation is halved, while the quantity of goods exchanged remains constant, the price level will be undisturbed. Likewise, it will be undisturbed if the quantity of money is doubled and the quantity of goods is doubled, while the velocity of circulation remains the same. To double the quantity of money, therefore, is not always to double prices. We must distinctly recognize that the quantity of money is only one of three factors, all equally important in determining the price level.... We now come to the strict algebraic statement of the equation of exchange.... Let us denote the total circulation of money, _i. e._, the amount of money expended for goods in a given community during a given year, by _E_ (expenditure); and the average amount of money in circulation in the community during the year by _M_ (money). _M_ will be the simple arithmetical average of the amounts of money existing at successive instants separated from each other by equal intervals of time indefinitely small. If we divide the year's expenditures, _E_, by the average amount of money, _M_, we shall obtain what is called the average rate of turnover of money in its exchange for goods, _E_/_M_ that is, the velocity of circulation of money. This velocity may be denoted by _V_, so that _E_/_M_ = _V_; then _E_ may be expressed as _MV_. In words: the total circulation of money in the sense of money expended is equal to the total money in circulation multiplied by its velocity of circulation or turnover. _E_ or _MV_, therefore, expresses the money side of the equation of exchange. Turning to the goods side of the equation, we have to deal with the prices of goods exchanged and quantities of goods exchanged. The average price of sale of any particular good, such as bread, purchased in the given community during the given year, may be represented by _p_ (price); and the total quantity of it purchased, by _Q_ (quantity); likewise the average price of another good (say coal) may be represented by _p'_ and the total quantity of it exchanged, by _Q'_; the average price and the total quantity of a third good (say cloth) may be represented by _p''_ and _Q''_ respectively; and so on, for all other goods exchanged, however numerous. The equation of exchange may evidently be expressed as follows: _MV_ = _pQ_ + _p'Q'_ + _p''Q''_ + etc.