IRVING FISHER[43]: Overlooking the influence of deposit currency, or checks, the price level may be said to depend on only three sets of causes: (1) the quantity of money in circulation; (2) its "efficiency" or velocity of circulation (or the average number of times a year money is exchanged for goods); and (3) the volume of trade (or amount of goods bought by money). The so-called "quantity theory,"[44] _i.e._, that prices vary proportionately to money, has often been incorrectly formulated, but (overlooking checks) the theory is correct in the sense that the level of prices varies directly with the quantity of money in circulation, provided the velocity of circulation of that money and the volume of trade which it is obliged to perform are not changed. The quantity theory has been one of the most bitterly contested theories in economics, largely because the recognition of its truth or falsity affected powerful interests in commerce and politics. It has been maintained--and the assertion is scarcely an exaggeration--that the theorems of Euclid would be bitterly controverted if financial or political interests were involved. The quantity theory has, unfortunately, been made the basis of arguments for unsound currency schemes. It has been invoked in behalf of irredeemable paper money and of national free coinage of silver at the ratio of 16 to 1. As a consequence, not a few "sound money men," believing that a theory used to support such vagaries must be wrong, and fearing the political effects of its propagation, have drifted into the position of opposing, not only the unsound propaganda, but also the sound principles by which its advocates sought to bolster it up.[45] These attacks upon the quantity theory have been rendered easy by the imperfect comprehension of it on the part of those who have thus invoked it in a bad cause. Personally, I believe that few mental attitudes are more pernicious, and in the end more disastrous, than those which would uphold sound practice by denying sound principles because some thinkers make unsound application of those principles. At any rate, in scientific study there is no choice but to find and state the unvarnished truth. The quantity theory will be made more clear by the equation of exchange, which is now to be explained.