What, then, is T? Perhaps another question will aid us in answering this. What does it mean to _multiply_ ten pounds of sugar by seven cents? What sort of product results? Is the answer seventy pounds of sugar, or seventy cents, or some new two-dimensional hybrid? One multiplies feet by feet to get _square_ feet, and square feet by feet to get cubic feet. But in general, the multiplication of _concrete_ quantities by _concrete_ quantities is meaningless.[142] One of the generalizations of elementary arithmetic is that concrete quantities may usually be multiplied, not by other concrete quantities, but rather by _abstract_ quantities, pure numbers. Then the product has meaning: it is a concrete quantity of the same denomination as the multiplicand. If the Q's, then, are to be multiplied by their respective p's, the Q's must be interpreted, not as bushels or pounds or yards of concrete goods, but merely as abstract numbers. And T must be, not a sum of concrete goods, but a sum of abstract numbers, and so itself an abstract number. Thus interpreted, T is equally increased by adding a hundred papers of pins,[143] a hundred diamonds, a hundred tons of copper, or a hundred newspapers. This is not Professor Fisher's rendering of T, but it is the only rendering which makes an intelligible equation. We return, then, to the question with which we set out: in what sense is there an equality between the two sides of Professor Fisher's equation? The answer is as follows: on one side of the equation we have M, a quantity of money, multiplied by V, an abstract number; on the other side of the equation, we have P, a quantity of money, multiplied by T, an abstract number. The product, on each side, is a _sum of money_. These sums are equal. They are equal because they are _identical_. The equation asserts merely that what is _paid_ is equal to what is _received_. This proposition may require algebraic formulation, but to the present writer it does not seem to require any formulation at all. The contrast between the "money side" and the "goods side" of the equation is a false one. There is no goods side. Both sides of the equation are money sides. I repeat that this is not Professor Fisher's interpretation of his equation. But it seems the only interpretation which is defensible.