The capitalization theory, however, is of no use for the purpose in hand. Money does not obey the general law in the relation which the magnitude of the income bears to the rate of interest. In general, the income and the rate of discount are independent variables. Their influence, operating in opposite directions, fixes the capital value, increasing income increasing the capital value, increasing discount rate reducing it. In the case of money, however, the two factors are not independent. The short time money rate is not, to be sure, identical with the long time rate of interest, which is the rate of discount for the purpose in hand. But the two tend to vary together in the long run average in fact, and they are related in the _expectation_ of those who are concerned in the capitalization process. In our chapter on the "Functions of Money," in Part III, it will be shown that normally there tends to be a difference between the money rates and the long time interest rates, the long time rates tending to be higher than the rates on short loans, the rate on very short loans being lower than the rate on somewhat longer short time loans, and the call loan rate being lowest of all. The explanation of this must be deferred till we have analyzed the functions of money. But the important thing, for present purposes, is that the money rates, though lower than the "pure rate" of interest, tend to vary, in long time averages, with that "pure rate,"[59] and that, consequently, the income from renting money, and the discount rate to be applied in capitalizing that income, are not independent magnitudes, but tend to vary together. They thus tend to neutralize one another. If money rates go up, and if they are expected to stay up long enough to justify (on the ordinary capitalization theory) a rise in the capital value of money, we have a counteracting influence in the long time interest rate, which also rises, and tends to pull down the capital value of money. To recur to our illustration of the candle and the disk, as the disk increases in diameter, the distance between the candle and the disk grows greater, and so the _shadow_ tends to remain the same.