IN THE JANUARY, 1937, number of ECONOMETRICA I had an article entitled in Theory and Income Taxation in Practice. One of its contentions was that to tax and later to tax income from those savings, involves a subtle form of double taxation. I had made this same contention in 1906 in The Nature of Capital and Income. Long afterward, through Professor E. R. A. Seligman, I learned that John Stuart Mill had also called attention to this double taxation. Apparently he was first to do so. Strange to say, such double taxation, though ably affirmed by many other writers, notably Marshall and Pigou in England and Einaudi in Italy, has not, to this day, been universally accepted. In a forthcoming book on Tax Spendings not Savings, I am including a general review of whole question-if question it be. In course of renewed study involved, I have gradually become conscious of a companion principle. Apparently it has hitherto been overlooked. This principle is that to tax works extensive destruction upon and spendings. Because of this destructiveness, several paradoxes emerge which have both theoretical and practical interest. In an article on this subject published in Taxes, the Tax Magazine, in August, 1941, I have excluded, as unsuitable for such a journal, underlying mathematics, merely asserting that contentions made can be mathematically demonstrated. The present article gives demonstrations referred to. At close of year zero, say 1900, let Co be value of a certain capital-for instance an automobile plant. Let j be rate at which this initial value Co would increase during first year (1901) without taxes; and, for simplicity, let us suppose that said rate continues uniformly for n years, at end of which period-say at end of 1940-the owner of capital dies. Then Coj would be capital-increase in dollars in first year (1901) (called savings in title to this article); and capitalvalue C1 at end of that year would be C1 = Co(l +j). At end of second year, capital value would be C2= Co (1 +j) 2; of rth year (1) C,r = Co(1 + )r,