IN the assessment and collection of income tax there is one principle to which Chancellors of the Exchequer adhere and that relates to the progression of the tax. This principle is that the persons with the higher income in relation to their responsibilities must pay not only a higher tax but also a higher average rate of tax. Expressed mathematically we should say that the amount of tax (t) is an increasing function of income (x) of a form such that the marginal rate is always greater than the average rate of tax. Thus :t =f(x) dt is positive.