1939] N ESSAY IN DYNAMIC THEORY 17 The value of C is inversely proportional to the period chosen C per annum =4 in this case. 1 The value of C depends on the state of technology and the nature of the goods constituting the increment of output. It may be expected to vary as income grows and in different phases of the trade cycle; it may be some- what dependent on the rate of interest Now, it is probably the case that in any period not the whole of the new capital is destined to look after the increment of output of consumergoods. There may be long-range plans of capital development or a transformation of the method of producing the pre-existent level of output. These facts will be allowed for in due course. For the moment let it be assumed that all new capital goods are required for the sake of the increment of output of consumers' goods accruing Hin. serving proof for the next paragraph, we may now write the undamental Equation in its simplest form 2 It should be noticed that the warranted rate of growth of the system appears here as an unknown term, the value of which is determined by certain " fundamental conditions"-namely, the propensity to save and the state of technology, ete. Those who define dynamic as having a cross-reference to two points of time may not regard this equation as dynamic; that particular defini tion of dynamic has its own interest and field of reference I prefer to define dynamic as referring to propositions in which rate of growth appears as an unknown variable. This equation is clearly more fundamental than those expressing lags of 5. The proof is as follows. Let Cp stand for the value of the increment of capital stock in the period divided by the increment of total output. Cp is the value of the increment of capital per a month is the unit, the number of shoes added per period is 1, if a year 144. The value of G per annum is 12 times as great as that of G per month, since the numerator of G per annum is 144 times as great and the denominator 12 times as great as the numerator and denominator respectively of G per month The number of machines added per month is l E 48 shoes E 48 units ofineremen of output. C per month 48. The number of machines added per year is 12 =48x 12 shoes. Thug the value in shoes of the annual increment of eapital required to produce an annual increment of 144 shoes is 48 x 12 units. There fore C per annum =144 of C per month. a Since the value of G varies directly and that of C inversely with the unit period chosen, and the value of a is independent of the unit, the validity of the equation is independent of the unit period chosen. No. 193.-VOL. XLIX