With the help of results on the metabolism and the carcinogenic activities of polycyclic aromatic hydrocarbons (PAH), the comprehensive metabolic process in vivo is discussed. It is thought that the carcinogenic activity exhibited by a PAH is determined by the competition between the carcinogenesis and detoxification in which it participates. It is suggested that the essential agent of carcinogenesis should be, as a rule, the highest delocalization energy (beta unit) of the carbonium ion at the aromatic angular ring (A region), which is obtained by the pertubational molecular orbit (PMO) method. Since there are no essential distinctions in the molecular geometry and delocalization energy states between two carbonium ions of the aromatic angular ring and of the bay region, the A region can be looked upon as the extended bay region. On the basis of discussion of the overall metabolism, evaluation of the detoxification efficacy of each kind of the competing carcinogenic factors, including the biological factor B and three structural factors of the PAH molecule: K, A and L, was made. After making necessary approximation, K = 0.228, A = 0.5, L = 1.22 and B = 0.7 are obtained. It can be seen from these values that the L region plays the most important role in detoxification processes, and the K region plays the least important role. The effect of biological factor B is approximately the sum of the K region and the A region. This paper suggests the concept of a carcinogenic constant. For the PAHs with the same number of aromatic rings (N), C is a constant. The curve of function C = f(N), including the extensional line, is an isosceles triangle. The author suggests that it should be called the 'Pyramid Rule'. The final form of the quantitative equation is log R = C[delta E3deloc/(0.7 + 0.228nk + 0.5na + 1.22n1)]. The values for 50 PAHs which had been tested by animal experiments were calculated. Of these, 92% of the PAHs are in agreement with experiments on carcinogenic activities.