In discussion of the magnitudes of animal or fish populations the Verhulst logistic equation has usually been taken as a point of departure. In this expression, density-dependent causes of mortality could affect the abundance of either the existing adult stock and the young which it produces. But, on the contrary, W. E. R_ICKER treats subjects of populations and equilibrium level of exploitation from reproduction curve under the assumption that no compensatory mortality occurs among mature stock. Both in earlier treatments and in R_ICKER's, dynamic population parameters are implicit, though static characteristies are considered.<br> In this paper, the writer attempts to summarize the basic theoretical information expressed in the differential equation of population dynamics, recognizing in his formulation the formal distinction between stock and recruitment. It is concerned with predicting what change of stock or catch can be obtained from a given aspect of young fish recruited to a fishery. That is, changes cf abundance of stock, s, are related with recruitment, r, by the fundamental equations (1) and (2). Population parameters α, α_n and α are instantaneous mortality rates-total, natural and fishing respectively: c is total catch. Recruitment will not mean, the initial number of eggs or newborn young, but the number of young surviving to the specific age or the commercial size.<br> Refering analogously to other dynamic systems, recruitment is the intensive quantity like excitation potential, signal or input voltage and stock is the extensive quantity like response or output by the adequate transformation of corresponding variables. In an electrical system (Figs. 1 and 2, eqns. (3) and (4)), electric current, i, or output voltage e₀, corresponds to stock. Exciting or input voltage, e or e_i, corresponds to recruitment. Elements of circuit (inductance L, resistance R and capacity C) determine system parameter α or time constant T (reciprocal of α). In a mechanical system (Fig. 3 and eqn. 5), external force F, and displacement x, correspond to recruitment and stock respectively, α or T is determined by elasticity of recovering spring and damping resistance of dash pot. In a hydraulic surface system (Fig. 4 and eqn. (6)), head of hydraulic surface x and inflow v, stand for stock and recruitment respectively. Surface area and dimensions of outflow tube determine system parameters.<br> With application of these transformative relationships, an analogue computer could be built up in order to elucidate the mathematical problems of populations and to obtain graphically the variation of catch.<br> If r is impulsive, indicial and sinusoidally periodic, s is expressed in egns (7), (11) and (13), Fig. 5 and 6. Provided r is generally periodic and of random form, s is expressed in egns, (19), (10) and (23) by the principle of superposition.<br> In the present investigation attention has been directed toward a dynamic study of the explicit reiation between the magnitude of population and recruitment in the case of a single fish population. But fishing changes the absolute abundance of mature fish in a stocx, and may affect the numbers of recruits in subsequent years. Furthermore, it is important to consider the case of two or more coexisting populations. The writer will attempt to discuss these problems in later papers, regarding them as the feedback problems of networks of circuit systems.<br> The example given here deals with the fishery for anchovy larvae and young at Maisaka in.