This paper deals with the theory of the action of the flume-type anti-rolling tank. Let q be the quantity of water which passes through the unit width of the section of the flume per unit time, when the tank is fitted on a ship with apparent rolling θ_a. Then, q can be obtained by solving the equation of motion (7), with the end conditions (8) and (9). The elevation of the water surface in the flume h and the change of the level of the side tanks H can be deduced from q as (19) and (20). The anti-rolling moment given rise to by the tank will be calculated as (26) and the resultant rolling amplitude θ_o of the ship is given by (28). Resonance curves of one example of numerical Calculation is shown in Fig. 7, where the abscissa and ordinate gives the tuning factor and rolling amplitude/max. wave slope respectively. From this figure, it is seen that the action of the flume type is similar to that of Frahm type. In this trieatment, it is considered that the center tank behaves as the origin of the resistance to q, and as far as the present theory concerns, the resistance seems to be most important in this type.
