The correct answer is A) the dimensions of the liquid surface and the vessel's displacement. The effect of free surface on initial stability depends on the dimensions of the liquid surface and the vessel's displacement. As the liquid moves, it creates a free surface that can shift the vessel's center of gravity and reduce the vessel's initial stability. The larger the free surface area and the higher the vessel's displacement, the greater the effect on initial stability. The other options are incorrect because B) the vertical position of the liquid is not the only factor, C) the amount of liquid is not the sole determinant, and D) the length of the compartment alone does not determine the free surface effect.