When a layer of fluid is heated uniformly from below, a convection occurs in a regular cellular pattern for the values of the Rayleigh number in excess of a critical value. A perturbation method is presented here to determine the form and amplitude of this steady convection. The essential point is to expand functions describing the field (velocity and temperature) in a power series of a parameter ε, while the Rayleigh number is put as a product of its critical value times (1+ε2). A set of inhomogeneous equations thus obtained can be solved by the perturbation method used in non-linear oscillation problems. In the two-dimensional case the slope of heat transport curve steepens abruptly at the critical Rayleigr number. As another example which can be dealt with in this way, a convection in a sphere is studied. This is an extention of Chandrasekhar's linearized stability theory.
