Abstract
This paper extends the work of Part I (Proc. Roy. Soc. Ser. A,1978) in which the onset of finite amplitude Bénard convection in a shallow cylindrical container of large radius L with an imperfectly insulated sidewall was investigated. In the present study the effect of finite $\log L$ is examined, in which case the solutions of the amplitude equation have a weak singularity at the origin. It is demonstrated that as $( {\log L} )^{ - 1} \to 0$ the critical Rayleigh number is less, by an amount $O( L^{ -2 } )$, than its value when $( {\log L} )^{ - 1} = 0$ and is in agreement with the value obtained for the two-dimensional annulus.
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