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We extend a method devised by Lord Rayleigh to enable the calculation of the transport properties of circular cylinders in square and hexagonal arrays. The theory is confirmed by measurements on arrays of perfectly conducting cylinders, and also is compared with asymptotic formulae due to Keller (1963) and O’Brien (1977). It is used to furnish plots of equipotential lines within the array. It is also applied to the calculation of the optical properties of films with columnar structure. Detailed studies for copper films show both the good solar selectivity possible with voided structures and the transition from a good reflector to a metal black consequent upon structural changes.