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The analysis of the insulated antenna in a relatively dense medium is modified to apply to a thin cylindrical dipole antenna in a glass tube filled with a homogeneous cold plasma. Account is taken of the finite radius of the plasma column and of the thickness of the containing tube. Complex wavenumbers, distributions of current and charge, and driving-point admittances have been calculated for dipoles with electrical lengths up to two wavelengths. The effect of the thickness and permittivity of the glass tube on the wave number and admittance is determined. Numerous graphs and tables are provided.