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Critical phenomena in the two-dimensional Ising model with a defect line arestudied using boundary conformal field theory on the $c=1$ orbifold. Novelfeatures of the boundary states arising from the orbifold structure, includingcontinuously varying boundary critical exponents, are elucidated. New featuresof the Ising defect problem are obtained including a novel universality classof defect lines and the universal boundary to bulk crossover of the spincorrelation function.Comment: 9 pages, 2 figures in EPS and LaTeX attached (References added +  Minor corrections

Defect Lines in the Ising Model and Boundary States on Orbifolds