We investigate the continuity of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem − Δ u ( x ) = λ g ( x ) u ( x ) , x ∈ B R ( 0 ) ; u ( x ) = 0 , | x | = R , where B R ( 0 ) is a ball in ℝ N , and g is a smooth function, and we show that λ 1 + ( R ) and λ 1 − ( R ) are continuous functions of R .