The author makes ingenious use of the Sturm comparison theorem to provide upper and lower bounds for the zeros of the Jacobi polynomial , is case -. He shows that an asymptotic formula, involving zeros of Bessel functions, due to Frenzen and Wong, in fact provides a lower bound for these zeros (and also an upper bound, using He also shows that between any pair of zeros there occurs at least one root of a certain transcendental equation involving elementary functions. In the case of the kth zero, , , of the ultraspherical polynomial , this leads to the inequalities
where and . Comparisons are made with known bounds and numerical examples are given to illustrate the sharpness of the new inequalities.