Zeros of first derivatives of Bessel functions of the first kind, j'n(x), 21

are frequently required for the solution of problems in mathematical physics and engineering. Typical problems of this kind occur in the theory of heat conduction [1],1 hydrodynamics, finite Hankel transforms, Fourier-Bessel expansions, etc. In conjunction with a heat transfer problem [2], the authors conducted a literature search in the spring of 1961 to find a table of zeros of J~(x). No adequate tables were found at that time, and a table of such zeros for 0 ~ n ~ 51, 0 ~ x ~ 100 was generated. It was subsequently learned that the new Royal Society Tables [3], published in 1960 and available in 1961, contained zeros of J;,(x ) for orders 0 ~ n ~ 20. For this reason the present table is given for orders 21 ~ n ~ 51 and 0 ~ x ~ 100. A thorough summary of existing tables is given on page 411 of volume I [4].