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1 Daniel Shanks, "A Logarithm Algorithm," MTAC, v. 8, 1954, p. 60-64. 2 See, e.g., J. Tropfke, Geschichte der Elementar-Mathematik. Bd. 11:3. Aufl., 1933, p. 241-242. 3 In applying (I) we can of course replace the division by p by the multiplication with M = l/p = log<i0 e, i.e., with the module of the logarithms to the base a0. In this way we replace two divisions indicated in (I) by one division and one multiplication. 4 A. Khintchine, Metrische Kettenbruchprobleme. Comp. Math., v. 1, 1935, p. 360-382, especially p. 376, 377. 5 Dr. D. Shanks to whom this note was submitted in manuscript made the very interesting remark that the use of p = lna0 can be eliminated from my formula (I) in replacing p by

Iterative procedures for taking roots based on square roots