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1. The method of computing by series is so extensive and useful a part of the mathematics, that any device which facilitates the operation by them will undoubtedly be acceptable to those who are proper judges of these matters. In this persuasion I have employed an hour of that little leisure which my present situation affords me, in improving a calculation of Napier's, for finding the hyperbolic logarithm of 10, which was given by the justly celebrated William Jones, Esq. F. R. S. in p. 180 of hisSynopsis Palmariorum Matheseos .

philosophical transactions of the royal society of london

VII. Mr. Jones's computation of the hyperbolic logarithm of 10 improved: being a transformation of the series which he used in that computation to others which converge by the powers of 8o. To which is added a postscript, containing an improvement of Mr. Emerson's computation of the same logarithm