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Note on the Calculation of Logarithms to a large number of places by means of Factor Tables

Published online by Cambridge University Press:  18 August 2016

J. W. L. Glaisher
J. W. L. Glaisher*
Affiliation:
Trinity College, Cambridge
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Extract

There are several cases in which the factors of a number may be of use in ordinary mathematical processes; as for example, in the calculation of logarithms. This, although not the raison d’être of such a table, is so important an application as to deserve special notice, for by its means the number of numbers whose logarithms are known is greatly extended. For example, Abraham Sharp’s table contains 61-decimal Briggian logarithms of primes to 1,100, so that the logarithms of all numbers whose greatest prime factor does not exceed this number, may be obtained by simple addition. Similarly, Wolfram’s table gives 48-decimal hyperbolic logarithms of primes up to 10,009. Thus a factor table forms a very valuable complement to many-place logarithmic tables, the range of which must necessarily be comparatively limited ; and even in the case of large prime numbers, or numbers exceeding the limits of the factor table, it affords a very convenient method of calculating logarithms.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 22 , Issue 5 , October 1880 , pp. 346 - 352
Copyright
Copyright © Institute and Faculty of Actuaries 1881

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References

page 347 note * Wolfram's table gives hyperbolic logarithms of all numbers up to 2,200, and of primes (as well as of a great many composite numbers) up to 10,009, to 48–decimal places. It first appeared in Schulze's Sammlung (1778), and was reprinted in Vega's Thesaurus (1794).

page 348 note * See Mr. C. W. Merrifield's letter, vi. 298, On Formulæ for using Tables of Logarithms.—ED. J.I.A.

page 351 note * I formed this table upwards of twenty years ago, for a special purpose, which is explained on p. [39] of the work named in the foregoing editorial note. It answered its end most efficiently.