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On Interpolation, Summation and the Adjustment of Numerical Tables

Published online by Cambridge University Press:  18 August 2016

Extract

Interpolation, generally considered, is the process of determining numerical values intermediate to a series of other values that are already known, and it is of extraordinary utility in many calculations, and especially in the formation of extensive tables. If, in the direct calculation of a table, the values to be tabulated depend upon a complicated function, difficult of calculation, considerable labour and corresponding risk of error may usually be avoided by computing the values for a certain succession of equidistant intervals, and afterwards determining by interpolation all other values that may be requisite to complete the table and adapt it to the practical purposes for which it is constructed. In such case the method is made use of as a powerful auxiliary at the option of the computer.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1864

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References

page 71 note * Mr. William Godward, Jun., of the Nautical Almanac Office, some years ago constructed some improved Astronomical Interpolation Tables, printed in 1857, in which he ingeniously introduced an expedient of a similar kind to that which is here adopted, and thereby essentially simplified the extensive work of interpolation carried on in that Office. The method of proceeding by continuous summation was originally suggested, many years ago, by Mr. Richard Farley, another gentleman in the same Office, who possesses a remarkable and instinctive talent for computation.

page 72 note * It may not be considered necessary to repeat the leading figures in these columns.

page 86 note * In the formula (p), page 67, which tare reference to the original epoch V0, n may be either even or odd.

page 87 note * See Note, page 86.