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Note on Finding the Logarithmic Sines and Tangents of Small Arcs
Published online by Cambridge University Press: 15 September 2014
Extract
In geodetical and astronomical computations it frequently happens that we have to use the logarithmic sines or tangents of small arcs, or to find the small angles corresponding to their artificial sines or tangents; and in all trigonometrical tables directions are given to guide the learner in these operations. It might seem, then, superfluous to refer to such a matter. A variety of methods in the solution of a simple problem has, however, sometimes advantages, and the method I have been in the habit of using, though obvious enough, is not usually given.
In Vega's great Thesaurus Logarithmorum Completus (1794), based on A. Vlack's Tables, the rules for the functions of small arcs make use of second differences; and the 7th and later editions of Hutton's Tables (1830, 10th ed., 1846) follow the same method.
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- Copyright © Royal Society of Edinburgh 1899
References
page 265 note * The rule given in Shortrede's Logarithmic Tables (1858) applies only when the fraction of a second is ½.
page 269 note † Approximately the correction may be represented by 
+,016015a 2+,00008447a 3+,0000797a 4−,0000011566a 5+,000000010737a 6).
The comma is used to indicate the separation of the 7th and 8th places of decimals.
page 269 note † 9°57ʹ is nearly 10°; and —,123 × 10 × 23″ = − 28,3 = corr.
