XVII.—On the Reduction of Observations of Underground Temperature; with Application to Professor Forbes' Edinburgh Observations, and the continued Calton Hill Series

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Abstract
1. Every purely periodical function is, as is well known, expressible by means of a series of constant coefficients multiplying sines and cosines of the independent variable with a constant factor and its multiples. This important truth was arrived at by an admirable piece of mathematical analysis, called for by Daniel Bernouilli, partially given by La Grange, and perfected by Fourier.