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My dear Sir, The results of some of your late experiments on the pen­dulum having led me to reflect on the possible inequalities in the arrangement of gravitating matter within the earth’s sub­stance, as well as on the methods of appreciating the accuracy of a long series of observations in general, I have thought that it might be agreeable to you, to receive the conclusions which I have obtained from my investigations, in such a form as might serve either to accompany the report of your operations, or to be laid before the Royal Society as a distinct communication. 1.On the estimation of the advantage of multiplied ob­servations . It has been a favourite object of research and speculation, among the authors of the most modern refinements of ma­thematical analysis, to determine the laws, by which the pro­bability of occurrences, and the accuracy of experimental re­sults, maybe reduced to a numerical form. It is indeed true, that this calculation has sometimes vainly endeavoured to substitute arithmetic for common sense, and at other times has exhibited an inclination to employ the doctrine of chances as a sort of auxiliary in the pursuit of a political object, not otherwise so easily attainable ; but we must recollect, that at least as much good sense is required in applying our mathe­matics to objects of a moral nature, as would be sufficient to enable us to judge of all their relations without any mathe­matics at all : and that a wise government and a brave people may rely with much more confidence on the perma­nent sources of their prosperity, than the most expert calcu­lators have any right to repose in the most ingenious combi­nations of accidental causes.

philosophical transactions of the royal society of london

V. Remarks on the probabilities of error in physical observations, and on the density of the earth, considered, especially with regard to the reduction of experiments on the pendulum. In a letter to Capt. Henry Kater, F. R. S. By Thomas Young, M. D. For. Sec. R. S