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**SIMPSON’S LAW OF AVERAGES, 1755**

SIMPSON, T(homas). **A Letter to the Right Honourable George, Earl of Macclesfield, President of the Royal Society, as to the Advantage of Taking the Mean of a Number of Observations in Practical Astronomy. FROM (generaly title page present): Philosophical Transactions, Volume 49, pp. 82-93. **London: L. Davis and C. Reymers, Printers to the Royal Society, 1756. Octavo, modern marbled boards. $1850.

*First edition of Simpson’s mathematical proof that the average of a number of observations is nearer to the truth than any single observation, the first demonstration of this fundamental scientific concept.*

Simpson was the first to characterize the errors in observations as independent events, taking positive and negative values with equal probability, and the first to provide an exact expression for the probability that the error in the mean result will lie between assigned limits (Todhunter, 309). This paper was later reprinted (revised) in Simpson’s *Miscellaneous Tracts* (1757) and is considered a milestone in statistical inference, a forerunner of Legendre-Gauss’ Least Squares, and “the earliest statistical advice from a mathematician to experimental scientist” (Stigler, 93). “A conceptual shift which would have radical consequences for scientific practice” (*Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences*, 1379).

Tiny hole in title page, just affecting imprint. Text clean. A near-fine copy.