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be called a strictly independent method, since it isbased on the theory of gravity, which could not havebeen established without an accurate determination ofthe moon’s distance.
In showing that the earth’s attraction keeps themoon in her observed orbit, Newton had to take intoaccount the moon’s distance. He reasoned that theearth’s attraction reduced as the square of the dis-tance would be competent at the moon’s distance tocause the observed deflection of the moon from thetangent to her path. He assumed the lunar parallaxto be 57' 30", corresponding to a distance of 237,000miles ; and he found that the terrestrial attractioncalculated for that distance corresponded very closelywith the observed lunar motions, so closely as toleave no doubt of the truth of the theory he wasdealing with. But now, when once the theory ofgravity is admitted, we have in the observed lunarmotions the means of forming an exact estimate ofthe earth’s attraction at the moon’s distance, and aswe know her attraction at the earth’s surface, we areenabled to infer the moon’s distance. And in passingit may be observed that this process is not, as itmight seem at a first view, mere arguing in a circle.Observation had already given a sufficiently accurateestimate of the moon’s distance to supply an initialtest of the theory that it is the earth’s attractionreduced as the square of the distance which retainsthe moon in her orbit. This theory being accepted,and other tests applied, we may fairly reason back