Page talk:Newton's Principia (1846).djvu/475
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Newton made a numerical mistake in the Scholium (see ‘The Mathematical Papers of Isaac Newton’, by D. T. Whiteside, Cambridge University Press, 1967-1981, Vol 6, pp 505-507)
it should read:
'....ξn in proportion to μB as 3MI to 4Mμ....'
In fact, the exact expression is:
nξ = ξµ.Iq.(Iq+3Sµ.IM/Iµ)/4Sµ(3Sµ + Iµ) in terms of Iq, where Iq is a solution of
Iq4/16Sµ2 + Iq3.IM/(4Sµ.Iµ) + Iq2 = µB2 since nξ in the Scholium is a function of µB. Also
ξµ2 = (3Sµ + Iµ)2 – 3Sµ.IM2⁄ Iµ and Iµ = Mµ