Page talk:Newton's Principia (1846).djvu/475

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