The Hollow World of Edmond Halley

Abstract

Three hundred years ago in 1692, an article by Edmond Halley proposed that the Earth was hollow.' Its theory was based on the value of lunar relative density given by Isaac Newton. The first edition of Newton's Principia (1687) found that " ... the mass of the Moon will be to the mass of the Earth as 1 to 26, approximately", citing the relative densities of Moon to Earth as 9 to 5. 2 This value of lunar relative mass was in excess by a factor of three, as the true mass ratio is 1:81. Arguably the most significant error in the Principia's Book III, it left an ultra-dense Moon circling our Earth." Edmond Halley simply invoked these figures: "Sir Isaac Newton has demonstrated the Moon to be more solid than our Earth, as 9 to 5; why may we not then suppose four ninths of our globe to be cavity?"4 It is remarkable that so erroneous a figure, having such unlikely implications, could be thus presented without need for further justification.Halley's theory appeared as the first significant deduction to be drawn from the Principia.Newton's estimate oflunar relative density was derived from the relative tideraising powers of the Sun and Moon. The Principia had ascertained fairly well the relative density of the Sun, as a quarter that of the Earth (Book III, Prop. 37, Cor. 3), and so by comparing the components of tidal attraction of the two luminaries the lunar relative density was thereby inferred. This was a quite valid method, as shown by the way that French theoretical astronomers used it in the mid-eighteenth century to obtain their estimates of lunar relative mass.' However, the Principia's treatment thereof went greatly astray. It started from the difference between spring and neap tides which occurred twice each month, taking data from Plymouth and in the Bristol channel that gave that ratio as 41 to 23, or 9 to 5.Newton apprehended (in Proposition 37) that the tide-raising forces of the Sun and Moon varied inversely as the cube of their distances from Earth:' only thus would the Moon have a stronger attraction for the tides than the Sun." It was evident to Newton that the solar gravity pull (varying inversely as the square of the distance) was several hundred times stronger than that of the Moon, whatever assumptions about relative densities were made. The Principia's tidal argument hinged upon this inverse-cube relationship, with little by way of demonstration. Its method of inferring lunar relative density from such considerations would have baffled his contemporaries. Astronomy textbooks by Newtonians such as Whiston and Gregory in the early eighteenth century omitted this argument, for they had no means of following it.The Principia formulated the equation (S+L)/(S-L) = 9/5, where Sand L

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