The attraction of the pyramids: virtual realization of Hutton's suggestion to improve Maskelyne's 1774 Earth&amp;#160;density estimate

John R Smallwood

doi:10.5194/hgss-9-1-2018

Abstract

Abstract. Charles Hutton suggested in 1821 that the pyramids of Egypt be used to site an experiment to measure the deflection of the vertical by a large mass. The suggestion arose as he had estimated the attraction of a Scottish mountain as part of Nevil Maskelyne's (1774) “Schiehallion Experiment”, a demonstration of Isaac Newton's law of gravitational attraction and the earliest reasonable quantitative estimate of Earth's mean density. I present a virtual realization of an experiment at the Giza pyramids to investigate how Hutton's concept might have emerged had it been undertaken as he suggested. The attraction of the Great Pyramid would have led to inward north–south deflections of the vertical totalling 1.8 arcsec (0.0005∘), and east–west deflections totalling 2.0 arcsec (0.0006∘), which although small, would have been within the contemporaneous detectable range, and potentially given, as Hutton wished, a more accurate Earth density measurement than he reported from the Schiehallion experiment.

Highlights

Following his analysis as part of Astronomer Royal Nevil Maskelyne’s experiment to measure Earth’s mean density on the Scottish mountain Schiehallion in 1774, Charles Hutton suggested that another plumb-line experiment at a geometrically simpler large mass would be preferable to address some of the challenges he had encountered (Maskelyne, 1775a; Hutton, 1821)
The first attempt to carry out the plumb-line deflection experiment was that of Pierre Bouguer, who, encouraged by the scale of the Andean mountains, undertook such an experiment in 1738 as one of his contributions to the Paris Academy’s meridian arc expedition (Bouguer, 1749)
This study shows that Hutton, possibly the most prominent British mathematician of his generation (Wardhaugh, 2017), had suggested a viable method by which the plumb-linederived Earth density estimate could have been improved

Summary

Introduction

Following his analysis as part of Astronomer Royal Nevil Maskelyne’s experiment to measure Earth’s mean density on the Scottish mountain Schiehallion in 1774, Charles Hutton suggested that another plumb-line experiment at a geometrically simpler large mass would be preferable to address some of the challenges he had encountered (Maskelyne, 1775a; Hutton, 1821). His suggestion was that a similar experiment be conducted at the pyramids in Giza, Egypt (Fig. 1). The deflection is very small, as outweighing the advantage of its proximity, the mass is small relative to the mass of the Earth

Background

Discussion

Conclusions