Early explanation of the lunar method to find longitudeDepartment of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

Who Used It?

The following 'Newtonian' astronomers in the early eighteenth century prepared tables based upon TMM: These tables were all published in one form or another, except for that of Delisle, whose work remained in manuscript. Delisle claimed to be the first to have repared tables based upon the Newtonian theory (ie, TMM). They all gave worked examples of their method (again, except for Delisle, or, if he did, none remains). Leadbetter published in 1742 a more comprehensive astronomy treatise than the above, which abandoned the Newtonian theory. Halley drew up his version of the theory around 1720, and used it while he was Astronomer Royal, but it was only published posthumously in 1749, by which time it was out-of-date. In mid-eighteenth century France, the most widely used (lunar) tables were those of Halley and LeMonnier, according to the historian D'Alembert (1754, p. iv). Slight differences between the two versions were noted, e.g., Halley had omitted the seventh equation, while LeMonnier kept it.

The First Computation

The first TMM-based calculation on record was published in the Philosophical Transactions of 1710, by 'the Reverend Mr H. Cressner, M.A., Fellow of the Royal Society.' Cressner compared this with a computation based on Flamsteed's theory as published by William Whiston, which method he called , 'Horroxian' . The occasion was a lunar eclipse observed at Streatham in South London in 1710. Thus, at the dawn of the Age of Enlightenment, there existed two rival British lunar theories. Mr Cressner claimed that he was the first to do this:

'There being therefore no Examples of any Calculation (that I know of) according to that Theory, nor of the Theory's Agreement with Observations yet made Public; I thought it proper to offer this one to this learned Society's perusal...I have added the Calculation from the famous Mr Flamsteed's Tables, according to Horrox's Theory, as I find them published in the Ingenious Mr Whiston's Astronomical Lectures...'

He reported that the Newtonian version was considerably more exact.

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998