Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

Finding the Longitude

At the dawn of the new century, there appeared the first two textbooks of Newtonian astronomy: Gregory's Astronomiae Physicae of 1702, and Whiston's Praelectiones Astronomicae of 1707. They were meant to challenge the Cartesian philosophy then being taught in the schools of England, and both contained the full text of Isaac Newton's Theory of the Moon's Motion (hereinafter referred to as 'TMM'). Though occupying a mere five pages of Gregory's book, it formed an essential part of that challenge, for it purported to show that the new Newtonian philosophy had a practical and not merely theoretical significance.

Few were the sailors who made grey hairs, as the saying went, in those days. As their ships sailed back, laden with chocolate from South America or silks from India, they were as we still say today, quite 'at sea' once land disappeared. Huge prizes were offered for any means to find longitude. 'Finding the longitude' entered the vernacular as meaning something ultimately desirable, but which one despaired of achieving. And yet, Britain's two most distinguished astronomers of the time - Captain Edmond Halley and the Reverend John Flamsteed - had more or less diametrically opposed opinions as to the real value of TMM. The former claimed that it profoundly improved lunar prediction, while the latter averred that it gave no real improvement upon existing tables.

At least one of these books definitely claimed that TMM had achieved what was then regarded as well-nigh impossible: showing how to predict the Moon's position in the sky well enough to be of service for finding longitude. French astronomical treatises in the opening decades of the eighteenth century struck a rather sceptical note over this claim, while British ephemerides-composers tended to regard TMM as a kind of Holy Grail: something which would render possible the production of what was most desired, a reliable lunar ephemeris, if only it could be rightly interpreted.

Historians of science have been reluctant to comment upon the matter. Bernard Cohen was not exaggerating when in 1975 he stated:

'...this work [TMM] has hardly ever been discussed (or even referred to) in the literature concerning Newton or the history of astronomy (Cohen, p.1)

As the literature there alludes to is of no small volume, such an omission shows that this opus was not regarded as being significant. Yet, TMM was frequently reprinted through the first half of the eighteenth century, more often than any other single work of Newton's. Just about everything except the authorship of TMM has been unsettled. Was TMM in fact used, and if so, would its prescriptions have defined the much-sought lunar position, to anything resembling the claim made by its publisher?

The onward-rolling tercentenary process has now passed by the anniversary of the commencement at Greenwich in 1691 of the most accurate series of positional astronomy readings ever made, has passed by Flamsteed's marriage, Newton's nervous breakdown, and the historic commencement of the collaboration between these two on the great endeavour in 1694-5, not without strife, a linking together of theory and practice. Newton abandoned the whole endeavour in late 1695, when he left the groves of academe for London to become involved in the reminting of the nation's coinage at the Royal Mint.

The fruits of his labour did not surface until the beginning of the new century. Some have taken the view of Richard Westfall, that TMM had been composed some years earlier and was merely given to Gregory at this date (1980, p.547). My researches did not confirm this view, mainly because of the anguished sense of failure which haunted Newton over this endeavour, so well described in Whiteside's 1976 essay. As this issue is rather crucial, let us quote Newton's words written to Flamsteed in February 1694, optimistically expressing his intention:

'For I find this theory so very intricate, and the theory of gravity so necessary to it, that I am satisfied it will never be perfected but by somebody who understands the theory of gravity as well, or better than I do.'

These words were to be vindicated by the mighty labours of Clairaut, Lagrange and Laplace in the next century, using the Leibnizian calculus. But at that time, Newton was confronted by abject failure: he later wrote wrathfully to Flamsteed on hearing that the latter proposed to make public the fact that he had supplied Newton with over a hundred and fifty lunar positions.

'I was concerned to be publicly brought upon the stage about what, perhaps, will never be fitted for the public, and thereby the world put into an expectation of what, perhaps, they are never like to have' (January 6, 1699)

That was his last known comment upon his endeavour with the lunar theory prior to TMM's composition, which is curious. Flamsteed had wanted to tell the world that, as the King's Observatory, he had spent a year obtaining lunar data for Newton, by way of explaining what he was up to. He received a stern Newtonian rebuke denying him this option.

That doesn't sound like deception, for which reason we may accept David Gregory's view that TMM was only composed at the start of the eighteenth-century. Historians may have been silent about it because it contained no gravity theory. It has been little appreciated that Halley spent eighteen years checking out how well Newton's TMM worked on a more or less daily basis. One could say (as Whiteside did, in the 1975 essay) that the six extra equations which Newton formulated were one of the first attempt to grapple with the three-body problem, of dynamical interactions between Earth,Moon and Sun.

Readers of Dava Sobell's historical novel may not fully appreciate the extent to which the lunar method of finding terrestrial longitude was successful. As a result of its success, the worldwide adoption of GMT and of the zero of longitude through Greenwich took place. The star-maps of Flamsteed's Historia Coelestis Brittanica of 1729 became more widely used than any others in the eighteenth century by European sailors, as also contributed to the adoption of the Greenwich longitude. To quote Derek Howse, 'The heyday of lunars was probably from about 1780 to 1840' (Nov. 1993, p.7). The lunar method was generally preferred to use of chronometers because it was cheaper. Also, it was required as a backup even if a ship had invested in a chronometer. The lunar method was first used at sea with success in 1753 by Nicholas-Louis de Lacaille while crossing the Atlantic crossing (Howse 1993 p.4).

Eight decades after Newton and Gregory visited Flamsteed in the Autumn of 1694 at Greenwich, there inspecting tables of discrepancies between theoretical and observed values of lunar longitude, which stimulated the mathematician to begin that great endeavour, the problem was resolved. The intractable three-body problem had been dealt with. Ultimately this was a story of success, of successful endeavour, in the course of which the stars received their numbers from the first Astronomer Royal, time became measured from the setting of his clock, and longitude divisions of the globe were marked from his workplace.

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rev: February 1998