Science & Technology Studies

Nicholas Kollerstrom's

Newton's 1702 Lunar Theory

- slightly altered the mean motions adding 10" to the mean Moon, eg, and1'40" to the mean apse.
- altered the sequence, so that TMM's 6th equation became its 4th;
- omitted the small seventh equation. The 'Variation' inequality, which Newton put as the fifth step, thereby became his last equation, the sixth.

In all, I found that these several adjustments made Halley's
version of TMM *less *accurate than, say, LeMonnier's tables, which
perfectly embodied the 1702 instructions.

- '...the Faults of the Computus
formed therefrom rarely exceed a quarter Part of what is found in the best
Lunar Tables before that time extant…By this it was evident that Sir Isaac
had spared no Part of that Sagacity and Industry peculiar to himself, in
settling the Epoches, and other Elements of the Lunar Astronomy, the Result
many times, for whole Months together, rarely differing two Minutes of
Motion from the Observations themselves..' (Halley. 1731/2.

This was the reason why he spent his entire tenure as Astronomer Royal observing lunar transits and computing therefrom the error-values generated by the Newtonian theory (TMM), or rather his version of it. The graph shows a month of these eror- values, after Halley had been plodding along doing this for ten years. From the year 1732, this was around the time he gave the progress report to the Royal Society, above quoted. It can be seen that a sizeable baseline-drift has occurred, of about two arcminutes, in mean motion error; the error-values fluctuate to something resembling the lunar month; and they are generally within several arcminutes of that dispaced-zero position. For comparison, two further continuous lines have been added: the errors that would have been generated by using TMM over this period (red line), and the larger errors that would be generated by using Halley's tinkered-with version thereof (blue line).

A second graph shows just the same things plotted for one year later. It must have been a shock, as Halley found himself recording up to eight arcminutes of error, from Newton's lunar theory, repeating at 30-day intervals. About 2.5 arcminutes of this was due to cumulative drift in the mean-motion values, i.e., a systematic error. Still, the theory was coming up with errors far larger than he had indicated two years earlier to be possible. Alas we lack any comment from Halley on this matter. One can see how he was regularly taking the meridian-transit observations on the downward slope, as the theory-error was increasing, then left off each month after it had peaked - to get some sleep!

Halley was the first astronomer to be overtaken by the
pace of progress: by the time his Tables were published (finally in 1749),
they were obsolete and the era of the Newtonian Lunar Theory had ended.
The new theories of Mayer and Euler arriving from the Continent, truly
based on Newton's theory of gravitation, superceded it.

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