ADAMS DATED COMPUTATIONS

Amidst a welter of assumptions and retrospectively-constructed histories, the dated pages in Adams’ manuscripts offer us a firm basis for reconstructing the sequence of events. There happen to be eight of these in the year prior to Neptune’s discovery:

1845

1846

No less than four of these are about finding the Uranus vector - the crucial question which Airy had put to him, following Adams’ abortive September 1845 visit to Greenwich. His letter of September 2nd to Airy was his first on the subject of the predicted planet, and his only pre-discovery letter on the subject and it gave both his ‘Hyp I’ and ‘Hyp II’ solutions. It was not sent off following his finding a solution on August 20th - only when he had resolved the radius vector problem, with which he appears to have been wrestling for some months, did he have the confidence to send it, including his radius vector solution.

With remarkable uniformity, accounts of the Neptune-discovery have cited Adams’ opinion that Airy’s question put to him about the radius vector was ‘trivial’ (eg, Grosser p94), and that this was the reason why he never bothered to reply to the Astronomer Royal’s letter. However, this remark was only made decades later, to Glaisher, and as such should hardly be preferred to the testimony of his own current notebooks.

A 'solution' here alludes to the angle in celestial longitude, between the mean positions of Uranus and ‘Neptune,’ at the epoch position he chose to use, in 1810. Two such solutions are found, in his manuscripts. His notebooks do not give the sequence of computations, to derive the value required in practice, from these 'solutions' It would first be necessary to add a mean Uranus longitude to give mean helio longitude of the predicted planet, then convert to a suitable discovery-epoch in 1845 or ‘46, and finally to apply the equation of center to obtain the ‘true’ helio longitude. For the last step one requires values of both eccentricity and apse line position. Airy in November 1846 produced an undated and unaddressed piece of paper (see The Crown Jewels Document), with Adams’ predicted elements of the new-planet position, claiming to have received them in October 1845; Challis likewise averred he had been given a comparable scrap of paper a month earlier than Airy, but did not ever produce it, or even specify its content! (see Challis’ Unseen Testimony).

It would thus be incorrect to say that Adams notebooks give a dated solution in late 1845. They give a dated mean motion, but not the ‘bridge’ required to have something useful for astronomers, by moving from circular mean motion to elliptical ‘true’ or actual position using the Equation of Centre. That is (I believe) why he wanted to discuss things with Airy. Adams claimed to have made his first (unannounced) visit to Airy in Greenwich in September ‘soon after his calculations were finished’ (Sedgwick to Airy, 6th December 1846, relating Adams story told to him earlier that day). That would have been after Sept 18th, when his notebook shows him reaching a mean-motion value.

The Perturbation-Function

There is probably more worth saying about Adams’ December 5th manuscript perturbation formula. It is clearly derived from Pontécoulant’s Du Systeme du Monde, pp.475-6. This is alluded to in a letter of his (to an RAS fellow, Dec 17th 1846): ‘In fact, in the more usual way of calculating the perturbations, those of the Radius Vector are computed first and those of longitude derived from them, and this was the method which I actually followed in my first solution. The formula for this purpose are well-known and are given in Pontécoulant Vol 1 pages 475 & 476.’ (see "The Radius Vector: A Trivial Question) Something resembling these calculations appears in his final RAS presentation, of November 13th (his section 11, p.433 (MRAS 54), which comprise the perturbation-terms used to derive the values for his ‘Hyp 1’). Why was this perturbation-expression set up after he had supposedly obtained his ‘final values’ in September and communicated them to Challis? The expressions are complex and no doubt required the utmost concentration to work them. Would we not have expected some earlier date on them, under the circumstances?

As regards Adams ‘solution’ of late 1845, a computation finding both mean helio longitude and apse position was given for Sept. 18th. Sampson (1904 p.166) wrongly claimed that its eccentricity was also given on these pages, the inclusion of which would have amounted to a solution (E III, pp.6-12, Sampson's pagination): it would enable one to move from mean to true heliocentric longitude, and thereby tell where to point one’s telescope. The November 12th radius vector solution is preceded by eight pages of high-level mathematics to find the formula, based upon the mathematics of Pontecoulant (B VIII, p.8, Sampson's pagination). Why was he doing this, if, as he later claimed, he had finished his computation in September?

Adams portrait by permission of the Master & Fellows of St John’s College, Cambridge