
ADAMS
DATED COMPUTATIONS
Amidst a welter of assumptions and retrospectivelyconstructed
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
September 
18th A 'solution',  50°
34’

November 
12th A formula for the Uranus radius
vector perturbation
28th More on the radius vector

December 
15th A perturbationformula 16th
The same 24th Log of radius vector 
1846
August 
20th The ‘Hyp II’
solution,  42° 52’

September 
1st the Uranus vector perturbation computed,
for 18301840. 


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 prediscovery 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 Neptunediscovery 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 discoveryepoch 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 newplanet 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 meanmotion value.
The PerturbationFunction
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.4756. 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 wellknown
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 perturbationterms used to derive the values
for his ‘Hyp 1’). Why was this perturbationexpression
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.612, 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 highlevel
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
