than compete directly against astronomers of the calibre of Flamsteed,
Cassini and Hevelius, the young enthusiast thought to make his reputation
in what was almost virgin territory. When he returned to England,
his Catalogum stellarum Australium (1678) earned him the honorific
title of ‘The Southern Tycho’, a fellowship in the Royal
Society and the degree of MA per litteras regias, awarded by direct
order of King Charles II.
thus became, at a very early age, a full member of Britain’s
scientific elite. For over sixty years he played a highly active
role in the Royal Society as a Fellow, as Clerk for a few years,
and as editor of the Philosophical Transactions from 1685 until
1693. Halley contributed no fewer than eighty-four papers to the
journal, largely devoted to astronomy (star charts, lunar theory,
comets, eclipses, transits of Venus, the dimensions of the solar
system, novae and nebulae), although questions of geophysics (terrestrial
magnetism, trade winds, monsoons, tidal theory) are also prominent.
Other papers touch on areas of pure mathematics, optics, ballistics,
hydrostatics, pneumatics and social statistics – Halley
was a pioneer in the use of mortality tables for calculating annuities.
great practical problem facing the astronomers of Halley’s
age was that of determining longitude at sea. The Admiralty had
offered a prize for the first workable solution, and Halley spent
much of his life pursuing three different approaches to the problem.
A sufficiently accurate lunar theory would, in principle, provide
a solution, the observed motions of the Moon against the background
of the stars serving as a sort of great clock. But lunar theory
was not yet up to the job. The periodic motions of the satellites
of Jupiter provided another possible method, but observing those
bodies required a long telescope which could not be kept steady
on a tossing ship.
quite different method would be to make use of the variation in
the magnetic declination (i.e. the angle between magnetic and
geographical north) at different points on the Earth’s surface.
From 1698 to 1700 Halley served as a naval captain plotting degrees
of magnetic declination throughout much of the Atlantic Ocean,
and plotting isogonics (later renamed ‘Halleyan lines’)
connecting points of equal declination. The intersection of one
of these lines with a line of latitude would, it was hoped, enable
sailors to fix their position. None of Halley’s three methods
provided, within his lifetime, an adequate solution to the problem;
in his later years, he would see the early models of Harrison’s
famous marine chronometer succeed where astronomical and geophysical
methods had failed.
in 1684 Halley found himself speculating about the mechanics of
the solar system. In company with Robert Hooke and Christopher
Wren, he had hit on the idea that the attractive force that keeps
the planets in their orbits varies as the inverse square of their
distance from the Sun. None of the three men, however, could solve
the mathematical problem of deriving Kepler’s laws of planetary
motion from the proposed inverse square law. Halley decided to
call on Isaac Newton (already well known to members of the Royal
Society as a mathematician of formidable powers) and put the problem
momentous visit took place in August 1684. Newton told Halley
that he had already solved the problem years ago, and promised
to send him the proof. On receiving the desired proof, Halley,
fully aware of its significance, returned to Cambridge for a second
meeting with Newton. It was during the course of this second visit
that Halley realized the extent of Newton’s achievement,
and persuaded him to publish it in book form. The idea of the
Principia was born.
not only had to persuade Newton to publish the Principia; he also
found himself having to see it through the printers at his own
expense. (The Royal Society was going through one of its periodic
financial crises.) Worse still, a priority dispute sprang up,
with the irascible Hooke claiming credit for the inverse square
law, and Newton threatening to suppress the whole of Book 3 of
his masterpiece, the great System of the World. Halley, fortunately,
was on good terms with both these difficult men, and was able,
by a combination of diplomacy and hard labour, to see Newton’s
‘divine treatise’ through the press in July 1687.
Rarely in the history of science can one man’s masterpiece
have owed such a debt to the labours of another.
a Preface to the first edition of the Principia, Halley composed
an ‘Ode to Newton’, in which he refers to the order
of the solar system as ‘eternal’ – this may
have been a mere lapse on Halley’s part, or a little poetic
licence, but it was enough to excite the wrath of the clergy.
He was accused of the heresy of ‘eternalism’, i.e.
of denying both the creation of our physical universe ex nihilo
and its eventual destruction in the universal conflagration prophesied
in Scripture. There were also reports, spread by enemies such
as Flamsteed and William Whiston, of Halley as a ‘sceptic
and banterer of religion’.
1691, when he applied for the Savilian Professorship of Astronomy
at Oxford, he was examined by Edward Stillingfleet and Bentley,
on the suspicion of holding materialist views. On this occasion,
he did not get the job. When the second edition of the Principia
was being edited by Bentley in 1713, the ‘eternalist’
sections of Halley’s ode were quietly deleted. The charge
of irreligion seems to have stuck: it is widely believed that
the ‘infidel mathematician’ to whom Berkeley addressed
his Analyst (1734) was Halley.
Halley really an ‘eternalist’? According to Kubrin
(1971), he was speculating, at around this period, on the possible
role of comets in the economy of the solar system. An idea suggested
in an unpublished paper of 1694 is that our Earth is in decline,
and will continue to decay until a catastrophic collision with
a comet restores it to its pristine vigour. This would entail
a sort of cyclical cosmogony, with an endless succession of ‘Earths’,
each no doubt furnished with its proper inhabitants. Small wonder
that the paper was not published until 1724, when Halley felt
his position to be much more secure.
disappointed by his failure in 1691, Halley set out to establish
his orthodoxy in a number of papers refuting eternalism. If the
planets are moving through a very subtle aetherial medium, he
suggests, the drag of this medium will eventually cause the solar
system to collapse. Halley claimed to have observational evidence
of the existence of such a gradual retardation of the planets’
motions. Evidence of the finite age of our Earth can also be found
in the oceans. If the rivers bring so much salt per annum to the
sea, one can in principle project the process back to estimate
the age of the Earth. Eternalism will thus be refuted –
but so too will be a literal interpretation of scriptural chronology.
The Earth will turn out to be very much older than the Bible tells
protestations of orthodoxy, aided by the efforts of powerful friends
at court, enabled him to succeed in 1703 where he had failed in
1691, when he became Savilian Professor of Geometry at Oxford.
As Savilian Professor one of his great achievements was a scholarly
Latin edition of Apollonius’s treatise on Conic Sections,
reconstructed from fragments of the original Greek and of an Arabic
translation. For Book 8 there was no manuscript text, and Halley
had to reinvent its probable contents. The Conics was not merely
of historical interest to Halley: it is a work of crucial importance
to any mathematician wanting to master Newton’s Principia.
scientific achievement for which Halley is best known today is,
of course, his work on comets. In the first edition of the Principia,
Newton had applied his principles to the motions of comets, but
had supposed that they follow parabolic paths about the focal
point of the Sun. (A parabola and an ellipse are almost indistinguishable
over the small parts of its orbit for which a comet can be observed.)
It was Halley who delved through the historical records of the
appearances of comets in an attempt to substantiate his thesis
that they move in elliptical orbits of high eccentricity, and
can thus be expected to return with a regular periodicity. And
it was Halley’s prediction, in his Synopsis of the Astronomy
of Comets (1705) – that a given comet, with a period of
about seventy-six years, could be expected to return in 1758 –
that provided the Newtonian theory with one of its most spectacular
triumphs. Hitherto objects of mystery and superstitious dread,
comets had been shown to be subject to the same universal laws
as the rest of the solar system. One could hardly ask for a clearer
illustration of the predictive power of Newtonian mechanics.
unresolved question of Newtonian cosmology was that of the finitude
or infinitude of the universe. Newton had of course discussed
the issue in his famous correspondence with Bentley; Halley would
no doubt have been familiar with Newton’s views on the subject.
In his own paper, published in the Philosophical Transactions
for 1720, Halley argues for an infinite universe with an even
distribution of stars. If the universe had a central point, he
argues, all its matter would collapse towards that point; to maintain
stability, there must therefore be an equilibrium of forces, which
in turn requires an infinity of stars. Halley’s theory raises
both gravitational and optical problems which he could not adequately
resolve, but he deserves credit none the less as one of the pioneers
of modern physical cosmology.
Boyle and Newton, Halley was an atomist in his theory of matter.
In October 1689 he presented to the Royal Society a paper on the
size of atoms, calculated on the basis of some observations on
the thinness of gold leaf. If one cannot see through gold leaf,
he reasoned, it must be at least one atom thick (probably more).
But the film was, he estimated, only one 134,560th of an inch
thick. This entails that the atoms ‘are necessarily less
than 1/2433000000 part of the cube of the hundredth part of an
inch, and probably many times lesser, if the united surface of
the gold without pores or interstices be considered’ (quoted
from Ronan, p. 98). This may appear to be a sort of quantitative
measure of the size of atoms; in reality, however, it only sets
an upper bound – the conclusion is only that atoms are unimaginably
relations with John Flamsteed, the first Astronomer-Royal, had
initially been friendly, but soon deteriorated into open hostility.
Flamsteed was compiling a great map of the stars, the Historia
coelestis, but his progress was very slow, and many influential
people blamed him for his tardiness and reluctance to release
his results. Halley was a leading member of the committee appointed
by Prince George of Denmark to take charge of Flamsteed’s
tables and see them through the press. This ‘pirated’
edition of the Historia coelestis appeared, against Flamsteed’s
will, in 1712; the ‘official’ version only saw the
light of day much later, after Flamsteed’s death.
1720, Halley succeeded his arch-rival, becoming the second Astronomer-Royal.
He seems to have had more success than his predecessor in getting
funds for instruments, while a visit from Queen Caroline in 1729
led to a pay-rise. For much of his last twenty years Halley laboured,
at the Observatory at Greenwich, to perfect lunar astronomy, but
he was never to win the sought-after prize for the solution of
the problem of longitude – applying Newtonian principles
to this notorious three-body problem continued to perplex mathematicians
of the calibre of Euler, Clairaut and d’Alembert.