Edmund Halley, one of the greatest astronomers of an age which produced
many, was born at a country house named Haggerston, in the parish of St.
Leonard, Shoreditch, October 29, 1656. His father, a wealthy citizen and
soap-boiler, intrusted the care of his son’s education to Dr. Gale,
master of St. Paul’s School. Here young Halley applied himself to the
study of mathematics and astronomy with what was then considered great
success; for, before he left school, he understood the use of the
celestial globe, and could construct a sun-dial; and, as he has himself
informed us, had already observed the variation of the needle. In 1673,
being in the seventeenth year of his age, he was entered of Queen’s
College, Oxford, and two years afterwards gave the first proof of his
astronomical genius by publishing, in the Philosophical Transactions,
1676, “a direct and geometrical method of finding the Aphelia and
Eccentricities of the Planets.” His father, who seems to have had none
of that antipathy to a son’s engaging in literary or scientific
pursuits, which is represented as common to men of commerce by the
writers of that age, supplied him liberally with astronomical
instruments. Thus assisted, he made many observations, particularly of
Jupiter and Saturn, by means of which he discovered that the motion of
Saturn was slower, and that of Jupiter quicker than could be accounted
for by the existing tables; and made some progress in correcting those
tables accordingly. But he soon found that nothing could be done without
a good catalogue of the stars. This, it appears, he had some intention
of forming; but finding that Hevelius and Flamsteed were already
employed on the same work, he proposed to himself to proceed to the
southern hemisphere, and to complete the design by observing those stars
which never rise above the horizons of Dantzic and Greenwich. Having
obtained his father’s consent, and an allowance of £300 a-year; and
having fixed upon St. Helena as the most convenient spot, he applied to
Sir Joseph Williamson and Sir Jonas Moor, the Secretary of State and the
Surveyor of the Ordnance. These gentlemen represented his intention in a
favourable light to Charles II., and also to the East-India Company, who
promised him every assistance in their power. Thus protected, he set out
for St. Helena in 1676; his principal instruments being a sextant of
five feet and a half radius, and a telescope of twenty-four feet in
length. He found the climate not so favourable as he had been led to
believe, and moreover describes himself as disgusted with the treatment
he received from the Governor. Under these disadvantages, he
nevertheless formed a catalogue of 350 stars, which he afterwards
published under the name of ‘Catalogus Stellarum Australium.’ He called
a new constellation which he had observed, by the title of _Robur
Carolinum_, in honour of the well-known oak of Charles II. While at St.
Helena he also observed a transit of Mercury, and suggested the use
which might be made of similar phenomena in the determination of the
sun’s distance from the earth. He first observed the necessity of
shortening the pendulum as it approached the equator; or, at least, when
Hook afterwards mentioned the circumstance to Newton, it was the first
time the latter had heard of the fact.
Soon after his return to England, in November, 1678, Halley obtained the
degree of M.A. from the University of Oxford, by royal mandate, and was
elected Fellow of the Royal Society. This body had been requested by
Hevelius to select some person who might add the southern stars to his
catalogue. A dispute was also pending between him and Hook, as to the
use of telescopes in observing the stars, to which the former objected.
To aid Hevelius, as well as to decide upon the character of his
observations, Halley went to Dantzic, and it is related, as a proof of
the energy of his character, that in one month from the time of his
landing in England he published his catalogue, procured a mandate, took
the degree, was elected F.R.S., arranged to go to Dantzic, and wrote to
Hevelius. He arrived on the 26th of May, 1679, and the same night
entered upon a series of observations with Hevelius, which he continued
till July, when he returned to England, fully satisfied of his
coadjutor’s accuracy.
In 1680 he again visited the continent. Between Paris and Calais he had
a sight of the celebrated comet of that year, well known as the one by
observations of which the orbit of these bodies was discovered to be
nearly a parabola. He returned from his travels in the year 1681, and
shortly after married the daughter of a Mr. Tooke then Auditor of the
Exchequer, which union lasted fifty-five years. He settled at Islington,
where, for more than ten years, he occupied himself with his usual
pursuits, of the results of which we shall presently speak more
particularly.
In 1691 the Savilian Professorship of Astronomy became vacant, and, as
Whiston relates, on the authority of Dr. Bentley, Bishop Stillingfleet
was requested to recommend Mr. Halley. But the astronomer’s avowed
disbelief of Christianity interfered with his election in this instance,
and the Professorship was given to Dr. Gregory. It is related by Sir
David Brewster that Halley, when inclined to enter upon religious
subjects with Newton, always received a check in words like the
following, “You have not studied the subject—I have.”
After the above-mentioned failure, our astronomer received from King
William the commission of Captain in the Navy, with command of a small
vessel. The singularity of the reward need not surprise us, when the
same monarch offered a company of dragoons to Swift: indeed the pursuits
of Captain Halley were nearly akin to those of navigation, and he
himself might be almost as well qualified for sailing, though perhaps
not for fighting a ship, as most of his brother officers. In his new
character Halley made two voyages, the first to the Mediterranean, the
Brazils, and the West Indies, for the purpose of ascertaining the
variation of the magnet, a subject in which he was much interested, and
of which he afterwards published a chart; the second to ascertain the
latitudes and longitudes of the principal points in the British Channel,
and the course of the tides. In 1703 he was elected Savilian Professor
of Geometry, on the death of the celebrated Wallis. He received, about
the same time, the degree of Doctor of Laws, which is conferred without
requiring subscription to the Articles of the Church. In his connexion
with the University he superintended several parts of the edition of the
Greek Geometers, which was printed at the University press.
Halley succeeded Sir Hans Sloane, in 1713, as Secretary to the Royal
Society; and, in 1719, on the death of Flamsteed, he was appointed
Astronomer Royal at Greenwich. In this employment he continued till his
death, under the patronage of Queen Caroline, wife of George II., who
procured for him the half-pay of the rank he formerly held in the navy.
In 1737 he was seized with a paralytic disorder; but nevertheless
continued his labours till within a short time of his death, which took
place in January, 1742, at the age of eighty-five. He was interred at
Lee, near Blackheath, where a monument was erected to him and his wife
by their two daughters.
In person Dr. Halley was rather tall, thin, and fair, and remarkable as
well for energy as vivacity of character. He cultivated the friendship
and acquired the esteem of his most distinguished contemporaries, and
particularly of Newton, spite of their very different opinions. Indeed
it may be said that to him we owe, in some degree, the publication of
the ‘Principia;’ for Halley being engaged upon the consideration of
Kepler’s law, as it had been discovered by observation, viz., that the
squares of the periodic times of planets are as the cubes of their
distances, and suspecting that this might be accounted for on the
supposition of a centripetal force, varying inversely as the square of
the distance, applied himself to prove the connexion geometrically, in
which he was unable to succeed. In this difficulty he applied to Hook
and Wren, neither of whom could help him, and was recommended to consult
Newton, then Lucasian Professor at Cambridge. Following this advice, he
found in Newton all he wanted; and did not rest until he had persuaded
his new acquaintance to give the results of his discoveries to the
world. In about two years after this, the first edition of the
‘Principia’ was published, and the proofs were corrected by Halley, who
supplied the well-known Latin verses which stand at the beginning of the
work.
In conversation, Halley appears to have been of a jocose and somewhat
satirical disposition. The following anecdote of him, which is told by
Whiston, displays the usual modesty of the latter, when speaking of
himself: “On my refusal from him of a glass of wine on a Wednesday or
Friday, he said he was afraid I had a pope in my belly, which I denied,
and added somewhat bluntly, that had it not been for the rise now and
then of a Luther or a Whiston, he would himself have gone down on his
knees to St. Winifred or St. Bridget, which he knew not how to
contradict.” It is related that when Queen Caroline offered to obtain an
increase of Halley’s salary as Astronomer Royal, he replied, “Pray, your
Majesty, do no such thing, for should the salary be increased, it might
become an object of emolument to place there some unqualified needy
dependant, to the ruin of the institution.” And yet the sum which he
would not suffer to be increased was only £100 a-year.
To give even a catalogue of the various labours of Halley, would require
more space than we can here devote to the subject. For a more detailed
account both of his life and discoveries, we must refer the reader to
the Biographia Britannica, to Delambre, Histoire de l’Astronomie au
dix-huitième Siecle, livre II., and the Philosophical Transactions of
the time in which he lived; or better perhaps to the Miscellanea
Curiosa, _London_, 1726, a selection of papers from the Transactions,
containing the most remarkable of those written by Halley. We shall,
nevertheless, proceed briefly to notice a few of the discoveries on
which the fame of our astronomer is built.
The most remarkable of them, to a common reader, is the conjecture of
the return of a comet. Some earlier astronomers, as Kepler, had imagined
the motion of these bodies to be rectilinear. Newton, in explaining the
principle of universal gravitation, showed how a comet might describe a
parabola, and also how to calculate its motion, and compare it with
observation. Hevelius had already indicated the curvature of a comet’s
path, and Dörfel, a Saxon clergyman, had calculated the path of the
comet of 1680 upon this supposition. Halley, in computing the parabolic
elements of all the comets which had been well observed up to his time,
suspected, from the general likeness of the three, that the comets of
1531, 1607, and 1682, were the same. He was the more confirmed in this,
by knowing that comets had been seen, though no good observations were
recorded, in the years 1305, 1380, and 1456, giving, with the former
dates, a chain of differences of 75 and 76 years alternately. Halley
supposed, therefore, that the orbit of this comet was, not a parabola,
but a very elongated ellipse, and that it would return about the year
1758. The truth of his conjecture was fully confirmed in January, 1759,
by Messier. The first person, however, who saw Halley’s comet, as it is
now called, was George Palitzch, a farmer in the neighbourhood of
Dresden, who had studied astronomy by himself, and fitted up a small
observatory.
But a much more useful exertion of Halley’s genius and power of
calculation is to be found in his researches on the lunar theory. It is
to him that we are indebted for first starting the idea of finding the
longitude at sea by means of the moon’s place, which is now universally
adopted. The principle of this problem is as follows. An observer at sea
can readily find the time of day by means of the sun or a star, and can
thereby correct a watch. If he could at the same moment in which he
finds his own time, also discover that at Greenwich, the difference
between the two, turned into degrees, minutes, and seconds, would be his
longitude east or west of Greenwich. If, therefore, he carries with him
a Nautical Almanac, in which the times of various astronomical phenomena
are registered, as they will take place at Greenwich, or rather as they
will be seen by an observer placed at the centre of the earth with a
Greenwich clock, he can observe any one of these phenomena, and reduce
it also to the centre. He will then know the corresponding moments of
time, for his own position and that of Greenwich. The moon traverses the
whole of its orbit in little more than 27 days, and therefore moves
rapidly with respect to the fixed stars, its motion being nearly a whole
sign of the zodiac in 48 hours. If we observe the distance between the
moon and a star, and find it to be ten degrees, the longitude of the
place in which the observation is made can be known as aforesaid, if the
almanac will tell what time it was at Greenwich when the moon was at
that same distance from the star. In the time of Halley, though it was
known that the moon moved nearly in an ellipse, yet the elements of that
ellipse, and the various irregularities to which it is subject, were
very imperfectly ascertained. It had, however, been known even from the
time of the Chaldeans, that some of these irregularities have a
_period_, as it is called, of little more than eighteen years, that is,
begin again in the same order after every eighteen years; the periods
and quantities of several other errors had also been discovered with
something like accuracy. To make good lunar tables, that is, tables from
which the place of the moon might be correctly calculated beforehand,
became the object of Halley’s ambition. He therefore observed the moon
diligently during the whole of one of the periods of eighteen years,
that is, from the end of 1721 to that of 1739, and produced tables which
were published in 1749, after his death, and were of great service to
astronomers. He also made another observation on the motion of the moon,
which has since given rise to one of the finest discoveries of Laplace.
In calculating from our tables the time of an ancient eclipse, observed
at Babylon, B. C. 720, he found that, had the tables been correct, it
would have happened three hours sooner than, according to Ptolemy, it
did happen. This might have arisen from an error in the Babylonian
observation; but on looking at other eclipses, he found that the ancient
ones always happened later than the time indicated by his table, and
that the difference became less and less as he approached his own time.
From hence he concluded that the moon’s average daily motion is subject
to a very small acceleration, so that a lunar month at present is in a
very slight degree shorter than a month in the time of the Chaldeans.
This was afterwards shown by Laplace to arise from a very slow
diminution in the eccentricity of the earth’s orbit, caused by the
attraction of the planets. For a further account of Halley’s
astronomical labours, we may refer to the History of Astronomy in the
Library of Useful Knowledge, page 79.
We must also ascribe to Halley the first correct application of the
barometer to the measurement of the heights of mountains. Mariotte, who
first enunciated the remarkable law that the elastic forces of gases are
in the inverse proportion of the spaces which they occupy, had
previously given a formula for the determination of these same heights,
entirely wrong in principle, and inapplicable in practice. Halley, whose
profound mathematical knowledge made him fully equal to the task,
investigated and discovered the common formula, which, with some
corrections for the temperature of the mercury in the barometer and the
air without it, is in use at this day. We have already mentioned that
Halley sailed to various parts of the earth with a view to determine the
variation of the magnet. The result of his labours was communicated to
the Royal Society in a map of the lines of equal variation, and also of
the course of the trade-winds. He attempted to explain the phenomena of
the compass by supposing that the earth is one great magnet, having four
poles, two near each pole of the equator; and further accounts for the
variation which the compass undergoes from year to year in the same
place, by imagining a magnetic sphere, interior to the surface of the
earth, which nucleus or inner globe turns on an axis with a velocity of
rotation very little differing from that of the earth itself. This
hypothesis has shared the fate of many others purely mathematical; that
is, invented to show how the observed phenomena might be produced,
without any ground of observation for believing that they really are so
produced. If we put together the astronomical and geographical
discoveries of Halley, and remember that the former were principally
confined to those points which bear upon the subjects of the latter, we
shall be able to find a title for their author less liable to cavil than
that of the Prince of Astronomers, which has sometimes been bestowed
upon him; we may safely say that no man, either before or since, has
done more to improve the theoretical part of navigation, by the diligent
observation alike of heavenly and earthly phenomena.
We pass over many minor subjects, such as his improvement of the
diving-bell, or his measurement of the quantity of fluid abstracted by
evaporation from the sea, to come to an application of science in which
he led the way,—the investigation of the law of mortality. From
observations communicated to the Royal Society of the births and deaths
in the city of Breslau, he constructed the first table of mortality,
which was in a great measure the foundation of the celebrated hypothesis
of De Moivre, that the decrements of human life are nearly equal at all
ages; that is, that out of eighty-six persons born, one dies every year,
until all are gone. Halley’s table as might be expected, was not very
applicable to human life in England, either then or now, but the effect
of example is conspicuous in this instance. Before the death of Halley
the tables of Kerseboom were published, and four years afterwards, those
of De Parcieux.
We will not enlarge on the purely mathematical investigations of Halley,
which would possess but little interest for the general reader. We may
mention, however, his method for the solution of equations, his ‘Analogy
of the Logarithmic Tangents to the Meridian Line, or sum of the
secants,’ his algebraic investigation of the place of the focus of a
lens, and his improvement of the method of finding logarithms. From the
latter we quote a sentence, which, to the reader, for whose benefit we
have omitted entering upon any discussion of these subjects, will appear
amusing enough, if indeed he does not shrink to see how much he has
degenerated from his ancestors. After describing a process which
contains calculation enough for most people; and which further directs
to multiply sixty figures by sixty figures, he adds, “If the curiosity
of any gentleman that has leisure, would prompt him to undertake to do
the logarithms of all prime numbers under 100,000 to 25 or 30 figures, I
dare assure him that the facility of this method will invite him
thereto; nor can anything more easy be desired. And to encourage him, I
here give the logarithms of the first prime numbers under 20 to 60
places.” One look at these encouraging rows of figures would be
sufficient for any but a calculating boy.
No one who is conversant with the mathematics and their applications can
read the life of the mathematicians of the seventeenth century without a
strong feeling of respect for the manner in which they overcame
obstacles, and of gratitude for the labour which they have saved their
successors. The brilliancy of later names has, in some degree, eclipsed
their fame with the multitude; but no one acquainted with the history of
science can forget, how with poor instruments and imperfect processes,
they achieved successes, but for which Laplace might have made the first
rude attempts towards finding the longitude, and Lagrange might have
discovered the law which connects the coefficients of the binomial
theorem. But even of these men the same thing may one day be said; and
future analysts may wonder how Laplace, with his paltry means of
investigation, could account for the phenomenon of the acceleration of
the moon’s motion; and future astronomers may, should such a sentence as
the present ever meet their eyes, be surprised that the observers of the
nineteenth century should hold their heads so high above those of the
seventeenth.
[Illustration:
_Engraved by W. Holl._