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.