August 17, 1905] 



NA TURE 



575 



More than this, we know that Newton's great treatise 

 saw the light only through Halley's persuasive insistence, 

 through his unwearying diligence in saving Newton all 

 •cares and trouble and even pecuniary expense, and through 

 his absolutely self-sacrificing devotion to what he made 

 an unwavering duty at that epoch in his life. Again, he 

 appears to have been the first organiser of a scientific 

 expedition, as distinct from a journey of discovery, towards 

 the Southern Seas ; he sailed as far as the fifty-second 

 degree of southern latitude, devised the principle of the 

 sextant in the course of his voyaging, and, as a result of 

 the voyage, he produced a General Chart of the Atlantic 

 Ocean, with special reference to the deviation of the 

 compass. Original, touched with genius, cheery of soul, 

 strenuous in thought and generous by nature, he spent 

 his life in a continuously productive devotion to astro- 

 nomical science, from bovhood to a span of years far 

 beyond that which satisfied the Psalmist's broodings. I 

 have selected a characteristic incident in his scientific 

 activity, one of the most brilliant (though it cannot be 

 claimed as the most important) of his astronomical achieve- 

 ments ; it strikes me as one of the most chivalrously bold 

 acts of convinced science within my knowledge. It is only 

 the story of a comet. 



I have just explained, very briefly, Halley's share in 

 the production of Newton's " Principia ": his close concern 

 with it made him the Mahomet of the new dispensation 

 of the astronomical universe, and he was prepared to view 

 all its phenomena in the light of that dispensation. A 

 comet had :ippeared in 1682 — it was still the age when 

 scientific men could think that, by a collision between the 

 earth and a comet, " this most beautiful order of things 

 would be entirely destroyed and reduced to its ancient 

 chaos " ; but this fear was taken as a " by-the-bye," which 

 happily interfered with neither observations nor calcula- 

 tions. Observations had duly been made. The data were 

 used to obtain the elements of the orbit, employing 

 Newton's theory as a working hypothesis; and he expresses 

 an incidental regret as to the intrinsic errors of assumed 

 numerical elements and of recorded observations. It then 

 occurred to Halley to calculate similarly the elements of 

 the comet which Kepler and others had seen in 1607, and 

 of which records had been made; the Newtonian theory 

 gave elements in close accord with those belonging to the 

 comet calculated from the latest observations, though a 

 new regret is expressed that the 1607 observations had not 

 been made with more accuracy. On these results he com- 

 mitted himself (being then a man of forty-nine years of 

 age) to a prophecy (which could not be checked for fifty- 

 three years to come) that the comet would return about 

 the end of the year 1758 or the beginning of the next 

 succeeding year ; he was willing to leave his conclusion 

 " to be discussed by the care of posterity, after the truth 

 is found out by the event." But not completely content 

 with this stage of his work, he obtained with difficulty 

 a book by Apian, giving an account of a comet seen in 

 153 1 and recording a number of observations. Halley, 

 constant to his faith in the Newtonian hypothesis, used 

 that hypothesis to calculate the elements of the orbit of 

 the Apian comet ; once more regretting the uncertainty 

 of the data and discounting a very grievous error com- 

 mitted by Apian himself, Halley concluded that the Apian 

 comet of 1531, and the Kepler comet of 1607, and the 

 observed comet of 1682 were one and the same. He con- 

 firmed his prediction as to the date of its return, and he 

 concludes his argument with a blend of confidence and 

 patriotism : — 



" Wherefore if according to what we have already said 

 it should return again about the year 1758, candid posterity 

 will not refuse to acknowledge that this was first discovered 

 by an Englishman." 



Such was Halley's prediction published in the year 1705. 

 The comet pursued its course, and it was next seen on 

 Christmas Day, 1758. Candid posterity, so far from 

 refusing to acknowledge that the discovery was made by 

 an Englishman, has linked Halley's name with the comet, 

 possibly for all time. 



We all now could make announcements on the subject 

 of Halley's comet ; their fulfilment could be awaited 

 serenely. No vision or inspiration is needed ; calculations 



NO. 1868, VOL. 72] 



and corrections will suffice. The comet was seen in 1835, 

 and it is expected again in 1910. No doubt our astro- 

 nomers will be ready for it ; and the added knowledge of 

 electrical science, in connection particularly with the 

 properties of matter, may enable them to review Bessel's 

 often-discussed conjecture as to an explanation of the 

 emission of a sunward tail. But Halley's announcement 

 was made during what may be called the immaturity of 

 the gravitation theory ; the realisation of the prediction 

 did much to strengthen the belief in the theory and to 

 spread its general acceptance ; the crown of conviction 

 was attained with the work of Adams and Leverrier in 

 the discovery, propounded by theory and verified by observ- 

 ation, of the planet Neptune. I do not know an apter 

 illustration of Bacon's dictum that has already been 

 quoted, " All true and fruitful natural philosophy hath a 

 double scale, ascending from experiments to the invention 

 of causes, and descending from causes to the invention of 

 new experiments." The double process, when it can be 

 carried out, is one of the most effective agents for the 

 increase of trustworthy knowledge. But until the event 

 justified Halley's prediction, the Cartesian vorte.x-theory 

 of the universe was not completely replaced by the New- 

 tonian theorv ; the Cartesian votaries were not at once 

 prepared to obev Halley's jubilant, if stern, injunction 

 to " leave off trifling . . . with their vortices and their 

 absolute plenum . . . and give themselves up to the study 

 of truth." 



The century that followed the publication of Halley's 

 prediction shows a world that is steadily engaged in the 

 development of the inductive sciences and their appli- 

 cations. Observational astronomy continued its activity 

 quite steadily, reinforced towards the end of the century 

 by the first of the Herschels. The science of mathematical 

 (or theoretical) astronomy was created in a form that is 

 used to this day ; but before this creation could be effected, 

 there had to be a development of mathematics suitable for 

 the purpose. The beginnings were made by the BernouUis 

 (a family that must be of supreme interest to Dr. Francis 

 Galton in his latest statistical compilations, for it con- 

 tained no fewer than seven mathematicians of mark, dis- 

 tributed over three generations), but the main achievements 

 are due to Euler, Lagrange, and Laplace. In particular, 

 tTie infinitesimal calculus in its various branches (including, 

 that is to sav, what we call the differential' calculus, the 

 integral calculus, and differential equations) received the 

 development that now is familiar to all who have occasion 

 to work in the subject. When this calculus was developed, 

 it was applied to a variety of subjects ; the applications, 

 indeed, not merely influenced, but immediately directed, 

 the development of the mathematics. To this period is 

 due the construction of analytical mechanics at the hands 

 of Euler, d'Alembert, Lagrange, and Poisson ; but the 

 most significant achievement in this range of thought is 

 the mathematical development of the Newtonian theory of 

 gravitation applied to the whole universe. It was made, 

 in the main, by Lagrange, as regards the wider theory, 

 and by Laplace, as regards the amplitude of detailed 

 application. But it was a century that also saw the 

 obliteration of the ancient doctrines of caloric and 

 phlogiston, through the discoveries of Rumford and Davy 

 of the nature and relations of heat. The modern science 

 of vibrations had its beginnings in the experiments of 

 Chladni, and, as has already been stated, the undulatory 

 theorv of light was rehabilitated by the researches of 

 Thomas Young. Strange views as to the physical con- 

 stitution of the universe then were sent to the limbo of 

 forgotten ignorance by the early discoveries of modern 

 chemistry; and engineering assumed a systematic and 

 scientific activity, the limits of which seem bounded only 

 by the cumulative ingenuity of successive generations. But 

 in thus attempting to summarise the progress of science 

 in that period, I appear to be trespassing upon the domains 

 of other Sections ; my steps had better be retraced so as 

 to let us return to our own upper air. If I mention one 

 more fact (and it will be a small one), it is because of its 

 special connection with the work of this Section. As you 

 are aware, the elements of Euclid have long been the 

 standard treatise of elementary geometry in Great Britain ; 

 and the Greek methods, in Robert Simson's edition, have 

 been imposed upon candidates in examination after ex- 



