A Short History of Astronomy - Arthur Berry (read along books .txt) 📗
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But whereas the questions left unanswered by Ptolemy, Coppernicus, and Kepler were in whole or in part answered by their successors, that is, their unexplained facts or laws were shewn to be necessary consequences of other simpler and more general laws, it happens that up to the present day no one has been able to answer, in any satisfactory way, these questions which Newton left unanswered. In this particular direction, therefore, Newton’s laws mark the boundary of our present knowledge. But if any one were to succeed this year or next in shewing gravitation to be a consequence of some still more general law, this new law would still bring with it a new Why.
If, however, Newton’s laws cannot be regarded as an ultimate explanation of the phenomena of the solar system, except in the historic sense that they have not yet been shewn to depend on other more fundamental laws, their success in “explaining,” with fair accuracy, such an immense mass of observed results in all parts of the solar system, and their universal character, gave a powerful impetus to the idea of accounting for observed facts in other departments of science, such as chemistry and physics, in some similar way as the consequence of forces acting between bodies, and hence to the conception of the material universe as made up of a certain number of bodies, each acting on one another with definite forces in such a way that all the changes which can be observed to go on are necessary consequences of these forces, and are capable of prediction by any one who has sufficient knowledge of the forces and sufficient mathematical skill to develop their consequences.
Whether this conception of the material universe is adequate or not, it has undoubtedly exercised a very important influence on scientific discovery as well as on philosophical thought, and although it was never formulated by Newton, and parts of it would probably have been repudiated by him, there are indications that some such ideas were in his head, and those who held the conception most firmly undoubtedly derived their ideas directly or indirectly from him.
195. Newton’s scientific method did not differ essentially from that followed by Galilei (chapter VI., § 134), which has been variously described as complete induction or as the inverse deductive method, the difference in name corresponding to a difference in the stress laid upon different parts of the same general process. Facts are obtained by observation or experiment; a hypothesis or provisional theory is devised to account for them; from this theory are obtained, if possible by a rigorous process of deductive reasoning, certain consequences capable of being compared with actual facts, and the comparison is then made. In some cases the first process may appear as the more important, but in Newton’s work the really convincing part of the proof of his results lay in the verification involved in the two last processes. This has perhaps been somewhat obscured by his famous remark, Hypotheses non fingo (I do not invent hypotheses), dissociated from its context. The words occur in the conclusion of the Principia, after he has been speaking of universal gravitation:—
“I have not yet been able to deduce (deducere) from phenomena the reason of these properties of gravitation, and I do not invent hypotheses. For any thing which cannot be deduced from phenomena should be called a hypothesis.”
Newton probably had in his mind such speculations as the Cartesian vortices, which could not be deduced directly from observations, and the consequences of which either could not be worked out and compared with actual facts or were inconsistent with them. Newton in fact rejected hypotheses which were unverifiable, but he constantly made hypotheses, suggested by observed facts, and verified by the agreement of their consequences with fresh observed facts. The extension of gravity to the moon (§ 173) is a good example: he was acquainted with certain facts as to the motion of falling bodies and the motion of the moon; it occurred to him that the earth’s attraction might extend as far as the moon, and certain other facts connected with Kepler’s Third Law suggested the law of the inverse square. If this were right, the moon’s acceleration towards the earth ought to have a certain value, which could be obtained by calculation. The calculation was made and found to agree roughly with the actual motion of the moon.
Moreover it may be fairly urged, in illustration of the great importance of the process of verification, that Newton’s fundamental laws were not rigorously established by him, but that the deficiencies in his proofs have been to a great extent filled up by the elaborate process of verification that has gone on since. For the motions of the solar system, as deduced by Newton from gravitation and the laws of motion, only agreed roughly with observation; many outstanding discrepancies were left; and though there was a strong presumption that these were due to the necessary imperfections of Newton’s processes of calculation, an immense expenditure of labour and ingenuity on the part of a series of mathematicians has been required to remove these discrepancies one by one, and as a matter of fact there remain even to-day a few small ones which are unexplained (chapter XIII., § 290).
OBSERVATIONAL ASTRONOMY IN THE 18TH CENTURY.
“Through Newton theory had made a great advance and was ahead of observation; the latter now made efforts to come once more level with theory.”—Bessel.
196. Newton virtually created a new department of astronomy, gravitational astronomy, as it is often called, and bequeathed to his successors the problem of deducing more fully than he had succeeded in doing the motions of the celestial bodies from their mutual gravitation.
To the solution of this problem Newton’s own countrymen contributed next to nothing throughout the 18th century, and his true successors were a group of Continental mathematicians whose work began soon after his death, though not till nearly half a century after the publication of the Principia.
This failure of the British mathematicians to develop Newton’s discoveries may be explained as due in part to the absence or scarcity of men of real ability, but in part also to the peculiarity of the mathematical form in which Newton presented his discoveries. The Principia is written almost entirely in the language of geometry, modified in a special way to meet the requirements of the case; nearly all subsequent progress in gravitational astronomy has been made by mathematical methods known as analysis. Although the distinction between the two methods cannot be fully appreciated except by those who have used them both, it may perhaps convey some impression of the differences between them to say that in the geometrical treatment of an astronomical problem each step of the reasoning is expressed in such a way as to be capable of being interpreted in terms of the original problem, whereas in the analytical treatment the problem is first expressed by means of algebraical symbols; these symbols are manipulated according to certain purely formal rules, no regard being paid to the interpretation of the intermediate steps, and the final algebraical result, if it can be obtained, yields on interpretation the solution of the original problem. The geometrical solution of a problem, if it can be obtained, is frequently shorter, clearer, and more elegant; but, on the other hand, each special problem has to be considered separately, whereas the analytical solution can be conducted to a great extent according to fixed rules applicable in a larger number of cases. In Newton’s time modern analysis was only just coming into being, some of the most important parts of it being in fact the creation of Leibniz and himself, and although he sometimes used analysis to solve an astronomical problem, it was his practice to translate the result into geometrical language before publication; in doing so he was probably influenced to a large extent by a personal preference for the elegance of geometrical proofs, partly also by an unwillingness to increase the numerous difficulties contained in the Principia, by using mathematical methods which were comparatively unfamiliar. But though in the hands of a master like Newton geometrical methods were capable of producing astonishing results, the lesser men who followed him were scarcely ever capable of using his methods to obtain results beyond those which he himself had reached. Excessive reverence for Newton and all his ways, combined with the estrangement which long subsisted between British and foreign mathematicians, as the result of the fluxional controversy (chapter IX., § 191), prevented the former from using the analytical methods which were being rapidly perfected by Leibniz’s pupils and other Continental mathematicians. Our mathematicians remained, therefore, almost isolated during the whole of the 18th century, and with the exception of some admirable work by Colin Maclaurin (1698-1746), which carried Newton’s theory of the figure of the earth a stage further, nothing of importance was done in our country for nearly a century after Newton’s death to develop the theory of gravitation beyond the point at which it was left in the Principia.
In other departments of astronomy, however, important progress was made both during and after Newton’s lifetime, and by a curious inversion, while Newton’s ideas were developed chiefly by French mathematicians, the Observatory of Paris, at which Picard and others had done such admirable work (chapter VIII., §§ 160-2), produced little of real importance for nearly a century afterwards, and a large part of the best observing work of the 18th century was done by Newton’s countrymen. It will be convenient to separate these two departments of astronomical work, and to deal in the next chapter with the development of the theory of gravitation.
197. The first of the great English observers was Newton’s contemporary John Flamsteed, who was born near Derby in 1646 and died at Greenwich in 1720.111 Unfortunately the character of his work was such that, marked as it was by no brilliant discoveries, it is difficult to present it in an attractive form or to give any adequate idea of its real extent and importance. He was one of those laborious and careful investigators, the results of whose work are invaluable as material for subsequent research, but are not striking in themselves.
He made some astronomical observations while quite a boy, and wrote several papers, of a technical character, on astronomical subjects, which attracted some attention. In 1675 appointed a member of a Committee to report on a method for finding the longitude at sea which had been offered to the Government by a certain Frenchman of the name of St. Pierre. The Committee, acting largely on Flamsteed’s advice, reported unfavourably on the method in question, and memorialised Charles II. in favour of founding a national observatory, in order that better knowledge of the celestial bodies might lead to a satisfactory method of finding the longitude, a problem which the rapid increase of English shipping rendered of great practical importance. The King having agreed, Flamsteed was in the same year appointed to the new office of Astronomer Royal, with a salary of £100 a year, and the warrant for building an Observatory at Greenwich was signed on June 12th, 1675. About a year was occupied in building it, and Flamsteed took up his residence there and began work in July 1676, five years after Cassini entered upon his duties at the Observatory of Paris (chapter
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