A Short History of Astronomy by Arthur Berry (best novels for students .TXT) 📕

If, as in fig. 78, the shape of the earth is drawn in accordance with Newton’s views, the figure shews at once that the arcs A A1, A1 A2, etc., each of which corresponds to 10° of latitude, steadily increase as we pass from a point A on the equator to the pole B. If the opposite hypothesis be adopted, which will be illustrated by the same figure if we now regard A as the pole and B as a point on the equator, then the successive arcs decrease as we pass from equator to pole. A comparison of the measurements made by Eratosthenes in Egypt (chapter II., § 36) with some made in Europe (chapter VIII., § 159) seemed to indicate that a degree of the meridian near the equator was longer than one in higher latitudes; and a similar conclusion was indicated by a comparison of different portions of an extensive French arc, about 9° in length, extending from Dunkirk to the Pyrenees, which was measured under the superintendence of the Cassinis in continuation of Picard’s arc, the result being published by J. Cassini in 1720. In neither case, however, were the data sufficiently accurate to justify the conclusion; and the first decisive evidence was obtained by measurement of arcs in places differing far more widely in latitude than any that had hitherto been available. The French Academy organised an expedition to Peru, under the management of three Academicians, Pierre Bouguer (1698-1758), Charles Marie de La Condamine (1701-1774), and Louis Godin (1704-1760), with whom two Spanish naval officers also co-operated.

The expedition started in 1735, and, owing to various difficulties, the work was spread out over nearly ten years. The most important result was the measurement, with very fair accuracy, of an arc of about 3° in length, close to the equator; but a number of pendulum experiments of value were also performed, and a good many miscellaneous additions to knowledge were made.

But while the Peruvian party were still at their work a similar expedition to Lapland, under the Academician Pierre Louis Moreau de Maupertuis (1698-1759), had much more rapidly (1736-7), if somewhat carelessly, effected the measurement of an arc of nearly 1° close to the arctic circle.

From these measurements it resulted that the lengths of a degree of a meridian about latitude 2° S. (Peru), about latitude 47° N. (France) and about latitude 66° N. (Lapland) were respectively 362,800 feet, 364,900 feet, and 367,100 feet.124 There was therefore clear evidence, from a comparison of any two of these arcs, of an increase of the length of a degree of a meridian as the latitude increases; and the general correctness of Newton’s views as against Cassini’s was thus definitely established.

The extent to which the earth deviates from a sphere is usually expressed by a fraction known as the ellipticity, which is the difference between the lines C A, C B of fig. 78 divided by the greater of them. From comparison of the three arcs just mentioned several very different values of the ellipticity were deduced, the discrepancies being partly due to different theoretical methods of interpreting the results and partly to errors in the arcs.

A measurement, made by Jöns Svanberg (1771-1851) in 1801-3, of an arc near that of Maupertuis has in fact shewn that his estimate of the length of a degree was about 1,000 feet too large.

A large number of other arcs have been measured in different parts of the earth at various times during the 18th and 19th centuries. The details of the measurements need not be given, but to prevent recurrence to the subject it is convenient to give here the results, obtained by a comparison of these different measurements, that the ellipticity is very nearly 1∕292, and the greatest radius of the earth (C A in fig. 78) a little less than 21,000,000 feet or 4,000 miles. It follows from these figures that the length of a degree in the latitude of London contains, to use Sir John Herschel’s ingenious mnemonic, almost exactly as many thousand feet as the year contains days.

222. Reference has already been made to the supremacy of Greenwich during the 18th century in the domain of exact observation. France, however, produced during this period one great observing astronomer who actually accomplished much, and under more favourable external conditions might almost have rivalled Bradley.

Nicholas Louis de Lacaille was born in 1713. After he had devoted a good deal of time to theological studies with a view to an ecclesiastical career, his interests were diverted to astronomy and mathematics. He was introduced to Jacques Cassini, and appointed one of the assistants at the Paris Observatory.

In 1738 and the two following years he took an active part in the measurement of the French arc, then in process of verification. While engaged in this work he was appointed (1739) to a poorly paid professorship at the Mazarin College, at which a small observatory was erected. Here it was his regular practice to spend the whole night, if fine, in observation, while “to fill up usefully the hours of leisure which bad weather gives to observers only too often” he undertook a variety of extensive calculations and wrote innumerable scientific memoirs. It is therefore not surprising that he died comparatively early (1762) and that his death was generally attributed to overwork.

223. The monotony of Lacaille’s outward life was broken by the scientific expedition to the Cape of Good Hope (1750-1754) organised by the Academy of Sciences and placed under his direction.

The most striking piece of work undertaken during this expedition was a systematic survey of the southern skies, in the course of which more than 10,000 stars were observed.

These observations, together with a carefully executed catalogue of nearly 2,000 of the stars125 and a star-map, were published posthumously in 1763 under the title Coelum Australe Stelliferum, and entirely superseded Halley’s much smaller and less accurate catalogue (§ 199). Lacaille found it necessary to make 14 new constellations (some of which have since been generally abandoned), and to restore to their original places the stars which the loyal Halley had made into King Charles’s Oak. Incidentally Lacaille observed and described 42 nebulae, nebulous stars, and star-clusters, objects the systematic study of which was one of Herschel’s great achievements (chapter XII., §§ 259-261).

He made a large number of pendulum experiments, at Mauritius as well as at the Cape, with the usual object of determining in a new part of the world the acceleration due to gravity, and measured an arc of the meridian extending over rather more than a degree. He made also careful observations of the positions of Mars and Venus, in order that from comparison of them with simultaneous observations in northern latitudes he might get the parallax of the sun (chapter VIII., § 161). These observations of Mars compared with some made in Europe by Bradley and others, and a similar treatment of Venus, both pointed to a solar parallax slightly in excess of 10″, a result less accurate than Cassini’s (chapter VIII., § 161), though obtained by more reliable processes.

A large number of observations of the moon, of which those made by him at the Cape formed an important part, led, after an elaborate discussion in which the spheroidal form of the earth was taken into account, to an improved value of the moon’s distance, first published in 1761.

Lacaille also used his observations of fixed stars to improve our knowledge of refraction, and obtained a number of observations of the sun in that part of its orbit which it traverses in our winter months (the summer of the southern hemisphere), and in which it is therefore too near the horizon to be observed satisfactorily in Europe.

The results of this—one of the most fruitful scientific expeditions ever undertaken—were published in separate memoirs or embodied in various books published after his return to Paris.

224. In 1757, under the title Astronomiae Fundamenta, appeared a catalogue of 400 of the brightest stars, observed and reduced with the most scrupulous care, so that, notwithstanding the poverty of Lacaille’s instrumental outfit, the catalogue was far superior to any of its predecessors, and was only surpassed by Bradley’s observations as they were gradually published. It is characteristic of Lacaille’s unselfish nature that he did not have the Fundamenta sold in the ordinary way, but distributed copies gratuitously to those interested in the subject, and earned the money necessary to pay the expenses of publication by calculating some astronomical almanacks.

Another catalogue, of rather more than 500 stars situated in the zodiac, was published posthumously.

In the following year (1758) he published an excellent set of Solar Tables, based on an immense series of observations and calculations. These were remarkable as the first in which planetary perturbations were taken into account.

Among Lacaille’s minor contributions to astronomy may be mentioned: improved methods of calculating cometary orbits and the actual calculation of the orbits of a large number of recorded comets, the calculation of all eclipses visible in Europe since the year 1, a warning that the transit of Venus would be capable of far less accurate observation than Halley had expected (§ 202), observations of the actual transit of 1761 (§ 227), and a number of improvements in methods of calculation and of utilising observations.

In estimating the immense mass of work which Lacaille accomplished during an astronomical career of about 22 years, it has also to be borne in mind that he had only moderately good instruments at his observatory, and no assistant, and that a considerable part of his time had to be spent in earning the means of living and of working.

225. During the period under consideration Germany also produced one astronomer, primarily an observer, of great merit, Tobias Mayer (1723-1762). He was appointed professor of mathematics and political economy at Göttingen in 1751, apparently on the understanding that he need not lecture on the latter subject, of which indeed he seems to have professed no knowledge; three years later he was put in charge of the observatory, which had been erected 20 years before. He had at least one fine instrument,126 and following the example of Tycho, Flamsteed, and Bradley, he made a careful study of its defects, and carried further than any of his predecessors the theory of correcting observations for instrumental errors.127

He improved Lacaille’s tables of the sun, and made a catalogue of 998 zodiacal stars, published posthumously in 1775; by a comparison of star places recorded by Roemer (1706) with his own and Lacaille’s observations he obtained evidence of a considerable number of proper motions (§ 203); and he made a number of other less interesting additions to astronomical knowledge.

226. But Mayer’s most important work was on the moon. At the beginning of his career he made a careful study of the position of the craters and other markings,