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

These observations fall into two chief divisions of unequal merit, those after 1749 having been made with some more accurate instruments which a grant from the government enabled him at that time to procure.

The main work of the Observatory under Bradley consisted in taking observations of fixed stars, and to a lesser extent of other bodies, as they passed the meridian, the instruments used (the “mural quadrant” and the “transit instrument”) being capable of motion only in the meridian, and being therefore steadier and susceptible of greater accuracy than those with more freedom of movement. The most important observations taken during the years 1750-1762, amounting to about 60,000, were published long after Bradley’s death in two large volumes which appeared in 1798 and 1805. A selection of them had been used earlier as the basis of a small star catalogue, published in the Nautical Almanac for 1773; but it was not till 1818 that the publication of Bessel’s Fundamenta Astronomiae (chapter XIII., § 277), a catalogue of more than 3000 stars based on Bradley’s observations, rendered these observations thoroughly available for astronomical work. One reason for this apparently excessive delay is to be found in Bradley’s way of working. Allusion has already been made to a variety of causes which prevent the apparent place of a star, as seen in the telescope and noted at the time, from being a satisfactory permanent record of its position. There are various instrumental errors, and errors due to refraction; again, if a star’s places at two different times are to be compared, precession must be taken into account; and Bradley himself unravelled in aberration and nutation two fresh sources of error. In order therefore to put into a form satisfactory for permanent reference a number of star observations, it is necessary to make corrections which have the effect of allowing for these various sources of error. This process of reduction, as it is technically called, involves a certain amount of rather tedious calculation, and though in modern observatories the process has been so far systematised that it can be carried out almost according to fixed rules by comparatively unskilled assistants, in Bradley’s time it required more judgment, and it is doubtful if his assistants could have performed the work satisfactorily, even if their time had not been fully occupied with other duties. Bradley himself probably found the necessary calculations tedious, and preferred devoting his energies to work of a higher order. It is true that Delambre, the famous French historian of astronomy, assures his readers that he had never found the reduction of an observation tedious if performed the same day, but a glance at any of his books is enough to shew his extraordinary fondness for long calculations of a fairly elementary character, and assuredly Bradley is not the only astronomer whose tastes have in this respect differed fundamentally from Delambre’s. Moreover reducing an observation is generally found to be a duty that, like answering letters, grows harder to perform the longer it is neglected; and it is not only less interesting but also much more difficult for an astronomer to deal satisfactorily with some one else’s observations than with his own. It is not therefore surprising that after Bradley’s death a long interval should have elapsed before an astronomer appeared with both the skill and the patience necessary for the complete reduction of Bradley’s 60,000 observations.

A variety of circumstances combined to make Bradley’s observations decidedly superior to those of his predecessors. He evidently possessed in a marked degree the personal characteristics—of eye and judgment—which make a first-rate observer; his instruments were mounted in the best known way for securing accuracy, and were constructed by the most skilful makers; he made a point of studying very carefully the defects of his instruments, and of allowing for them; his discoveries of aberration and nutation enabled him to avoid sources of error, amounting to a considerable number of seconds, which his predecessors could only have escaped imperfectly by taking the average of a number of observations; and his improved tables of refraction still further added to the correctness of his results.

Bessel estimates that the errors in Bradley’s observations of the declination of stars were usually less than 4″, while the corresponding errors in right ascension, a quantity which depends ultimately on a time-observation, were less than 15″, or one second of time. His observations thus shewed a considerable advance in accuracy compared with those of Flamsteed (§ 198), which represented the best that had hitherto been done.

219. The next Astronomer Royal was Nathaniel Bliss (1700-1764), who died after two years. He was in turn succeeded by Nevil Maskelyne (1732-1811), who carried on for nearly half a century the tradition of accurate observation which Bradley had established at Greenwich, and made some improvements in methods.

To him is also due the first serious attempt to measure the density and hence the mass of the earth. By comparing the attraction exerted by the earth with that of the sun and other bodies, Newton, as we have seen (chapter IX., § 185), had been able to connect the masses of several of the celestial bodies with that of the earth. To connect the mass of the whole earth with that of a given terrestrial body, and so express it in pounds or tons, was a problem of quite a different kind. It is of course possible to examine portions of the earth’s surface and compare their density with that of, say, water; then to make some conjecture, based on rough observations in mines, etc., as to the rate at which density increases as we go from the surface towards the centre of the earth, and hence to infer the average density of the earth. Thus the mass of the whole earth is compared with that of a globe of water of the same size, and, the size being known, is expressible in pounds or tons.

By a process of this sort Newton had in fact, with extraordinary insight, estimated that the density of the earth was between five and six times as great as that of water.122

It was, however, clearly desirable to solve the problem in a less conjectural manner, by a direct comparison of the gravitational attraction exerted by the earth with that exerted by a known mass—a method that would at the same time afford a valuable test of Newton’s theory of the gravitating properties of portions of the earth, as distinguished from the whole earth. In their Peruvian expedition (§ 221), Bouguer and La Condamine had noticed certain small deflections of the plumb-line, which indicated an attraction by Chimborazo, near which they were working; but the observations were too uncertain to be depended on. Maskelyne selected for his purpose Schehallien in Perthshire, a narrow ridge running east and west. The direction of the plumb-line was observed (1774) on each side of the ridge, and a change in direction amounting to about 12″ was found to be caused by the attraction of the mountain. As the direction of the plumb-line depends on the attraction of the earth as a whole and on that of the mountain, this deflection at once led to a comparison of the two attractions. Hence an intricate calculation performed by Charles Hutton (1737-1823) led to a comparison of the average densities of the earth and mountain, and hence to the final conclusion (published in 1778) that the earth’s density was about 4-1∕2 times that of water. As Hutton’s estimate of the density of the mountain was avowedly almost conjectural, this result was of course correspondingly uncertain.

A few years later John Michell (1724-1793) suggested, and the famous chemist and electrician Henry Cavendish (1731-1810) carried out (1798), an experiment in which the mountain was replaced by a pair of heavy balls, and their attraction on another body was compared with that of the earth, the result being that the density of the earth was found to be about 5-1∕2 times that of water.

The Cavendish experiment, as it is often called, has since been repeated by various other experimenters in modified forms, and one or two other methods, too technical to be described here, have also been devised. All the best modern experiments give for the density numbers converging closely on 5-1∕2, thus verifying in a most striking way both Newton’s conjecture and Cavendish’s original experiment.

With this value of the density the mass of the earth is a little more than 13 billion billion pounds, or more precisely 13,136,000,000,000,000,000,000,000 lbs.

220. While Greenwich was furnishing the astronomical world with a most valuable series of observations, the Paris Observatory had not fulfilled its early promise. It was in fact suffering, like English mathematics, from the evil effects of undue adherence to the methods and opinions of a distinguished man. Domenico Cassini happened to hold several erroneous opinions in important astronomical matters; he was too good a Catholic to be a genuine Coppernican, he had no belief in gravitation, he was firmly persuaded that the earth was flattened at the equator instead of at the poles, and he rejected Roemer’s discovery of the velocity of light. After his death in 1712 the directorship of the Observatory passed in turn to three of his descendants, the last of whom resigned office in 1793; and several members of the Maraldi family, into which his sister had married, worked in co-operation with their cousins. Unfortunately a good deal of their energy was expended, first in defending, and afterwards in gradually withdrawing from, the errors of their distinguished head. Jacques Cassini for example, the second of the family (1677-1756), although a Coppernican, was still a timid one, and rejected Kepler’s law of areas; his son again, commonly known as Cassini de Thury (1714-1784), still defended the ancestral errors as to the form of the earth; while the fourth member of the family, Count Cassini (1748-1845), was the first of the family to accept the Newtonian idea of gravitation.

Some planetary and other observations of value were made by the Cassini-Maraldi school, but little of this work was of first-rate importance.

221. A series of important measurements of the earth, in which the Cassinis had a considerable share, were made during the 18th century, almost entirely by Frenchmen, and resulted in tolerably exact knowledge of the earth’s size and shape.

The variation of the length of the seconds pendulum observed by Richer in his Cayenne expedition (chapter VIII., (§ 161) had been the first indication of a deviation of the earth from a spherical form. Newton inferred, both from these pendulum experiments and from an independent theoretical investigation (chapter IX., § 187), that the earth was spheroidal, being flattened towards the poles; and this view was strengthened by the satisfactory explanation of precession to which it led (chapter IX., § 188).

On the other hand, a comparison of various measurements of arcs of the meridian in different latitudes gave some support to the view that the earth was elongated towards the poles and flattened towards the equator, a view championed with great ardour by the Cassini school. It was clearly important that the question should be settled by more extensive and careful earth-measurements.

The essential part of an ordinary measurement of the earth consists in ascertaining the distance in miles between two places on the same meridian, the latitudes of which differ by a known amount. From these two data the length of an arc of a meridian corresponding to a difference of latitude of 1° at once follows. The latitude of a place is the angle which the vertical at the place makes with the equator, or, expressed in a slightly different form, is the angular distance of the zenith from the celestial equator. The vertical at any