order that there might be obtained a sufficient number of equations to determine all the unknown quantities: and, from the above named value of the sun's parallax, 8". 8, the distance of the sun from the earth is found to be equal to 23465 semi-diameters of the latter.

The eighteenth century is become celebrated, also, for the improvements made in telescopes and in the instruments employed for the purposes of nautical astronomy. The field of view, in the telescopes which had been in use before the middle of the century, was unavoidably small, and the illumination of the object consequently feeble, on account of the apparent distortion of the image, and the coloured fringes with which it was surrounded, when the aperture of the instrument was extensive enough to allow the admission of as much light as would render the object sufficiently brilliant; but, in 1757, Mr. Dollond, guided by the theories of Euler and Clairaut and by his own experiments on lenses formed of glass possessing different degrees of refractive power, invented, or at least made public, a construction in which the chromatic aberration, as it was called, was almost wholly removed, and the spherical aberration materially diminished. These ends were gained by forming a compound object glass consisting of a convex and concave lens having different degrees of dispersive power with respect to rays of the different colours, these being separated from each other in their passage through the glasses, whose surfaces act upon the light like those of a prism: in such compound lens, by a proper adaptation of the focal lengths of the two glasses, the rays of the different colours could be made to unite nearly in the place where the image is formed; and thus the latter was rendered sufficiently free from the colours with which, in the old construction, it was embarrassed. By a just adaptation of the curvature of the surfaces of the object glasses, and by dividing the whole refraction of the light coming from the image in the focus, among the four different eye-glasses of the telescope, the distortion of the image was also, nearly, corrected: and thus greater magnifying power and perfection of vision was obtained.

From that time scarcely any improvement can be said to have

been made in what are called, from the absence of the prismatic colours, achromatic telescopes; but the telescopes formed with metallic specula have undergone several changes, and the instruments of this kind, constructed by the late Sir William Herschell, far exceeding in magnifying power any of those formed wholly with glass lenses, have contributed materially to increase our knowledge of the constitution of the heavenly bodies.

In 1731, Mr. Hadley, the ingenious contemporary of Bradley and Molyneux, pursuing a principle which had been proposed by Newton, brought to a state of great perfection the reflecting octant and sextant, by which the altitudes of the sun, moon and stars, and the angular distances between them have ever since been measured for the purpose of obtaining, by celestial observations, the latitude and longitude of a ship at sea, or of a place on land, where the instruments employed in regular observatories are not to be had. A considerable change, however, has since taken place in instruments of this nature by making them completely circular, and capable of measuring the angle between the objects many times successively, in consequence of which the greatest correctness may be obtained. Mayer, of Gottingen, in 1758, first constructed such repeating circles, as they were called, and they have since been much improved; but that kind which possesses the highest character for accuracy was made public by the chevalier Borda, in 1789.

It appears from a report made by Newton, in 1714, to a committee of the House of Commons, on a method proposed by Whiston for finding the longitude of a ship at sea by the place of the moon, that the theory of the latter was not, then, accurate enough to determine that element within less than two or three degrees of the truth: but, in proportion as improvements were made in the instruments of observation, the inequalities of the moon's motions were more correctly determined; and Mayer, who had diligently applied himself to this branch of astronomy, succeeded in constructing a set of lunar tables from which the distance between the sun, or a star, and the moon, could be computed for any given time with sufficient correctness to become capable, by comparison with the observed distance, of

serving in the determination of the great problem of terrestrial longitude. These, and a set of improved solar tables, were published by Mayer in 1770; he did not, however, live to enjoy all the fruits of his labours, but his widow received from the British government the reward which it had previously offered to any one who should bring the tables to the required degree of accuracy. Since this period, therefore, the distances between the moon and sun, and between the moon and certain fixed stars have been computed for every three hours in each day, as they would appear at the places of some of the principal observatories in Europe, and are published in the Astronomical Ephemerides for years in advance; so that, by comparing them with the distances actually observed in other places, the difference between the corresponding time given in the Ephemeris and that found at the place of observation, which expresses the difference in the longitudes of the two places, is immediately found. This is not all the advantage derived from the publication of these Ephemerides; in them are also given, besides many other articles of great value to the practical astronomer, the times of the immersions and emersions of Jupiter's satellites, by which a scientific traveller, on land, (for the method is not practicable at sea on account of the motion of the ship,) observing the same phenomena in a telescope of sufficient magnifying power, can, also, determine his longitude by a comparison of the time found at the place of observation with that given in the Ephemeris.

But, to these means of facilitating the solution of that useful problem, must be added the perfection attained in the constructions of instruments for measuring time. In 1764, Harrison completed a chronometer which, having been taken across the Atlantic, and being found on its return to have deviated from the true time only 54 seconds, in an interval of 156 days, was considered as having fulfilled the conditions required to entitle the maker to the reward offered by government for a machine capable of keeping time with sufficient accuracy to serve for finding the longitude at sea; the promised sum, [£10,000,] was, consequently, paid to the ingenious mechanic, and the

use of chronometers, for that purpose, by nautical men, during long voyages, has ever since been general. A seaman, therefore, previously to his departure from the British shores, has only to set the index of the machine to the actual instant of mean time on the meridian of the Greenwich observatory; and, in any part of the world, however remote from thence, if he find his time by celestial observations, his distance, in longitude, from that meridian, will be expressed at once by the difference between the time thus found and that shewn by the chronometer.

CHAPTER XXII.

OPERATIONS FOR DETERMINING THE FIGURE OF THE EARTH.

An arc of the terrestrial meridian measured in France by Picard and Cassini.-The terrestrial spheroid supposed at first to be prolate.-Proof of the diminution of gravity in the equatorial regions.-Arcs of the meridian measured in Lapland and Peru.-The figure of the earth proved to be oblate.- Trigonometrical operations in England.-Arcs of the meridian measured in various parts of the world.--Great geodetical operations in France and Spain. -Experiments of Captain Sabine on the lengths of pendulums.-Ratio of the earth's equatorial and polar diameters.-Effects of local attractions in geodetical and astronomical observations.

IN the time of Newton the question of the dimensions and figure of the earth particularly engaged the attention of mathematicians, and several efforts were made to determine both, by ascertaining, and comparing together, the lengths of certain portions of the terrestrial meridian. The attempts of the ancient Greeks and Arabians to acquire a knowledge of the earth's magnitude have been already mentioned, and we may observe that similar attempts had, just before the time of which we are speaking, been made by Ricciolus, Fernel, and Snellius, on the continent, and by Norwood in England; but from their labours no satisfactory conclusion could be obtained, on account of the inaccuracy of their itinerary measurements. At length, about the year 1670, the French Academy of Sciences engaged Picard to determine the distance, in the direction of the meridian, from Malvoisine to Amiens, by means of a measured base line, and a series of triangles formed between those places. This base was made a side of one of the triangles, and the angles of all the triangles being taken with instruments, the lengths of the several sides were computed; from which, with the observed azimuths, or bearings of the sides from the meridian, the corresponding arcs of the meridian were found: finally, comparing the length of the whole arc with the difference, in latitude, between its