twelve hundred observations of Bradley, added much to the accuracy of the tables; and more recently, Bouvard, Burg, and Burckhardt, by the aid of the theoretic researches of Laplace, and the recorded observations of the Greenwich observatory, have improved them still farther. At the present time, the greatest error of the lunar tables, cannot exceed 15". But, whatever be the merit of these successive labours, and of those which must be undertaken hereafter, it is but just to say, that none of these tables are entirely new, but are no more than the tables of Mayer, adapted more closely to the results of more numerous observations. These tables will, therefore, render for ever famous, the name of Mayer, to whom may be applied the verse of Ovid.

"Cum Sole et Luna semper Aratus erit."

The method of lunar observations, thus prepared for application by the tables of Mayer, and the corrections of Mason, was fitted för general use by the exertions of Maskelyne, who, in preparing the requisite tables, and publishing in the nautical almanac, annually, rules for the calculations by which the observed distances are freed from the effects of parallax and refraction, rendered a most important service to mariners. In these useful labours he justly prided himself, and was hence led, in addition to his laborious duties as an observer, to superintend with the utmost attention, the calculations and publication of that Ephemeris. This interest could not be felt by his successor, and hence, for some years after his death, the reputation of the nautical almanac declined, until the board of longitude of Great Britain, with great judgment, confided it to another hand, and left the Astronomer Royal to devote his whole attention to the direct duties of his office.

With the same zeal for the extension of the practical benefits of his science, he took great interest, and applied no small labour in examining the fitness of the chronometers, proposed by Harrison, for the determination of the longitude; and upon his report, the remaining part of the reward of four thousand pounds sterling, one half of which we have seen adjudged to the tables of Mayer, was paid to that ingenious mechanic.

Having already devoted so much space to the history of observatories, we shall dwell no longer on that part of the subject, but proceed to follow the course suggested by the mention of Harrison.

Huygens, in adapting the pendulum to the clock, had furnished astronomers with a measure of time, far more accurate than any before employed. Still, it was not absolutely perfect. Besides various mechanical defects in the clock itself, many of which have since been removed or obviated, the pendulum cannot be made of materials which are not subject to dilatation and con

traction by changes of temperature. Hence arises a constant variation in the rate of the clock. Graham, in considering this subject, conceived, that were it possible to make the body of the pendulum of one metal, and the rod of another, in such proportion, that the expansion of the one upwards, should exactly counteract that of the other downwards, the centre of oscillation might, in the variation of the extreme distance between the ends of the pendulum, be retained in a constant position. The clock would thus be rendered isochronous under all varieties of temperature. In experiments on the solid metals, he found none that would answer his purpose; mercury, however, dilating more than any of them, was fitted to produce the desired effect, and by substituting a vase of that metal, supported from beneath by the rod of the pendulum, and thus supplying the place of the solid lens, he effected the compensation, and constructed what is called the Mercurial Pendulum. This is, perhaps, even at the present day, the best that can be used in a fixed observatory.

Harrison returned to the attempt to employ the solid metals; but abandoning the impracticable endeavour to make the lens of the pendulum of one, and the rod of another, he sought to compensate the latter alone. He succeeded in this, by a combination of bars of different metals, expanding and contracting in opposite directions. This compensation, although less perfect than that of Graham, is the most easy in its use, and particularly when the clock is not permanently fixed at a single place, but occasionally carried and set up at others.

A time-keeper, regulated by a pendulum, does not, however, go during the time of its removal from place to place, and is stopped by the motion of a vessel; neither is its rate the same in different latitudes. Hence it is useless, when we wish to convey the time of a given place to another, for the purpose of determining longitude, by the difference of apparent time at the two places. To such purposes, a watch, or time-keeper, regulated by a balance, is alone applicable. But this, like the clock, is affected in its rate, by variations of temperature changing the diameter of its balance, and the tension of the spring by which that regulator reacts upon the train of wheels. A remedy for this, was found by Harrison, who applied the same principle he had used in his gridiron-pendulum, to a curb acting upon the balance spring. Other mechanics have made the balance itself of two metals; cutting the circumference into several arcs, whose curvations change with changes of heat, and thus tend to alter the position of the centre of gyration of the wheel, as much as the dilatation or the contraction of the radii tends to move that point in an opposite direction. Even before the close of the eighteenth century, such instruments had attained a high degree

of accuracy, and have recently been still farther improved; so much so, indeed, that little more is left to be desired."

The improvement of instruments for observation, during the eighteenth century, was not less than that effected in time-keeping. We have spoken of the invention of the telescope, its proposed application to instruments for the measure of angles, by Picard, and its actual use by Roëmer and Flamstead. Still, it had many inherent imperfections. Constructed of spherical lenses, it was not capable of making a perfect image, and was, besides, affected by the unequal refrangibility of the rays of light. Before the time of Newton, a remedy had been sought for these defects, by increasing the length of the telescope, until it became too unwieldy to be managed; but on his discovery of the different refraction of the rays of light, it became obvious that this increased length was insufficient of itself. He therefore abandoned the attempt to improve refracting instruments, and pointed out the principle of the reflecting telescope. This received various successive improvements, until in the hands of Herschel it became the means of most important discoveries.

Newton had, however, in his experiments on refracting substances, been led into an error, when he inferred, that the refractive and dispersive powers of different transparent substances, always followed the same law. A striking proof to the contrary exists, in the structure of the eyes of animals; and an analogous, artificial combination was sought, by which, while the power of convergence should be retained, that of dispersion might be counteracted. Euler pursued this investigation, by mathematical methods alone, and was not successful; but Dollond, an English maker of philosophical instruments, discovered experimentally, a combination of glasses that answered the purpose. Some years before his time, an attempt had been made, and had succeeded, to produce a similar result, by the union of a solid, with a transparent liquid; but it had never come into general use, and was forgotten, until recalled to memory, by the improvement of Dollond. Since his day, telescopes of high power, yet of no great length, and entirely free from the chromatic aberration, have been within the reach of astronomers, not only for the mere view of the heavenly bodies, but set up as transits, and forming the sights of instruments for the measurement of angles.

The graduation of instruments for the measurement of angles, was, during the whole of the eighteenth century, receiving improvements. That of great instruments for fixed observatories, is performed originally, and de novo, in each case, by the aid of proper geometrical methods and apparatus. In the successive hands of Graham, Bird, Ramsden, and the two Troughtons, this branch of the art has reached a very high degree of perfection. It is, however, too expensive, and requires too high a degree

both of theoretic knowledge and practical skill, to be applied to the construction of the more usual instruments employed in practical astronomy. Hence, in the early part of the century, such were either too expensive for common use, or so imperfect as to be of little value. Ramsden, however, invented an instrument, which, if once accurately constructed, can be applied to transfer to the limb of any circle whatsoever, if only less in radius than itself, divisions as accurate as its own. This method of Ramsden, is now used in the construction of all instruments except great murals, and has tended, in a high degree, to the promotion of practical astronomy, by facilitating the fabrication of instruments, and reducing them to a lower price.

The astronomical quadrant, was originally used, as we have seen, by Ptolemy. It was the most important graduated instrument of his successors, and finally, in the hands of Flamstead, had superseded all others, in fixed observatories. Two quadrants, one by Graham, and the other by Bird, suspended upon the same wall, and turned to the two opposite arcs of the meridian, had been successively used by Bradley and Maskelyne. Until towards the very close of the eighteenth century, the observations of Greenwich, were so superior, both from the quality of the instruments, and the attention of the astronomers, as to be looked up to as models of accuracy in every possible respect. When, however, observations began to be multiplied, by men of equal skill and accuracy, with instruments of equal, or even greater nicety of structure and division, discrepancies began to be noted, which it was finally discovered could only arise from differences in the instruments themselves. No sooner were these thus shown to exist, than theory pointed out physical causes of error in the quadrants, to which they might be ascribed.

However accurately and carefully an arc of a circle may be graduated; the very nature of the materials, and the imperfection of workmanship, together with the fact that the divisions cannot be strict mathematical lines, will render the spaces unequal among themselves. When a heavy instrument is suspended upon a wall, its own weight will tend to change its figure, however strongly it may be braced, and thus a new cause of error is introduced, for the arc will be no longer circular. The alternations of temperature acting upon the braces, and upon the arc, will cause a third set of errors; and these last will be constantly varying. Finally, the telescope cannot be placed so as to move with absolute certainty around the centre of the arc; and thus, did even no other source of error exist, the observed angle would differ from that cut off upon the graduated limb.

These causes of error, existing in the very nature of the materials and of the workmanship, it became necessary, so soon as the accuracy of observation was so far improved as to cause them

to interfere with that of the result, to seek a remedy. This has been found in the substitution of the entire circle for a quadrantal arc. The observations of Roëmer had been performed with such an instrument; and it is probable, that had his records been preserved, the error and the remedy would have long before been detected.

Ramsden, being employed to make an instrument for the observatory at Palermo, since rendered illustrious, by its astronomer Piazzi, was the first, in recent times, to construct a great circle for fixed observations. They have finally entirely superseded the quadrant; but their introduction into other observatories belongs to the history of the astronomy of our own age.

In a circular instrument, the angle may be read upon various parts of the limb, each unequally affected by the several causes of error of division, and change of figure. If their sum include the whole circle, the sum of the errors is 0. The error of eccentricity is met by a mathematical property of the circle, and the result is, therefore, absolutely correct, so far as this is concerned.

The circle was introduced as a portable instrument, before it came into use as a mural. When thus applied, it is made to fulfil a condition originally proposed by the same Mayer, whom we have seen to have made such important improvements in the lunar tables. This consists in repeating the measure of an angle in succession, along the limb of the instrument, beginning each repetition at the point reached by the former measure. By this means, as a much greater arc will finally be passed over, and as the readings may be made on several points of the circle, all the usual causes of error are avoided, while, in addition, the smallest division of the instrument is subdivided as many times as the angle is repeated. Hence, a small, and even imperfect instrument, may be made to produce accuracy as great, or even greater, than the very largest and best of the old constructions. This principle of Mayer was introduced into astronomical instruments by Borda, and has tended most materially to the facility of multiplying accurate observations, in places where they would otherwise have been impossible. Nautical astronomy has been also much advanced by the introduction of instruments adapted to the peculiar circumstances of the place of observation, the deck of a vessel in motion. For such a purpose, the plumb-line and spirit-level are entirely useless. The principle of reflection, by which the image of an object might be brought into contact with another viewed directly, an operation whose certainty depends upon the direction of the places of mirrors, and the permanency of the objects viewed, but is independent of oscillations in the place of the spectator, was proposed by Newton; but, it did not receive a shape in its application, which fitted it for practical