of those minute variations in the positions of stars, from which their proper motions, as well as the finer elements of the planetary theory, are deduced. In Ptolemy's Tables, the smallest quantities that occur are twelfths of a degree, or angles of 5', from which it may be presumed that the astrolabe was incapable of measuring smaller angles. Tycho could not reckon on the errors of his observations being less than a minute; and Hevelius, the most careful of all observers, and with the finest instruments ever constructed prior to the great innovations made by the inventions to which we have alluded, could scarcely answer for less quantities. Such, however, has been the progress of the art of graduation, that in respect of the large instruments employed in our fixed observatories, the accumulated errors of the instrument and the reading can hardly be supposed to exceed two seconds. It is gratifying to reflect, that this great instrumental precision has been mainly brought about by the skill and persevering efforts of British artists, who, since the days of Graham, have maintained an unrivalled superiority in the construction and division of large instruments. The sectors and mural circles of Ramsden were long the admiration of astronomers of all countries. Mr Troughton, who at present stands at the head of our British opticians, has carried the art of dividing still farther, and constructed instruments-fortunately, not few in number-with regard to which, we are at a loss whether to admire most the exquisite execution, or the ingenuity of the contrivances employed to give stability, and to counteract the various permanent causes of derangement. The splendid circles and transit instruments with which he has furnished the Cambridge and Royal Observatories, may be regarded as the triumph of the combined powers of genius and mechanical skill.

Such instruments as those now alluded to can only, by reason of their great size and weight, be employed in permanent observatories; but for many essential purposes, particularly in relation to geodesy, it is absolutely indispensable to have them of portable dimensions; and hence it becomes an object of great importance to reduce the instrument, without diminishing far the accuracy of its performance. For this purpose the repeating circle was invented, which, though little known in this country till of late years, has long been in very general use on the Continent, where it has been employed for the most delicate purposes of astronomy. The idea of this instrument is due to the celebrated Tobias Mayer; but it was Borda who first caused it to be constructed, and recommended it to the attention of observers. In the hands of Reichenbach, it has received several important modifications. Its principal advantages are, that the results which it gives, are little affected by errors of division or

eccentricity; hence it is in a great measure independent of great dexterity on the part of the artist; and the error of reading off is nearly annihilated, by being spread over the total number of observations. These advantages are not, however, procured without some sacrifice; and it is only by a great expense of time and considerable trouble that extreme precision can be obtained from an instrument, whose radius cannot safely exceed nine inches. The observations also require longer computations for their reduction than those made with fixed instruments; and hence, however excellent in principle, it is not well adapted to the ordinary business of the observatory; but it is employed with great advantage in some fundamental determinations, such as the altitude of the pole, the obliquity of the ecliptic, &c.

The repeating circle was invented to obviate the imperfections of division; in proportion, therefore, as the art of dividing becomes more perfect, the instrument will become less necessary, or be replaced by others, affording results of equal accuracy, at a less expense of time and labour. Mr Troughton, in a Memoir which stands at the head of the collection now before us, has described an Altitude and Azimuth circle, which he considers as better adapted to the general wants of the astronomer, and possessing over Borda's circle several very decided advantages. He also thinks it probable, that the latter will soon be entirely superseded. On a subject of this nature, it would be presumptuous to controvert the opinion of that incomparable artist and experienced observer; but whatever may be the ultimate fate of the repeating instrument, it will always remain, in the history of observation, a proud monument of the resources of which science can avail itself, in supplying the imperfections of art.

With regard to instruments, it has been remarked, that a degree of perfection has frequently been expected from them, which it is in vain to hope for from any work executed by human hands; and when their imperfections have been demonstrated, they have been often cast aside, perhaps without good reason, to make room for untried novelties, recommended by the appearance of greater precision in the divisions. The fact is, that even in their most perfect state, they can afford only approximations to truth, and, beyond a certain point, the degree of approximation is not easily estimated. Although they were to leave the hands of their makers absolutely perfect, they could not long preserve that character, being constantly exposed to various causes of derangement which cannot be guarded against, and of which the effects elude calculation. The variations of temperature, and even the action of gravity on the metals of which they are composed, have a constant tendency to destroy the accuracy of the circle, and occasion errors which it requires the utmost vigilance on

the part of the observer, to prevent from attaining such magnitudes as would sensibly vitiate his results. And even if these sources of uncertainty were removed, nature itself, in the variable state of the atmosphere as to its refractive powers, has interposed an obstacle which sets human skill and ingenuity at deFor all these reasons, the probability is extremely small that greater instrumental accuracy will ever be attained, or the art of observing carried to a much greater degree of preci

sion.

The art of constructing optical instruments received a great impulse from the successful attempts of the late Sir William Herschel to increase the powers of the reflecting telescope. This instrument, as most of our readers must be aware, was first proposed by the celebrated James Gregory, in his Optica Promota, with a view to obviate the imperfections of the images formed by spherical lenses; and was afterwards recommended by Newton, who, not aware of the different ratio that subsists between the refractive and dispersive powers of different diaphanous substances, despaired of finding any means to avoid, in refracting telescopes, the colour produced by the unequal refrangibility of the rays of light. Sir W. Herschel succeeded in casting and polishing metallic specula, far surpassing in magnitude any thing of the kind that had before been attempted, and was, in consequence, enabled to construct telescopes of unrivalled powers, which yielded him a rich harvest of discovery. An ingenious amateur (Mr Ramage, of Aberdeen) has recently constructed telescopes on this principle, equally magnificent, and perhaps superior in some respects to those of Herschel. One of these telescopes, mentioned in a descriptive account which he has given of them in the second volume of the Memoirs, has a mirror, whose diameter is 21 inches, and focal length 54 feet. The speculum of Herschel's great telescope was, indeed, 48 inches in diameter, but the instrument was found to be by far too unwieldy to be of any practical use.

The great magnifying power which the reflecting telescope carries, renders it a most valuable instrument in exploring the heavens, but in practice it is attended by several grave inconveniences; and, in particular, the difficulty and expense of its construction, together with the trouble required in managing its cumbersome machinery, have hitherto prevented it from being commonly adopted in the observatory. It is found difficult to preserve the speculum, for any length of time, from being tarnished by oxidation; and its weight peculiarly exposes it to injury from a change of figure. But the greatest objection to it is, that it has not yet been found practicable to adapt it to transit instruments or azimuth circles; so that its use is confined to the

observation of phenomena of simple apparition, with regard to which the measurement of angles is unnecessary. For all these reasons the attention of astronomers has been anxiously directed to the means of augmenting the optical power of the achromatic refracting telescope, an instrument much more commodious, and adapted to every sort of observation. In the discovery of the different relations existing between the refractive and dispersive powers of different kinds of glass, Dolland removed the obstacle which Newton had judged insurmountable; and succeeded in fabricating object-glasses of a degree of excellence to rival which the Continental artists found all their efforts in vain, though guided by the profound theory of Clairaut and d'Alembert. But, however excellent in other respects, the object-glasses of Dolland were still of very limited dimensions, and all attempts to manufacture them on a larger scale failed, through the difficulty of procuring discs of flint-glass of the requisite size, sufficiently free from impurities. This difficulty was eventually overcome by Fraunhofer, an artist whose talents had raised him from the situation of a simple labourer in the manufactory of optical glasses at Munich, to that of superintendent of the establishment. After a long series of admirably conducted experiments, Fraunhofer at length discovered the secret (which, however, he seems never to have divulged) of the composition of flint-glass, of perfect homogeneity, and of any required dimensions. Formerly, the fabrication of achromatic object-glasses exceeding seven inches in diameter, was considered as impracticable. The magnificent telescope constructed by Fraunhofer, which was purchased by the Russian government for the observatory at Dorpat, has an objective of nine inches in diameter. Fraunhofer executed another of twelve inches, and even considered an objective of eighteen inches in diameter as not beyond the reach of his art. Other Continental artists have succeeded in manufacturing flint-glass of considerable size, and of the desired purity, but good specimens are still exceedingly rare, and consequently the prices demanded for them exorbitant; so much so, indeed, that Mr South, the present President of the Astronomical Society, thought himself fortunate in procuring lately, in Paris, an achromatic object-glass of eleven inches and seven-tenths clear aperture, at an expense, it is understood, of L.1000.*

*The flint-glass employed in the construction of this objective, was manufactured by the late Guinand le Père; and the grinding and polishing was executed by M. Cauchoix of Paris. Its focal length is 19 feet. Mr Troughton has undertaken to form with it an equatorial instrument; when completed, it will doubtless be the most magnificent in Europe.

It redounds little to the credit of this country to have lost the decided superiority she once possessed in the manufacture of an article, not only important in reference to astronomical purposes, but even of some consequence in a commercial point of view; and the cause has been usually ascribed to the operation of certain fiscal regulations, which prevent experiments, and compel the manufacturer to follow a blind routine. The directors of the Treasury, indeed, a few years ago, yielded so far to the solicitations and complaints of those interested in the progress of science, as to allow a committee of Fellows of the Royal Society to institute experiments on the subject, without being exposed to the intrusion of the tax-gatherer. Unfortunately, however, discoveries do not always arise when it is desirable they should; and although the researches of the Royal Society's committee have not been altogether unsuccessful, the object sought after has not yet been completely attained. In the meantime, therefore, our astronomers must procure their object-glasses whereever they can be found, even at the heavy prices demanded by those whom chance or skill has put in possession of the materials of their fabrication.

Such are the means possessed by the astronomer of the present day for exploring the heavens. Let us now look at the results which have been obtained, and enquire whether the recent progress of the science itself has kept pace with that of the assistant arts.

Astronomy, as we have already mentioned, underwent its last. great revolution in the hands of Bradley. Before the discovery of the aberration of light, and the nutation of the earth's axis, the observed places of the celestial bodies were affected by unaccountable anomalies, which rendered it impossible, by a comparison of different observations, to arrive at the exact values of the co-efficients of the astronomical tables. The rate of precession could not be accurately ascertained, nor the proper motions of the stars perceived at all, while general motions, of greater magnitude, and of which the laws were entirely unknown, affected the whole firmament. Picard, for instance, who introduced the micrometer, and who consequently was the first that observed with a degree of accuracy at all approaching to modern precision, found anomalous variations in the zenith distances of Polaris amounting to forty seconds, which Bradley happily demonstrated to be occasioned by the progressive motion of light, combined with that of the earth in its orbit. declinations likewise varied, through the effects of nutation, to the amount of sixteen or eighteen seconds. The observer, having thus no fixed terms of comparison, could never be very cer

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