THE methods of investigation adopted in this work are in accordance with what may be called the modern school of practical astronomy, or more istinctively the German school, at the head of which stands the unrivalled BESSEL. In this school, the investigations both of the general problems of Spherical Astronomy and of the Theory of Astronomical Instruments are distinguished by the generality of their form and their mathematical rigor. When approximative methods are employed for convenience in practice, their degree of accuracy is carefully determined by means of exact formulae previously investigated ; the latter being developed in converging series, and only such terms of these series being neglected as can be shown to be insensible in the cases to which the formulae are to be applied. A.nd it is an essential condition of all the methods of computation from data furnished by observation, that the errors of the computation shall always be practically insensible in relation to the errors of observation : so that our results shall be purely the legitimate deductions from the observations, and free from all avoidable error.

THE present volume has been prepared in response to a rather pressing demand for a text-book intermediate between the author's Elements of Astronomy and his Greneral Astronomy. The latter is found by many teachers to be too large for convenient use in the time at their disposal, while the former is not quite sufficiently extended for their purpose.

I BEGAN in the year 1843 a Course of Lectures on Practical Astronomy and Astronomical Instruments, having been at that time seven years Director of the Cambridge Observatory. Lectures on these subjects had already been given by Dr Peacock as Lowndean Professor, which he discontinued on the understanding that I would undertake to carry them on. The circumstances that an Astronomical Observatory so well appointed as that of Cambridge was near at hand, and was provided with various instruments of first-rate quality, appeared to me to give facilities for lecturing on Practical Astronomy which ought to be taken advantage of ; and accordingly I commenced lecturing in the abovenamed year, having previously produced a 'Syllabus' of the subjects of the lectures, and procured a considerable number of wooden models, which, together with some apparatus that had been collected by Professor Peacock, I made use of in conducting and illustrating the Lectures, I had also the advantage of having at command several portable instruments pertaining to the Observatory. At the end of the Syllabus a list of formulae applicable to the reduction of astronomical observations was introduced, accompanied by brief demonstrations...

THE subjects treated in elementary text-books of astronomy which are most difficult and discouraging to the beginner are those which deal with the diurnal motion of the heavens and the apparent motions of the sun, moon, and planets among the stars. A clear conception of these fundamental facts is, however, necessary to a proper understanding of many of the striking phenomena to which the study of astronomy owes its hold upon the intellect and the imagination...

THE rapid advance in the cultivation of Practical Astronomy which has recently been made in the United States is one of the most encouraging features of the age. It is less than twenty-five years since the first refracting telescope, exceeding those of a portable size, was imported into the United States, and the introduction of meridional instruments of the large class is of still more recent date. "We may now boast of two Observatories, liberally equipped with instruments of the best class, and provided with a permanent corps of observers, as also a considerable number of other establishments more or less complete, and a still larger number of telescopes of dimensions adequate to be employed in original research...

THE great progress of astronomical discovery, during the *ast few years, has induced the author of this work to prepare, with much labor and expense, a new edition, which should fully exhibit the features of the science in their latest physiognomy. Since the stereotype edition was first published, in 1844, numerous and important discoveries have been made, both in the solar system and among the fixed stars. The dimensions of the planetary system have been nearly doubled by the addition of the planet Neptune ; the number of the Asteroids has been increased from four to twenty-seven ; interesting discoveries have been made in the Rings of Saturn, and an eighth member has been added to his retinue of satellites ; and the subject of Comets has received a new impulse by the appearance of the remarkable cornet of 1843...

An attempt has been made in these pages to trace the evolution of intellectual thought in the progress of astronomical discovery, and,by recognising the different points of view of the different ages, to give due credit even to the ancients. No one can expect, in a history of astronomy of limited size, to find a treatise on "practical" or on "theoretical astronomy," nor a complete "descriptive astronomy," and still less a book on "speculative astronomy." Something of each of these is essential, however, for tracing the progress of thought and knowledge which it is the object of this History to describe...

THE chief authority for the Life of Sir William Herschel is Mrs. John Herschel's " Memoir of Caroline Herschel " (London, 1876). It embodies Caroline's Journals and Recollections, the accuracy of which is above suspicion. William himself, indeed, referred to her for dates connected with his early life. The collateral sources of information are few and meagre ; they yield mere gleanings, yet gleanings worth collecting. Professor E. S. Holden has had recourse to many of them for his excellent little monograph entitled "Herschel, his Life and Works" (London, 1881), which is usefully supplemented by "A Synopsis of the Scientific Writings of Sir William Herschel," prepared by the same author with the aid of Professor Hastings...

FOR a full explanation of the circumstances in virtue of which the matter forming the contents of this volume now appears dissociated from that to which it was joined in the first three editions of this work the reader is referred to Vol. I. of the 4th edition, published in September, 1889. Suffice it therefore now to state briefly what has been done to render the contents of this volume as acceptable as possible to the public.