The endeavour to understand events in nature is as old as civilisation. In each of its three great seminal areas the Chinese, the Indian and the West Asian-European men tried to find a logic in the mysterious and an order in the chaotic. They made many attempts, sometimes revealing strange similarities in these totally different societies, to express general truths from which particular events would follow as rational, comprehensible consequences. They tried to describe and analyse in order to understand, for men could not live in the world without seeking to assign causes to the things that happen in it.

ALL sciences are making an advance, but Astronomy is moving at the double-quick. Since the principles of this science were settled by Copernicus, four hundred years ago, it has never had to beat a, retreat. It is rewritten not to correct material errors, but to incorporate new discoveries.

In the following pages I have endeavoured to give a simple account of some of the more interesting " Recent Advances in Astronomy". To harmonize with the general scheme of the series of which this work forms a volume, it was at first suggested that I should develop recent progress in Astronomy jf historically.

In the following pages I have endeavoured to give a simple account of some of the more interesting " Recent Advances in Astronomy". To harmonize with the general scheme of the series of which this work forms a volume, it was at first suggested that I should develop recent progress in Astronomy historically. The difficulties in the way of treating any branch of science in such a manner are, however, very considerable ; especially when, as in the present instance, it is desired to present the subject in such a manner as to be readily followed by those who have but slight familiarity with its technicalities.

THE authorities which have been principally relied on in compiling the following work are : " Le Opere complete di Galileo Galilei," edited (1842-56) by Professor Eugo Alberi, from the Galileian manuscripts and correspondence preserved in the Palatine Library at Florence ; " La Primogenita di Galileo Galilei (1864)," by Professor Carlo Arduini, containing one hundred and twenty-one letters (also preserved in the Palatine Library) addressed to Galileo by his eldest daughter, the Franciscan nun Maria Celeste, eightyseven of which were first edited by Professor Arduini ; and u Galilee, son Proces, sa Condamnation," published by M. Henri de 1'Epinois in the " Revue des Questions Historiques (1867)." This last-named work supplies, what had hitherto been wanting, a mass of details concerning Galileo's trial, all of the highest interest, extracted by M. de 1'Epinois from the original trial papers now in the archives of the Vatican. It has been the endeavor of the compiler to place before the reader a plain, ungarbled statement of facts ; and as a means to this end, to allow Galileo, his friends, and his judges to speak for themselves as far as possible.

The following pages represent the result of several years' experience in presenting to students of engineering the elements of Practical Astronomy. Although the method and the extent of the discussion have been designed to meet the specialized requirements of such students, it is intended that the
work shall also serve as an introduction for those who desire a broader knowledge of the subject.

THIS volume, both in respect to matter and arrangement, is designed especially for the use of the cadets of the U. S. Military Academy, as a supplement to the course in General Astronomy at present taught them from the text-book of Professor 0. A. Young. It is therefore limited to that branch of Practical Astronomy which relates to Field Work, and more particularly to those subjects which are not discussed at sufficient length for practical work in Professor Young's volume. It is believed, however, that it will find a useful application in the hands of officers of the Army, who may be called upon to conduct such explorations and surveys for military purposes as the War Department may from time to time direct.