But indispensable as are these heavenly measures of time to our life and progress, and obvious as are the phenomena on which they rest, yet owing to the circumstance that, in the economy of nature, the day, the month, and the year are not exactly commensurable, some of the most difficult questions in practical astronomy are those by which an accurate division of time, applicable to the various uses of life, is derived from the observation of the heavenly bodies.  I have no doubt that, to the Supreme Intelligence which created and rules the universe, there is a harmony hidden to us in the numerical relation to each other of days, months, and years; but in our ignorance of that harmony, their practical adjustment to each other is a work of difficulty.  The great embarrassment which attended the reformation of the calendar, after the error of the Julian period had, in the lapse of centuries, reached ten (or rather twelve) days, sufficiently illustrates this remark.  It is most true that scientific difficulties did not form the chief obstacle.  Having been proposed under the auspices of the Roman pontiff, the Protestant world, for a century and more, rejected the new style.  It was in various places the subject of controversy, collision, and bloodshed.[A] It was not adopted in England till nearly two centuries after its introduction at Rome; and in the country of Struve and the Pulkova equatorial, they persist at the present day in adding eleven minutes and twelve seconds to the length of the tropical year.

[Footnote A:  Stern’s “Himmelskunde,” p. 72.]

GEOGRAPHICAL SCIENCE.

2.  The second great practical use of an Astronomical Observatory is connected with the science of geography.  The first page of the history of our Continent declares this truth.  Profound meditation on the sphericity of the earth was one of the main reasons which led Columbus to undertake his momentous voyage; and his thorough acquaintance with the astronomical science of that day was, in his own judgment, what enabled him to overcome the almost innumerable obstacles which attended its prosecution.[A] In return, I find that Copernicus in the very commencement of his immortal work De Revolutionibus Orbium Coelestium, fol. 2, appeals to the discovery of America as completing the demonstration of the sphericity of the earth.  Much of our knowledge of the figure, size, density, and position of the earth, as a member of the solar system, is derived from this science; and it furnishes us the means of performing the most important operations of practical geography.  Latitude and longitude, which lie at the basis of all descriptive geography, are determined by observation.  No map deserves the name, on which the position of important points has not been astronomically determined.  Some even of our most important political and administrative arrangements depend upon the cooperation of this science.  Among these I may mention the land system of the United