TWO HUNDRED YEARS.

One more century; another act in the great drama of empire; another French and Indian War beneath the banners of England; a successful Revolution, of which some of the most momentous events occurred within your limits; a union of States; a Constitution of Federal Government; your population carried to the St. Lawrence and the great Lakes, and their waters poured into the Hudson; your territory covered with a net-work of canals and railroads, filled with life and action, and power, with all the works of peaceful art and prosperous enterprise with all the institutions which constitute and advance the civilization of the age; its population exceeding that of the Union at the date of the Revolution; your own numbers twice as large as those of the largest city of that day, you have met together, my Friends, just two hundred years since the erection of the little church of Beverswyck, to dedicate a noble temple of science and to take a becoming public notice of the establishment of an institution, destined, as we trust, to exert a beneficial influence on the progress of useful knowledge at home and abroad, and through that on the general cause of civilization.

SCIENTIFIC PROGRESS.

You will observe that I am careful to say the progress of science "at home and abroad;" for the study of Astronomy in this country has long since, I am happy to add, passed that point where it is content to repeat the observations and verify the results of European research. It has boldly and successfully entered the field of original investigation, discovery, and speculation; and there is not now a single department of the science in which the names of American observers and mathematicians are not cited by our brethren across the water, side by side with the most eminent of their European contemporaries.

This state of things is certainly recent. During the colonial period and in the first generation after the Revolution, no department of science was, for obvious causes, very extensively cultivated in America—astronomy perhaps as much as the kindred branches. The improvement in the quadrant, commonly known as Hadley's, had already been made at Philadelphia by Godfrey, in the early part of the last century; and the beautiful invention of the collimating telescope was made at a later period by Rittenhouse, an astronomer of distinguished repute. The transits of Venus of 1761 and 1769 were observed, and orreries were constructed in different parts of the country; and some respectable scientific essays are contained and valuable observations are recorded in the early volumes of the Transactions of the Philosophical Society, at Philadelphia, and the American Academy of Arts and Sciences at Boston and Cambridge. But in the absence of a numerous class of men of science to encourage and aid each other, without observatories and without valuable instruments, little of importance could be expected in the higher walks of astronomical life.

AMERICAN OBSERVATIONS.

The greater the credit due for the achievement of an enterprise commenced in the early part of the present century, and which would reflect honor on the science of any country and any age; I mean the translation and commentary on Laplace's Mécanique Celeste, by Bowditch; a work of whose merit I am myself wholly unable to form an opinion, but which I suppose places the learned translator and commentator on a level with the ablest astronomers and geometers of the day. This work may be considered as opening a new era in the history of American science. The country was still almost wholly deficient in instrumental power; but the want was generally felt by men of science, and the public mind in various parts of the country began to be turned towards the means of supplying it. In 1825, President John Quincy Adams brought the subject of a National Observatory before Congress. Political considerations prevented its being favorably entertained at that time; and it was not till 1842, and as an incident of the exploring expedition, that an appropriation was made for a dépôt for the charts and instruments of the Navy. On this modest basis has been reared the National Observatory at Washington; an institution which has already taken and fully sustains an honorable position among the scientific establishments of the age.

Besides the institution at Washington, fifteen or twenty observatories have within the last few years, been established in different parts of the country, some of them on a modest scale, for the gratification of the scientific taste and zeal of individuals, others on a broad foundation of expense and usefulness. In these establishments, public and private, the means are provided for the highest order of astronomical observation, research, and instruction. There is already in the country an amount of instrumental power (to which addition is constantly making), and of mathematical skill on the part of our men of science, adequate to a manly competition with their European contemporaries. The fruits are already before the world, in the triangulation of several of the States, in the great work of the Coast Survey, in the numerous scientific surveys of the interior of the Continent, in the astronomical department of the Exploring Expedition, in the scientific expedition to Chili, in the brilliant hydrographical labors of the Observatory at Washington, in the published observations of Washington and Cambridge, in the Journal conducted by the Nestor of American Science, now in its eighth lustrum; in the Sidereal Messenger, the Astronomical Journal, and the National Ephemeris; in the great chronometrical expeditions to determine the longitude of Cambridge, better ascertained than that of Paris was till within the last year; in the prompt rectification of the errors in the predicted elements of Neptune; in its identification with Lalande's missing star, and in the calculation of its ephemeris; in the discovery of the satellite of Neptune, of the eighth satellite of Saturn, and of the innermost of its rings; in the establishment, both by observation and theory, of the non-solid character of Saturn's rings; in the separation and measurement of many double and triple stars, amenable only to superior instrumental power, in the immense labor already performed in preparing star catalogues, and in numerous accurate observations of standard stars; in the diligent and successful observation of the meteoric showers; in an extensive series of magnetic observations; in the discovery of an asteroid and ten or twelve telescopic comets; in the resolution of nebulæ which had defied every thing in Europe but Lord Rosse's great reflector; in the application of electricity to the measurement of differences in longitude; in the ascertainment of the velocity of the electro-magnetic fluid, and its truly wonderful uses in recording astronomical observations. These are but a portion of the achievements of American astronomical science within fifteen or twenty years, and fully justify the most sanguine anticipations of its further progress.

How far our astronomers may be able to pursue their researches, will depend upon the resources of our public institutions, and the liberality of wealthy individuals in furnishing the requisite means. With the exception of the observatories at Washington and West Point, little can be done, or be expected to be done, by the government of the Union or the States; but in this, as in every other department of liberal art and science, the great dependence,—and may I not add, the safe dependence?—as it ever has been, must continue to be upon the bounty of enlightened, liberal, and public-spirited individuals.

THE DUDLEY OBSERVATORY.

It is by a signal exercise of this bounty, my Friends, that we are called together to-day. The munificence of several citizens of this ancient city, among whom the first place is due to the generous lady whose name has with great propriety been given to the institution, has furnished the means for the foundation of the Dudley Observatory at Albany. On a commanding elevation on the northern edge of the city, liberally given for that purpose by the head of a family in which the patronage of science is hereditary, a building of ample dimensions has been erected, upon a plan which combines all the requisites of solidity, convenience, and taste. A large portion of the expense of the structure has been defrayed by Mrs. Blandina Dudley; to whose generosity, and that of several other public-spirited individuals, the institution is also indebted for the provision which has been made for an adequate supply of first-class instruments, to be executed by the most eminent makers in Europe and America; and which, it is confidently expected, will yield to none of their class in any observatory in the world.[A]

With a liberal supply of instrumental power; established in a community to whose intelligence and generosity its support may be safely confided, and whose educational institutions are rapidly realizing the conception of a university; countenanced by the gentleman who conducts the United States Coast Survey with such scientific skill and administrative energy; committed to the immediate supervision of an astronomer to whose distinguished talent had been added the advantage of a thorough scientific education in the most renowned universities of Europe, and who, as the editor of the American Astronomical Journal, has shown himself to be fully qualified for the high trust;—under these favorable circumstances, the Dudley Observatory at Albany takes its place among the scientific foundations of the country and the world.

WONDERS OF ASTRONOMY.

It is no affected modesty which leads me to express the regret that this interesting occasion could not have taken place under somewhat different auspices. I feel that the duty of addressing this great and enlightened assembly, comprising so much of the intelligence of the community and of the science of the country, ought to have been elsewhere assigned; that it should have devolved upon some one of the eminent persons, many of whom I see before me, to whom you have been listening the past week, who, as observers and geometers, could have treated the subject with a master's power; astronomers, whose telescopes have penetrated the depths of the heavens, or mathematicians, whose analysis unthreads the maze of their wondrous mechanism. If, instead of commanding, as you easily could have done, qualifications of this kind, your choice has rather fallen on one making no pretensions to the honorable name of a man of science,—but whose delight it has always been to turn aside from the dusty paths of active life, for an interval of recreation in the green fields of sacred nature in all her kingdoms,—it is, I presume, because you have desired on an occasion of this kind, necessarily of a popular character, that those views of the subject should be presented which address themselves to the general intelligence of the community, and not to its select scientific circles. There is, perhaps, no branch of science which to the same extent as astronomy exhibits phenomena which, while they task the highest powers of philosophical research, are also well adapted to arrest the attention of minds barely tinctured with scientific culture, and even to teach the sensibilities of the wholly uninstructed observer. The profound investigations of the chemist into the ultimate constitution of material nature, the minute researches of the physiologist into the secrets of animal life, the transcendental logic of the geometer, clothed in a notation, the very sight of which terrifies the uninitiated,—are lost on the common understanding. But the unspeakable glories of the rising and the setting sun; the serene majesty of the moon, as she walks in full-orbed brightness through the heavens; the soft witchery of the morning and the evening star; the imperial splendors of the firmament on a bright, unclouded night; the comet, whose streaming banner floats over half the sky,—these are objects which charm and astonish alike the philosopher and the peasant, the mathematician who weighs the masses and defines the orbits of the heavenly bodies, and the untutored observer who sees nothing beyond the images painted upon the eye.

WHAT IS AN ASTRONOMICAL OBSERVATORY?

An astronomical observatory, in the general acceptation of the word, is a building erected for the reception and appropriate use of astronomical instruments, and the accommodation of the men of science employed in making and reducing observations of the heavenly bodies. These instruments are mainly of three classes, to which I believe all others of a strictly astronomical character may be referred.

1. The instruments by which the heavens are inspected, with a view to discover the existence of those celestial bodies which are not visible to the naked eye (beyond all comparison more numerous than those which are), and the magnitude, shapes, and other sensible qualities, both of those which are and those which are not thus visible to the unaided sight. The instruments of this class are designated by the general name of Telescope, and are of two kinds,—the refracting telescope, which derives its magnifying power from a system of convex lenses; and the reflecting telescope, which receives the image of the heavenly body upon a concave mirror.

2d. The second class of instruments consists of those which are designed principally to measure the angular distances of the heavenly bodies from each other, and their time of passing the meridian. The transit instrument, the meridian circle, the mural circle, the heliometer, and the sextant, belong to this class. The brilliant discoveries of astronomy are, for the most part, made with the first class of instruments; its practical results wrought out by the second.

3d. The third class contains the clock, with its subsidiary apparatus, for measuring the time and making its subdivisions with the greatest possible accuracy; indispensable auxiliary of all the instruments, by which the positions and motions of the heavenly bodies are observed, and measured, and recorded.

THE TELESCOPE.

The telescope may be likened to a wondrous cyclopean eye, endued with superhuman power, by which the astronomer extends the reach of his vision to the further heavens, and surveys galaxies and universes compared with which the solar system is but an atom floating in the air. The transit may be compared to the measuring rod which he lays from planet to planet, and from star to star, to ascertain and mark off the heavenly spaces, and transfer them to his note-book; the clock is that marvelous apparatus by which he equalizes and divides into nicely measured parts a portion of that unconceived infinity of duration, without beginning and without end, in which all existence floats as on a shoreless and bottomless sea.

In the contrivance and the execution of these instruments, the utmost stretch of inventive skill and mechanical ingenuity has been put forth. To such perfection have they been carried, that a single second of magnitude or space is rendered a distinctly visible and appreciable quantity. "The arc of a circle," says Sir J. Herschell, "subtended by one second, is less than the 200,000th part of the radius, so that on a circle of six feet in diameter, it would occupy no greater linear extent than 1-5700 part of an inch, a quantity requiring a powerful microscope to be discerned at all."[A] The largest body in our system, the sun, whose real diameter is 882,000 miles, subtends, at a distance of 95,000,000 miles, but an angle of little more than 32; while so admirably are the best instruments constructed, that both in Europe and America a satellite of Neptune, an object of comparatively inconsiderable diameter, has been discovered at a distance of 2,850 millions of miles.

UTILITY OF ASTRONOMICAL OBSERVATIONS.

The object of an observatory, erected and supplied with instruments of this admirable construction, and at proportionate expense, is, as I have already intimated, to provide for an accurate and systematic survey of the heavenly bodies, with a view to a more correct and extensive acquaintance with those already known, and as instrumental power and skill in using it increase, to the discovery of bodies hitherto invisible, and in both classes to the determination of their distances, their relations to each other, and the laws which govern their movements.

Why should we wish to obtain this knowledge? What inducement is there to expend large sums of money in the erection of observatories, and in furnishing them with costly instruments, and in the support of the men of science employed in making, discussing, and recording, for successive generations, those minute observations of the heavenly bodies?

In an exclusively scientific treatment of this subject, an inquiry into its utilitarian relations would be superfluous—even wearisome. But on an occasion like the present, you will not, perhaps, think it out of place if I briefly answer the question, What is the use of an observatory, and what benefit may be expected from the operations of such an establishment in a community like ours?

1. In the first place, then, we derive from the observations of the heavenly bodies which are made at an observatory, our only adequate measures of time, and our only means of comparing the time of one place with the time of another. Our artificial time-keepers—clocks, watches, and chronometers—however ingeniously contrived and admirably fabricated, are but a transcript, so to say, of the celestial motions, and would be of no value without the means of regulating them by observation. It is impossible for them, under any circumstances, to escape the imperfection of all machinery the work of human hands; and the moment we remove with our time-keeper east or west, it fails us. It will keep home time alone, like the fond traveler who leaves his heart behind him. The artificial instrument is of incalculable utility, but must itself be regulated by the eternal clock-work of the skies.

RELATIONS BETWEEN NATURAL PHENOMENA AND DAILY LIFE.

This single consideration is sufficient to show how completely the daily business of life is affected and controlled by the heavenly bodies. It is they—and not our main-springs, our expansion balances, and our compensation pendulums—which give us our time. To reverse the line of Pope:

But for all the kindreds and tribes and tongues of men—each upon their own meridian—from the Arctic pole to the equator, from the equator to the Antarctic pole, the eternal sun strikes twelve at noon, and the glorious constellations, far up in the everlasting belfries of the skies, chime twelve at midnight;—twelve for the pale student over his flickering lamp; twelve amid the flaming glories of Orion's belt, if he crosses the meridian at that fated hour; twelve by the weary couch of languishing humanity; twelve in the star-paved courts of the Empyrean; twelve for the heaving tides of the ocean; twelve for the weary arm of labor; twelve for the toiling brain; twelve for the watching, waking, broken heart; twelve for the meteor which blazes for a moment and expires; twelve for the comet whose period is measured by centuries; twelve for every substantial, for every imaginary thing, which exists in the sense, the intellect, or the fancy, and which the speech or thought of man, at the given meridian, refers to the lapse of time.

Not only do we resort to the observation of the heavenly bodies for the means of regulating and rectifying our clocks, but the great divisions of day and month and year are derived from the same source. By the constitution of our nature, the elements of our existence are closely connected with celestial times. Partly by his physical organization, partly by the experience of the race from the dawn of creation, man as he is, and the times and seasons of the heavenly bodies, are part and parcel of one system. The first great division of time, the day-night (nychthemerum), for which we have no precise synonym in our language, with its primal alternation of waking and sleeping, of labor and rest, is a vital condition of the existence of such a creature as man. The revolution of the year, with its various incidents of summer and winter, and seed-time and harvest, is not less involved in our social, material, and moral progress. It is true that at the poles, and on the equator, the effects of these revolutions are variously modified or wholly disappear; but as the necessary consequence, human life is extinguished at the poles, and on the equator attains only a languid or feverish development. Those latitudes only in which the great motions and cardinal positions of the earth exert a mean influence, exhibit man in the harmonious expansion of his powers. The lunar period, which lies at the foundation of the month, is less vitally connected with human existence and development; but is proved by the experience of every age and race to be eminently conducive to the progress of civilization and culture.

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.

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 Cœlestium, 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 coöperation of this science. Among these I may mention the land system of the United States, and the determination of the boundaries of the country. I believe that till it was done by the Federal Government, a uniform system of mathematical survey had never in any country been applied to an extensive territory. Large grants and sales of public land took place before the Revolution, and in the interval between the peace and the adoption of the Constitution; but the limits of these grants and sales were ascertained by sensible objects, by trees, streams, rocks, hills, and by reference to adjacent portions of territory, previously surveyed. The uncertainty of boundaries thus defined, was a never-failing source of litigation. Large tracts of land in the Western country, granted by Virginia under this old system of special and local survey, were covered with conflicting claims; and the controversies to which they gave rise formed no small part of the business of the Federal Court after its organization. But the adoption of the present land-system brought order out of chaos. The entire public domain is now scientifically surveyed before it is offered for sale; it is laid off into ranges, townships, sections, and smaller divisions, with unerring accuracy, resting on the foundation of base and meridian lines; and I have been informed that under this system, scarce a case of contested location and boundary has ever presented itself in court. The General Land Office contains maps and plans, in which every quarter-section of the public land is laid down with mathematical precision. The superficies of half a continent is thus transferred in miniature to the bureaus of Washington; while the local Land Offices contain transcripts of these plans, copies of which are furnished to the individual purchaser. When we consider the tide of population annually flowing into the public domain, and the immense importance of its efficient and economical administration, the utility of this application of Astronomy will be duly estimated.

I will here venture to repeat an anecdote, which I heard lately from a son of the late Hon. Timothy Pickering. Mr. Octavius Pickering, on behalf of his father, had applied to Mr. David Putnam of Marietta, to act as his legal adviser, with respect to certain land claims in the Virginia Military district, in the State of Ohio. Mr. Putnam declined the agency. He had had much to do with business of that kind, and found it beset with endless litigation. "I have never," he added, "succeeded but in a single case, and that was a location and survey made by General Washington before the Revolution; and I am not acquainted with any surveys, except those made by him, but what have been litigated."

At this moment, a most important survey of the coast of the United States is in progress, an operation of the utmost consequence, in reference to the commerce, navigation, and hydrography of the country. The entire work, I need scarce say, is one of practical astronomy. The scientific establishment which we this day inaugurate is looked to for important coöperation in this great undertaking, and will no doubt contribute efficiently to its prosecution.

Astronomical observation furnishes by far the best means of defining the boundaries of States, especially when the lines are of great length and run through unsettled countries. Natural indications, like rivers and mountains, however indistinct in appearance, are in practice subject to unavoidable error. By the treaty of 1783, a boundary was established between the United States and Great Britain, depending chiefly on the course of rivers and highlands dividing the waters which flow into the Atlantic Ocean from those which flow into the St. Lawrence. It took twenty years to find out which river was the true St. Croix, that being the starting point. England then having made the extraordinary discovery that the Bay of Fundy is not a part of the Atlantic Ocean, forty years more were passed in the unsuccessful attempt to re-create the highlands which this strange theory had annihilated; and just as the two countries were on the verge of a war, the controversy was settled by compromise. Had the boundary been accurately described by lines of latitude and longitude, no dispute could have arisen. No dispute arose as to the boundary between the United States and Spain, and her successor, Mexico, where it runs through untrodden deserts and over pathless mountains along the 42d degree of latitude. The identity of rivers may be disputed, as in the case of the St. Croix; the course of mountain chains is too broad for a dividing line; the division of streams, as experience has shown, is uncertain; but a degree of latitude is written on the heavenly sphere, and nothing but an observation is required to read the record.

QUESTIONS OF BOUNDARY.

But scientific elements, like sharp instruments, must be handled with scientific accuracy. A part of our boundary between the British Provinces ran upon the forty-fifth degree of latitude; and about forty years ago, an expensive fortress was commenced by the government of the United States, at Rouse's Point, on Lake Champlain, on a spot intended to be just within our limits. When a line came to be more carefully surveyed, the fortress turned out to be on the wrong side of the line; we had been building an expensive fortification for our neighbor. But in the general compromises of the Treaty of Washington by the Webster and Ashburton Treaty in 1842, the fortification was left within our limits.[A]

Errors still more serious had nearly resulted, a few years since, in a war with Mexico. By the treaty of Guadalupe Hidalgo, in 1848, the boundary line between the United States and that country was in part described by reference to the town of El Paso, as laid down on a specified map of the United States, of which a copy was appended to the treaty. This boundary was to be surveyed and run by a joint commission of men of science. It soon appeared that errors of two or three degrees existed in the projection of the map. Its lines of latitude and longitude did not conform to the topography of the region; so that it became impossible to execute the text of the treaty. The famous Mesilla Valley was a part of the debatable ground; and the sum of $10,000,000, paid to the Mexican Government for that and for an additional strip of territory on the southwest, was the smart-money which expiated the inaccuracy of the map—the necessary result, perhaps, of the want of good materials for its construction.

It became my official duty in London, a few years ago, to apply to the British Government for an authentic statement of their claim to jurisdiction over New Zealand. The official Gazette for the 2d of October, 1840, was sent me from the Foreign Office, as affording the desired information. This number of the Gazette contained the proclamations issued by the Lieutenant Governor of New Zealand, "in pursuance of the instructions he received from the Marquis of Normanby, one of Her Majesty's principal Secretaries of State," asserting the jurisdiction of his government over the islands of New Zealand, and declaring them to extend "from 34° 30' North to 47° 10' South latitude." It is scarcely necessary to say that south latitude was intended in both instances. This error of 69° of latitude, which would have extended the claim of British jurisdiction over the whole breadth of the Pacific, had, apparently, escaped the notice of that government.

COMMERCE AND NAVIGATION.

It would be easy to multiply illustrations in proof of the great practical importance of accurate scientific designations, drawn from astronomical observations, in various relations connected with boundaries, surveys, and other geographical purposes; but I must hasten to

3. A third important department, in which the services rendered by astronomy are equally conspicuous. I refer to commerce and navigation. It is mainly owing to the results of astronomical observation, that modern commerce has attained such a vast expansion, compared with that of the ancient world. I have already reminded you that accurate ideas in this respect contributed materially to the conception in the mind of Columbus of his immortal enterprise, and to the practical success with which it was conducted. It was mainly his skill in the use of astronomical instruments—imperfect as they were—which enabled him, in spite of the bewildering variation of the compass, to find his way across the ocean.

With the progress of the true system of the universe toward general adoption, the problem of finding the longitude at sea presented itself. This was the avowed object of the foundation of the observatory at Greenwich;[A] and no one subject has received more of the attention of astronomers, than those investigations of the lunar theory on which the requisite tables of the navigator are founded. The pathways of the ocean are marked out in the sky above. The eternal lights of the heavens are the only Pharos whose beams never fail, which no tempest can shake from its foundation. Within my recollection, it was deemed a necessary qualification for the master and the mate of a merchant-ship, and even for a prime hand, to be able to "work a lunar," as it was called. The improvements in the chronometer have in practice, to a great extent, superseded this laborious operation; but observation remains, and unquestionably will for ever remain, the only dependence for ascertaining the ship's time and deducting the longitude from the comparison of that time with the chronometer.

It may, perhaps, be thought that astronomical science is brought already to such a state of perfection that nothing more is to be desired, or at least that nothing more is attainable, in reference to such practicable applications as I have described. This, however, is an idea which generous minds will reject, in this, as in every other department of human knowledge. In astronomy, as in every thing else, the discoveries already made, theoretical or practical, instead of exhausting the science, or putting a limit to its advancement, do but furnish the means and instruments of further progress. I have no doubt we live on the verge of discoveries and inventions, in every department, as brilliant as any that have ever been made; that there are new truths, new facts, ready to start into recognition on every side; and it seems to me there never was an age, since the dawn of time, when men ought to be less disposed to rest satisfied with the progress already made, than the age in which we live; for there never was an age more distinguished for ingenious research, for novel result, and bold generalization.

That no further improvement is desirable in the means and methods of ascertaining the ship's place at sea, no one I think will from experience be disposed to assert. The last time I crossed the Atlantic, I walked the quarter-deck with the officer in charge of the noble vessel, on one occasion, when we were driving along before a leading breeze and under a head of steam, beneath a starless sky at midnight, at the rate certainly of ten or eleven miles an hour. There is something sublime, but approaching the terrible, in such a scene;—the rayless gloom, the midnight chill,—the awful swell of the deep,—the dismal moan of the wind through the rigging, the all but volcanic fires within the hold of the ship. I scarce know an occasion in ordinary life in which a reflecting mind feels more keenly its hopeless dependence on irrational forces beyond its own control. I asked my companion how nearly he could determine his ship's place at sea under favorable circumstances. Theoretically, he answered, I think, within a mile;—practically and usually within three or four. My next question was, how near do you think we may be to Cape Race;—that dangerous headland which pushes its iron-bound unlighted bastions from the shore of Newfoundland far into the Atlantic,—first landfall to the homeward-bound American vessel. We must, said he, by our last observations and reckoning, be within three or four miles of Cape Race. A comparison of these two remarks, under the circumstances in which we were placed at the moment, brought my mind to the conclusion, that it is greatly to be wished that the means should be discovered of finding the ship's place more accurately, or that navigators would give Cape Race a little wider berth. But I do not remember that one of the steam packets between England and America was ever lost on that formidable point.

It appears to me by no means unlikely that, with the improvement of instrumental power, and of the means of ascertaining the ship's time with exactness, as great an advance beyond the present state of art and science in finding a ship's place at sea may take place, as was effected by the invention of the reflecting quadrant, the calculation of lunar tables, and the improved construction of chronometers.

BABBAGE'S DIFFERENCE MACHINE.

In the wonderful versatility of the human mind, the improvement, when made, will very probably be made by paths where it is least expected. The great inducement to Mr. Babbage to attempt the construction of an engine by which astronomical tables could be calculated, and even printed, by mechanical means and with entire accuracy, was the errors in the requisite tables. Nineteen such errors, in point of fact, were discovered in an edition of Taylor's Logarithms printed in 1796; some of which might have led to the most dangerous results in calculating a ship's place. These nineteen errors, (of which one only was an error of the press), were pointed out in the Nautical Almanac for 1832. In one of these errata the seat of the error was stated to be in cosine of 14° 18' 3". Subsequent examination showed that there was an error of one second in this correction; and, accordingly, in the Nautical Almanac of the next year a new correction was necessary. But in making the new correction of one second, a new error was committed of ten degrees. Instead of cosine 14° 18' 2" the correction was printed cosine 4° 18' 2" making it still necessary, in some future edition of the Nautical Almanac, to insert an erratum in an erratum of the errata in Taylor's logarithms.[A]

In the hope of obviating the possibility of such errors, Mr. Babbage projected his calculating, or, as he prefers to call it, his difference machine. Although this extraordinary undertaking has been arrested, in consequence of the enormous expense attending its execution, enough has been achieved to show the mechanical possibility of constructing an engine of this kind, and even one of far higher powers, of which Mr. Babbage has matured the conception, devised the notation, and executed the drawings—themselves an imperishable monument of the genius of the author.

I happened on one occasion to be in company with this highly distinguished man of science, whose social qualities are as pleasing as his constructive talent is marvelous, when another eminent savant, Count Strzelecki, just returned from his Oriental and Australian tour, observed that he found among the Chinese, a great desire to know something more of Mr. Babbage's calculating machine, and especially whether, like their own swampan, it could be made to go into the pocket. Mr. Babbage good-humouredly observed that, thus far, he had been very much out of pocket with it.

INCREASED COMMAND OF INSTRUMENTAL POWER.

Whatever advances may be made in astronomical science, theoretical or applied, I am strongly inclined to think that they will be made in connection with an increased command of instrumental power. The natural order in which the human mind proceeds in the acquisition of astronomical knowledge is minute and accurate observation of the phenomena of the heavens, the skillful discussion and analysis of these observations, and sound philosophy in generalizing the results.

In pursuing this course, however, a difficulty presented itself, which for ages proved insuperable—and which to the same extent has existed in no other science, viz.: that all the leading phenomena are in their appearance delusive. It is indeed true that in all sciences superficial observation can only lead, except by chance, to superficial knowledge; but I know of no branch in which, to the same degree as in astronomy, the great leading phenomena are the reverse of true; while they yet appeal so strongly to the senses, that men who could foretell eclipses, and who discovered the precession of the equinoxes, still believed that the earth was at rest in the center of the universe, and that all the host of heaven performed a daily revolution about it as a center.

It usually happens in scientific progress, that when a great fact is at length discovered, it approves itself at once to all competent judges. It furnishes a solution to so many problems, and harmonizes with so many other facts,—that all the other data as it were crystallize at once about it. In modern times, we have often witnessed such an impatience, so to say, of great truths, to be discovered, that it has frequently happened that they have been found out simultaneously by more than one individual; and a disputed question of priority is an event of very common occurrence. Not so with the true theory of the heavens. So complete is the deception practiced on the senses, that it failed more than once to yield to the suggestion of the truth; and it was only when the visual organs were armed with an almost preternatural instrumental power, that the great fact found admission to the human mind.

THE COPERNICAN SYSTEM.

It is supposed that in the very dawn of science, Pythagoras or his disciples explained the apparent motion of the heavenly bodies about the earth by the diurnal revolution of the earth on its axis. But this theory, though bearing so deeply impressed upon it the great seal of truth, simplicity, was in such glaring contrast with the evidence of the senses, that it failed of acceptance in antiquity or the middle ages. It found no favor with minds like those of Aristotle, Archimedes, Hipparchus, Ptolemy, or any of the acute and learned Arabian or mediæval astronomers. All their ingenuity and all their mathematical skill were exhausted in the development of a wonderfully complicated and ingenious, but erroneous history. The great master truth, rejected for its simplicity, lay disregarded at their feet.

At the second dawn of science, the great fact again beamed into the mind of Copernicus. Now, at least, in that glorious age which witnessed the invention of printing, the great mechanical engine of intellectual progress, and the discovery of America, we may expect that this long-hidden revelation, a second time proclaimed, will command the assent of mankind. But the sensible phenomena were still too strong for the theory; the glorious delusion of the rising and the setting sun could not be overcome. Tycho de Brahe furnished his Observatory with instruments superior in number and quality to all that had been collected before; but the great instrument of discovery, which, by augmenting the optic power of the eye, enables it to penetrate beyond the apparent phenomena, and to discern the true constitution of the heavenly bodies, was wanting at Uranienburg. The observations of Tycho as discussed by Kepler, conducted that most fervid, powerful, and sagacious mind to the discovery of some of the most important laws of the celestial motions; but it was not till Galileo, at Florence, had pointed his telescope to the sky, that the Copernican system could be said to be firmly established in the scientific world.

THE HOME OF GALILEO.

On this great name, my Friends, assembled as we are to dedicate a temple to instrumental Astronomy, we may well pause for a moment.

There is much, in every way, in the city of Florence to excite the curiosity, to kindle the imagination, and to gratify the taste. Sheltered on the north by the vine-clad hills of Fiesoli, whose cyclopean walls carry back the antiquary to ages before the Roman, before the Etruscan power, the flowery city (Fiorenza) covers the sunny banks of the Arno with its stately palaces. Dark and frowning piles of mediæval structure; a majestic dome, the prototype of St. Peter's; basilicas which enshrine the ashes of some of the mightiest of the dead; the stone where Dante stood to gaze on the Campanile; the house of Michael Angelo, still occupied by a descendant of his lineage and name, his hammer, his chisel, his dividers, his manuscript poems, all as if he had left them but yesterday; airy bridges, which seem not so much to rest on the earth as to hover over the waters they span; the loveliest creations of ancient art, rescued from the grave of ages again to enchant the world; the breathing marbles of Michael Angelo, the glowing canvas of Raphael and Titian, museums filled with medals and coins of every age from Cyrus the younger, and gems and amulets and vases from the sepulchers of Egyptian Pharaohs coëval with Joseph, and Etruscan Lucumons that swayed Italy before the Romans,—libraries stored with the choicest texts of ancient literature,—gardens of rose and orange, and pomegranate, and myrtle,—the very air you breathe languid with music and perfume;—such is Florence. But among all its fascinations, addressed to the sense, the memory, and the heart, there was none to which I more frequently gave a meditative hour during a year's residence, than to the spot where Galileo Galilei sleeps beneath the marble door of Santa Croce; no building on which I gazed with greater reverence, than I did upon the modest mansion at Arcetri, villa at once and prison, in which that venerable sage, by command of the Inquisition, passed the sad closing years of his life. The beloved daughter on whom he had depended to smooth his passage to the grave, laid there before him; the eyes with which he had discovered worlds before unknown, quenched in blindness: