United States Coast Survey. The coast survey of the United States is a national undertaking of high character and importance. Having an extended and dangerous seacoast, with a large foreign commerce, in the pursuit of which many thousand vessels annually enter and leave our ports, with an immense coast-Avise trade which employs many vessels and thousands of seamen, it is plainly our duty as a nation to provide every means which science and practical skill can afford for pointing out the dangers to which this commerce is exposed, and to furnish every facility for its successful prosecution. To accomplish these objects the coast survey was founded. It is designed to furnish accurate maps of the whole coast; to point out the positions for lighthouses, beacons, and other signals; to determine the character and course of the currents of the ocean along our shores; to develop and determine the laws of the tides; to ascertain the prevailing courses of the winds and the general laws of atmospheric influence, the changes which take place at the entrances of our harbors, the character of the bottom of the sea within the limits of soundings, and all other questions which contribute to a thorough knowledge of our coast and its adjacent waters.

It has also the further object of distributing this knowledge throughout the world, so that all nations may partake of its advantages. For the accomplishment of these objects a wide range of application of the practical sciences is required. Astronomy and geodesy furnish the means of projecting maps. The highest forms of mathematical science are required in the investigation of the laws of the tides and the figure of the earth. Geology explains the changes which are constantly taking place in all our harbors and rivers, and in the general form of the coast. Natural history accounts for the formation of those coral reefs in the southern waters, so long the terror of navigators, predicts their growth and extension, and investigates the forms of animal life at the bottom of the sea, thus affording new and unexpected aids to navigation. Physical science furnishes the electric telegraph, by which longitudes are determined, and the electrotype and photograph, by means of which engraved plates and charts are indefinitely multiplied. The mechanic arts supply the most delicate instruments; and the industrial arts of drawing, engraving, and printing are all required in their greatest perfection.

For the expanded conception of this great institution as it now exists; for the administrative skill which has perfected its organization; for the solution of many interesting questions of science which it has involved, especially those of the tides, the Gulf stream, and the magnetic force; for the genius which has brought to the highest perfection the scientific methods .mployed; for the untiring labor which, within a comparatively short period, has produced greater results than any other institution of the kind, the world is greatly indebted to Prof. A. D. Bache, the late superintendent. Since his death the work of the survey has been greatly extended, and its usefulness increased, by the present superintendent, Prof. Benjamin Peirce. The most important work set in operation since his accession to the position of superintendent is the great national triangulation - a geodetic survey which is intended to embrace the shores of the Atlantic and Pacific within its limits, and to form by means of triangulation a grand chain across the continent, which will serve in a most satisfactory manner to verify the independently determined longitudes of the Pacific coast.

This great work, together with the other improvements which have been made under the rule of the present superintendent, will be referred to in another place. - The first attempt to organize a national coast survey was made in 1807. In that year President Jefferson in his message to congress recommended the establishment of a national coast survey, "for the purpose of making complete charts of our coast, with the adjacent shoals and soundings." It is believed that to Prof. Patterson of Philadelphia is due the honor of having first suggested to the president the idea of a geodetic survey of the coast. At that time the only charts of our extended and dangerous seacoast were those of the " Atlantic Neptune " of Col. Des Barres, Romaine, and Gauldel, and compilations from those works by English and American publishers. Congress passed an act authorizing such a survey, and appropriated $50,000. Mr. Gallatin addressed circulars to the principal scientific men of our country, requesting their opinions with regard to the best methods of conducting the proposed work. The plan proposed by Mr. F. R. Hassler was adopted.

The plan was, essentially, to establish the positions of certain prominent points of the coast by astronomical observations, and to connect these points by trigonometrical lines, so as to form a basis upon which the nautical survey could be made. Mr. Hassler, a native of Switzerland, had been engaged in the trigonometrical survey of that country, and was eminently fitted by his scientific attainments for the execution of the task to which he was now called. On account of the threatening nature of our relations with Great Britain, nothing was done toward the actual prosecution of the survey till 1811, when Mr. Hassler was sent to Europe for the purpose of procuring the necessary instruments and standards of measure for commencing the work; and the war which followed caused him to be detained abroad as an alien enemy till 1815. On his return he was formally appointed superintendent of the coast survey, and commenced his labors in the field in 1817, in the vicinity of New York. His first work was the measurement of a base line in the rear of the Palisades, on the Hudson, as a foundation for the triangulation of New York harbor and the adjacent coast.

Before he could publish the results of his first year's labor, however, the coast survey was effectively discontinued; and another interval of ten years elapsed, during which some additions were made to a knowledge of our Atlantic coast through detached survevs of a few of the more important harbors, made by the navy and the topographical engineers of the army, and those of the Messrs. Blunt. In 1828 Samuel L. Southard, secretary of the navy, urged upon congress the importance of reestablishing the coast survey upon its original plan; and in 1832 Mr. Hassler was restored to his position, and enabled to resume the work. A quarter of a century had now elapsed since Mr. Hassler first urged his scheme of a thorough trigonometrical survey. He continued to superintend its operations until his death in 1843, when the survey had been extended from New York eastward to Point Judith, and southward to Cape Henlopen. He was succeeded by Prof. A. D. Bache. - On assuming charge of the coast survey, Prof. Bache saw the necessity of extending the plan so as to embrace all the objects of which we have spoken.

He urged upon congress the importance of carrying on all the principal operations at different points of the coast at the same time; the different sections to be conducted on the same general principles, and to be ultimately connected, so as to form a complete and continuous work. He saw that the great characteristic feature of the Atlantic, the Gulf stream, must be investigated; the laws of the tides developed, so that navigators might be furnished with correct information regarding their ebb and flow in the harbors and rivers; the infinite maze of currents produced by the tides, the Gulf stream, and the winds, combined, threaded out, and mapped; the magnetic force of the earth studied, and its laws along our coast determined; the changes of the weather at different seasons of the year, and the laws of storms, investigated. All these conceptions were far beyond any that had been entertained; and Prof. Bache at once organized those systematic observations which extended through the whole period of his administration, and are continued-at the present day. The most important results to navigation and to science have been and are being developed by these observations.

Under this plan of reorganization, as it may be called, the survey continued to advance with great success until the breaking out of the late civil war. By the secession of the southern states their immense seaboard became hostile coast, and the peaceful operations of the coast survey of necessity ceased. Several vessels employed in the work were captured, and some of the officers narrowly escaped. Debarred from the direct prosecution of the survey of the southern coast, Prof. Bache sought to turn at once to practical account the knowledge of the harbors and their adjacent coasts along the southern seaboard which his officers had acquired during the progress of their labors. Topographical engineers being much needed in the army, he supplied skilled topographers from his own corps. Pilots being necessary for the squadrons which operated on the enemy's coast, he furnished officers of the survey whose local knowledge enabled them safely to pilot the largest vessels of war into harbors from which buoys, lights, and all other aids to navigation had been purposely removed, and whose hydrographic knowledge enabled them in a short time to replace the old marks by others better adapted to the purposes of navigation.

During the war there was not an army in the field without one or more coast survey officers attached to the staff of the general commanding, as topographers, and rendering most efficient service; and no important naval demonstration was made upon the coast without the presence of some officer from the same service on the staff of the admiral commanding the fleet. The services thus rendered to the country during the war by the officers of the coast survey were of the utmost importance, and were thoroughly appreciated by the government. Added to this, the accurate charts of the coast and harbors which had been already made and published were of the greatest assistance to our vessels in their cruises up and down the coast. Worn down at length' with the labors of a busy life, Prof. Bache died in 1867, and Prof. Benjamin Peirce was installed as superintendent Feb. 26, 1867. Since his accession Prof. Peirce has continued with vigor the system inaugurated by his predecessor, and has greatly extended and enlarged the sphere of usefulness of the coast survey. The great system of a national triangulation, which extends the geodetic work, heretofore confined to the sea-coast, across the whole continent, owes its existence, and in a great measure its conception, to the present superintendent.

This work, which is now (1873) in successful operation, contemplates the establishment of a system of triangles connecting those already determined on the Atlantic with those on the Pacific coast. Thus in every state and territory geodetic points will be established-and accurately determined; and thus will be formed a base for a thorough topographical survey of the several states, which will equal if not surpass in beauty and accuracy the famous ordnance survey of Great Britain, while in point of magnitude and extent it will surpass anything in the world. Prof. Peirce, on assuming charge of the survey, encountered some difficulties in the way of a vigorous prosecution of the work. As before mentioned, several of the vessels belonging to the survey had been captured during the war; others were very old, and many were completely worn out and unfit for service; and the small number remaining were totally inadequate for such activity in the field as had always heretofore existed. But these difficulties are rapidly being overcome. Prof. Peirce has urged upon congress the passage of special appropriations for the building of new vessels, and several fine ones have already been built and are at work upon their stations.

The survey of the Pacific coast, which had been somewhat disorganized owing to the war, he established upon a new and firm basis, with an experienced officer at its head; and the work upon that coast has proceeded with unexampled rapidity. Much valuable scientific information has been obtained by the observations of the solar eclipses made by the superintendent and his assistants, under special acts of congress, in 1869 and 1870. Much has been done, and very valuable information collected, through the observations for deep-sea temperatures; and the many thousand specimens collected from the bottom of the sea at great depths have added much to our knowledge of the character of the great sea floor. The investigations which have been made of the tides are of great importance; they will be referred to in their proper place. A directory or coast pilot of the Pacific coast has been published for the use of mariners, and one is in preparation for the Atlantic and gulf coasts. Every year increases the general usefulness of the survey and the vigor and success of its prosecution. - These general facts with regard to the history and progress of the United States coast survey being stated, we come to the scientific and practical operations involved in its execution.

An explanation of these operations will embrace a variety of topics, and only a brief notice of each can be given. The first object of a work of this kind is an accurate determination of the shore line. This is done entirely by operations upon land. The object of a map or chart is, of course, to give a miniature representation of a portion of the earth's surface upon paper, in such a manner that the different parts of the drawing shall have the same relative positions and dimensions as are found in nature. To determine these dimensions by linear measurement, for the purpose of reducing them to the scale of the drawing, would be practically impossible; and hence the use of geodetic or trigonometrical surveying. - Geodesy - General Remarks. To illustrate this mode of measuring distances and establishing the relative positions of points on the earth's surface, let us suppose ourselves to be situated on a level plain, surrounded in the distance by high mountains, and that we wish to determine the distances from our position to the tops of those mountains, and the distances of the different mountain peaks from each other.

A line is measured on the plain, of such a length that if two lines be drawn from its extremities they will intersect at a considerable angle, and form with the measured lino a triangle of proper dimensions. Then, knowing the length of one side of this triangle, we may compute the length of the other two sides by a simple theorem of trigonometry, without any further labor than measuring the angles of the triangle. Taking now either of the computed sides as a new base, we may establish a second triangle upon this, and thus fix the position of another point. A third point may be established in the same manner, gradually expanding the system until the whole region we wish to embrace in the map is covered with a network of triangles; the length of the lines having been computed by measuring the first only, and then measuring the angles of the triangles. For the purpose of a map or chart, there are still two important elements wanting. we have yet no means of knowing the direction of any one of these lines with reference to the meridian, nor the place which the points occupy on the surface of the earth.

The survey thus far will give no means of knowing whether any two points are situated in a north and south or an east and west line; nor whether its site is near the equator or near the poles, or to the east or west of the first meridian. These wants are supplied by astronomical observations, by which the latitude and longitude of some point, and the directions of the lines with reference to the meridian, are determined. The system of triangles which we have described may be extended over large areas, or along a coast for several hundred miles, depending upon one measured base line. By determining the positions of the extremities of the base line and its direction by astronomical observations, the positions of all the other points of the system and the direction of the lines may be computed after the angles have been accurately measured. Accuracy requires that the computed positions should be frequently verified by actual observation, and the computed lengths of the lines occasionally verified also by the introduction of a measured base of verification.

The geodetic work thus involves the measurement of the base line, the measurement of the angles of the triangles, and astronomical determination of the latitude and longitude of the different points, and of the directions of the lines with reference to the meridian. This last is called the measurement of an azimuth. - Reconnoissance is the first operation in order. An experienced officer first travels over the country to be surveyed, and makes a preliminary examination for the purpose of selecting the trigonometrical points which will best fulfil the required conditions. Elevated positions are generally chosen, from which extended views can be taken. A site for a base line is selected on some level plain for convenience of measurement, and from which the triangulation can easily be expanded. In the selection of geodetic points great judgment is required; as upon this depends in a great measure the economy, accuracy, and success of the work. - Base Line. For the measurement of the base line a standard must he adopted.

The English use the yard, which is also the legal standard of length in the United States. But in the coast survey measurements the French metre is used, which is more convenient on account of bearing a certain relation to the magnitude of the earth, being equal to the ten millionth part of the earth's quadrant. The metre bar used as standard in the coast survey is one of those originally made by the French committee of weights and measures. For the actual measurement of base lines rods of wood, metal, or glass have been used; hut the changes of length caused by changes of temperature in a simple bar of any material have rendered it desirable to construct a special apparatus for the purpose, upon a compensating principle, which will retain the same length under all temperatures. The base apparatus of the coast survey, devised by the late Prof. Bache, is considered the best known. It has not only the same length at all stationary temperatures, but preserves it also while the temperature is changing. Bars of different metal, having the same dimensions and exposed to the same source of heat, will not heat equally in equal times.

The thickness and surface of the bars are therefore so proportioned to their relative power of conducting and absorbing heat, that they will equally follow changes of temperature. The principle of the level of contact has been applied to the apparatus; and the exactness of its operations is so great that lines of seven or eight miles in length may be measured with a probable error of only a fraction of an inch. Two sets of compensating bars are used, each 6 metres (nearly 20 feet) in length. Mounted on trestles, provided with every mechanical movement for adjusting the bars in height and direction, this apparatus is handled with such facility that on favorable ground a mile may be measured in an ordinary working day. - Triangulation. For the measurement of the angles theodolites of the most accurate construction are used. In the primary work on the Atlantic coast a large theodolite with a circle 30 inches in diameter is cm-ployed. This is carried to the summit of the hill or mountain where the angles are to be measured, and established carefully over the station point, where it is left standing until the measurements at that point are completed.

The party having this work in charge live in tents, or in some convenient dwelling near at hand, so as to take advantage of the occurrence of favorable weather for the observation of distant signals. The instrument is furnished with a powerful telescope, which will give a distinct view of such signals. The signals are usually straight poles supported by a tripod, erected at the various points; but on the long lines an instrument for giving signals is used, called a heliotrope. This is simply a round mirror about the size of a silver dollar, so mounted on a telescope that an assistant at any distant station is able to reflect the rays of the sun in the direction of the observer. The telescope is used to direct the instrument correctly toward the central position at which the observer is stationed. It is not unusual to see the heliotrope on the summits of mountains 80 or 90 miles distant, when the outlines of the mountains are not visible. The measurement of the angles at a primary station occupies three or four weeks. It is found to be impossible to work during the middle of the day, on acconnt of the agitation of the atmosphere caused by the heat of the sun; and hence only about two hours in the morning and evening can generally be devoted to this work.

Each angle is determined by about 30 measurements; and as at each station there are from 10 to 20 angles to be measured, only two or three primary stations can be occupied in one season. Depending upon the primary triangulation, and controlled by it, a network of secondary and tertiary triangles is formed along the seacoast, extending up the bays and rivers. The angles are measured with theodolites more portable than the one above mentioned, the circles varying from 6 to 12 inches in diameter according to the distances to be observed. These triangulations determine the relative positions of prominent points, at distances averaging from two to five miles, and thus form a skeleton map, in which the details of configuration of shore line and surface remain to be supplied by the topographer. If the figure of the earth were precisely known, it would suffice, in order to fix the situation of the whole network of triangles on the surface of the earth, to determine the latitude and longitude of some one point, and the direction with reference to the true meridian of one of its lines, i. e., its azimuth.

But, owing to the irregularities of the earth's figure, it is found necessary to repeat the determinations very frequently, by which means the work is checked and any accumulation of error avoided. - Latitude. All the known methods of determining latitude have been used in the coast survey, for the purpose of ascertaining their relative merits. Large vertical circles or repeating theodolites were first used for observing double altitudes; but these made way for more perfect and larger instruments, the zenith sector, the prime vertical transit, and the zenith telescope or equal altitude instrument. The first mentioned of these instru-ments, constructed according to the plan of Prof. Airy, gives very satisfactory results; but it is rather heavy for transportation, and the observations are laborious. The method of determining latitudes by observations of transits of stars over the prime vertical, first used by Bessel, is admirable in theory, but in practice a great loss of time and labor is often caused by clouds.

The zenith telescope, or equal altitude instrument, was first applied to the determination of latitudes by Capt. A. Talcott, a former officer of the United States army; it has been remodelled and specially adapted to the purpose in the coast survey, where it has become a favorite instrument on account of the great number and accuracy of the results that can be obtained in a given time, and the facility with which it is used. A large number of observa-vations (from 150 to 200) are made at each station, and the mean is taken as the result, the uncertainty of which is thus reduced to a small fraction of a second. Mr. George Davidson has devised an instrument, now in successful use both on the Atlantic and Pacific coasts, which combines in a simple and beautiful manner the principles of both the zenith telescope and the transit instrument, so that observations for longitude and latitude may be made by the one instrument at the same station. This instrument gives general satisfaction for its compactness, delicacy, and accuracy, and will doubtless soon be in general use. - Longitude. For the purpose of determining the longitude of all points in the coast survey, with reference to Greenwich and other European observatories, it is only necessary to ascertain that of one point, the difference of which from all others is known by the triangulation, and by differences of longitude obtained by means of the electric telegraph.

The observatory of Cambridge, Mass., has been used as such a point of reference. Its longitude from Greenwich has been determined by astronomical observations of eclipses and occupations of stars by the moon, and of moon culminations, made not only there, but at other observatories in the United States, the longitude of which from Cambridge has been determined by electric telegraph. Besides the as-' tronomical methods, a chronometric method has also been used. A large number of chronometers have been transported repeatedly and in different years between Cambridge and Liverpool, for the purpose of comparing the time of the observatories at those places. The results of these expeditions, in which special regard was had to the effect of temperature on the rates of the chronometers, show a pretty close agreement in different years, but differ from those by astronomical observations by about two seconds of time. The telegraphic determinations of longitude have been extended from Washington northward to Philadelphia, New York, Albany, Cambridge, Bangor, Calais, and Halifax; southward to Petersburg, Wilmington, Charleston, Savannah, Pen-sacola, Mobile, and New Orleans; and westward to Cincinnati, St. Louis, Salt Lake City, and San Francisco. Most successful results have also been obtained from the telegraphic campaigns between Heart's Content and Valen-tia over the British Atlantic cable; and equally good determinations have been secured between Havre, France, and Duxbury, Mass., over the French submarine cable.

The results have been entirely satisfactory, and have given the difference of longitude between Greenwich and Cambridge within the smallest limits of error. Through these methods the longitude of San Francisco on the Pacific coast is as accurately known as that of Cambridge or Greenwich. In the telegraphic method, which is by far the most accurate for determining difference of longitude, the coast survey has taken the lead, and has brought it to a state of perfection which subsequent operations of a similar nature executed in Europe have not yet reached. The idea of comparing the local time of different places by means of the electric telegraph is sufficiently obvious, and dates from the conception of the telegraph itself. But the refined methods by which the intervention of human senses and operations, and the consequent liabilities to error, are in the greatest possible degree avoided, and by which the time of transmission is measured and eliminated from the longitude, have been the result of careful study and long experience. The first experiments on the velocity of galvanic signals were made in 1848. They have since been frequently repeated; and the velocity is found to vary from 10,000 to 20,000 miles per second, according to the size and kind of wire employed.

The manner in which this experiment is made is essentially as follows: An astronomical clock is so connected with the telegraph wires as to graduate by its beat slips of paper delivered with uniform velocity into spaces representing seconds of time, each about an inch in length, both at the place where the clock is and at some distant station. If now, at the latter station, arbitrary signals are made between those given by the clock and transmitted to the clock station, the corresponding marks on the register of that place will appear later, or more distant from the preceding clock marks than on the register where they are made. The difference measures the whole time of transmission from the former to the latter station and back again. On the Pacific coast, besides the telegraphic determinations already spoken of, longitudes have been determined by the astronomical methods and also by chrono-metric expeditions. In 18G0 an expedition was undertaken from Point Hudson, Admiralty inlet, to Gray's harbor, Washington territory.

In 1801 another was made between San Francisco and Coos bay in Oregon. In 1867 the first Alaska expedition was undertaken from San Francisco, during which the ports of Victoria, Port Simpson, Sitka, St. Paul's harbor, Captain's harbor, Port Lincoln, and Stony island were visited. In 1809 the second Alaska expedition took place, and Astor point in Columbia river, Esquimalt on Vancouver's island, Victoria, Fort Wrangel, Kok-klux, and Sitka were visited. In 18(59 an expedition was made from San Francisco to Eureka in Hum-bolt bay, California; and in 1870 another between San Francisco and Pimta Arena. - Azimuth. The direction of the meridian is determined by observations on the pole star, or other close circumpolar stars, at the time of their passing the meridian, or of their greatest eastern or western elongation. The angle between the vertical plane passing through the star and that passing through one of the triangle sides is measured with a theodolite. The angle which the former plane makes with the meridian can be computed from the time of observation and the star's place; and thus the azimuth, or true bearing of the triangle side, becomes known, as well as the bearing of all other sides connected with it by triangulation. - Topography. This is a representation on paper of the natural features of the country.

The outlines of the shore, the irregularities of the surface, the forms and dimensions of hills, forests, streams, rocks, meadows, towns, and villages, are all represented by certain conventional modes of drawing, well understood by those who make use of the maps. The drawing presents to us the surface of the earth as it would appear to an observer from above it. The surveyor uses a table or board on which is fitted a sheet of drawing paper. On the latter several points of the triangulation are already plotted. For the mapping and delineation of intermediate points use is made of the alhidade in connection with the plane table, as the table mentioned above is called. The plane table is a well seasoned drawing board, about 30 inches in length and 24 in width; it is usually composed of several pieces of wood grooved together in such a manner as to prevent warping, and is supported upon three brass arms which are connected with and supported by a tripod arranged with levelling screws. The sheet upon which the country is to be mapped is fastened to the table by means of brass clamps. The alhidade consists of a brass rule about 22 inches long, having a circular level on its upper face.

Near the middle of the rule* is a perpendicular cylindrical column of brass called the standard; on the top of this standard is a square brass plate, which supports four columns; these in their turn .uphold two cross pieces, upon which rests the axis of a telescope. To one end of the axis is attached a vertical arc, which is used in the measurement of vertical angles for heights. The telescope itself has the usual cross bars and means of focal adjustment. In practice the operation of the plane table is as follows: The surveyor places his table upon the ground, properly adjusts it by the levelling screws, and determines its position on the sheet by drawing lines on the paper, in the directions of at least three of the trigonometrical points. The intersection of these lines on the paper will give the position which his table ought to occupy on the map. Having fixed this point, lie directs the telescope of his alhidade to any prominent points in sight, and draws lines in their direction by means of the ruler. Then going to a second point, and fixing his position in the same way, he sights to the same objects as before from his new position. The lines thus drawn on the sheet will fix by their intersection the places of all these points on the map.

It is in fact a practical continuation of the triangulation on a minute scale. Accidental details of ground and slight irregularities of shore line may be drawn by the eye. The topographical maps are generally surveyed on a scale of 1/10,000 of the natural dimensions. In localities where a great amount of detail is to be represented, such as large cities and their vicinity, a scale of 1/5000 is employed; and in some special surveys so large a scale as 1/500 has been used. On the other hand, on fiat and thinly settled ranges of the coast, a scale of 1/20,000 is employed. The extent of ground represented upon a single topographical sheet depends upon the scale. On a scale of 1/10,000, or about six inches to the mile, a square foot of the drawing represents about four square miles of the surface of the earth. The metre chain, which was frequently used in topo-graphical work to determine distances where the usual means of intersection could not be applied (as in roads, on beaches, &c), is now to a great extent superseded by a simple but very useful instrument called a telemeter.

This, as used in the coast survey, is simply a scale of equal parts, painted upon a wooden rod 10 feet long, 5 inches wide, and 11/4 inch thick, so graduated that the number of divisions upon it, as seen between the upper and lower horizontal wires of the telescope of the alhidade, is equal to the number of units in the distance between the observers eye and the rod held at right angles to the line of sight. In all cases it should be graduated experimentally for the particular instrument and eye of the observer who has it in use. Thus the topographer, without moving from his position, can determine with accuracy the distances from him of any number of points within 300 metres. The telemeter has 'given very satisfactory results. - Hydrography. The survey of the land having been completed by the method detailed, the hydrographer is ready to plot his soundings and observations in their proper places on the map. Under the head of hydrography are placed all those operations which are performed at sea for the determinations of the positions of the rocks and shoals, the depths of the water, and the investigations of tides, currents, etc.

The principal labor is that of sounding. "With the outlines of the shores furnished by the topographer, the hydrographer has only to measure certain angles upon the shore signals at regular intervals in the progress of a lino of soundings, and the position of his boat or vessel on the line is thus determined, and of necessity the soundings taken on the line. These determinations are so accurate that the navigator may run his course by the soundings given on his charts. The angles are measured by a sextant, and the positions plotted upon the chart. In practice, the position of the boat is determined at intervals which vary according to the depth of water, the speed of the boat, the force of the tidal current, the frequency with which the soundings are taken, and the character of the bottom. Thus in strong tideway, or in a rocky and uneven bottom, angles would be taken at very short intervals; while in smooth even bottom as much as five minutes is often allowed to elapse between any two angles. The intermediate soundings, being taken at equal intervals of time, are laid down at equal intervals between the positions determined by angles.

The number of soundings is generally so great that the features of the bottom of the sea, within a wide belt adjacent to the coast, are almost as well determined as those of the land; and with the further assistance of the specimens of the bottom which are brought up by the sounding-lead, the mariner may during foggy weather determine his position with considerable accuracy by soundings alone. - Physical Hyihography. The hydrographer determines the soundings alonir the coast and in the various harbors, the position and extent of the various shoals and rocks and the depth of water upon them, the rise and fall of the tides, the direction and velocity of the currents, and the various changes that take place in the channels and bars of our coast. Physical hydrography has for its province the investigation of the causes of these changes, with a view to determining the laws upon which they depend, and if possible to provide remedies. It studies in particular the whole subject of tidal currents, and their effect upon the harbor channels; the effect upon these channels of the increase of wharf lines in cities; the improvement of harbors by breakwaters and sea walls; the action of the sea upon beaches; and all of the many questions which arise in the discussion of the laws of change in harbors and on the coast.

The coast survey has done much in the way of investigations in this science, especially in the harbors of Boston and Portland. In the latter city extensive operations are in progress for improving the Back bay, the result of the recommendations of the present superintendent, based upon surveys and reports made by his officers. In Boston a most extensive system of improvements has been going on for years, which will in a short time greatly increase the value of that already excellent harbor. At Edgartown and Vineyard Haven in Massachusetts, at the harbor of Nantucket, and at Chatham, examinations have been made and improvements projected, which will ultimately redound greatly to the advantage of those harbors. Constant observations are made in New York harbor and its vicinity, and such improvements suggested as will arrest any unfavorable changes in the channel. This is a work of great labor and importance, and is increasing in success and usefulness year by year. - Tides. One of the most difficult questions presented to men of science is the solution of the problem of the tides.

The importance to the mariner of knowing the exact rise and fall, and the times of high and low water, may be appreciated when we consider that the entrances to many rivers and harbors on the Atlantic coast are obstructed by sand bars, which can only be crossed by vessels of more than ordinary draught at the highest stage of the water. It becomes therefore an object of immense importance to commerce and navigation to determine the laws which govern this rising and falling of the sea, and to furnish such rules as will enable the mariner to predict with certainty all the phenomena connected with this subject. There is indeed no subject which is so constantly in a sailor's thoughts, on approaching the entrance to harbors and rivers, as the tides. In many cases the safety of his ship and his life depend upon his precise knowledge of the time of high water, or the ebb and flow of the current. The theoretical solution of this question was one of the first results of Newton's theory of gravitation. The most casual observer may notice the close dependence of the tidal phenomena upon the moon's motion. The wave of high water follows the moon in her motion around the earth by a determinate interval of time; and the height of the tide depends also upon the position of the sun and moon.

As the elevation of the water is produced by the joint attraction of the sun and moon, the height "will be greatest, of course, when those bodies are in conjunction, that is, at new and full moon, giving rise to what mariners call spring tides. When the moon is 90° distant from the sun, or in quadratures, the joint effect will be least, and the neap tides will be produced. The discussion of this problem has engaged the attention of the most profound mathematicians since the days of Newton, particularly Laplace; and yet the mathematical theories, although correct, have failed until recently in giving results which have been confirmed by observations. The cause of the discrepancies has existed, not in the mathematical deductions, but in a want of knowledge of the physical geography of the globe, and of the depth and form of the bottom of the sea; and, although very important advances in our knowledge of this subject have been recently made by scientific men both at home and abroad, yet it may be said that it is still one of the most perplexing questions in physical science. Prof. Bache, on assuming charge of the coast survey, organized a system of tidal observations, embracing the entire coast.

It is the most extended system of ob-servations that has yet been attempted, and has already produced highly useful results. Of these the most important to mariners is the publication annually by the coast survey of a series of tide tables, by which they are enabled to predict with great accuracy the time and approximate height of the tides at any of our more important harbors for every day in the year. This useful publication has now been in existence for several years, and its advantages to the sailor are almost incalculable. Tidal observers in the coast survey service are required to note hourly the height of the water at each tidal station, by means of a staff placed in the water, by which also the precise times and height of high and low water can be determined. A self-registering machine is also much used, which, through the medium of clockwork, traces a curve on paper representing the successive changes in the height of the water. More than 900 tidal stations have been established on the Atlantic coast; and on the western coast observations have been made at frequent intervals for a distance of about 1,500 miles. The observations at the principal stations are continued through several years.

Their investigation of course involves very laborious computations; the great object being to combine their results with theory, in such a manner as to furnish rules for the prediction of future results. The results of this branch of investigation in the survey have been published in the annual reports of the superintendent as the work has proceeded, showing the success which has attended the operation of the system. The report for 1856 contains tables of comparison of predicted tides of Boston harbor with the results of actual observation, in which the predicted times of high water coincide with the times observed within four minutes. Such accurate results had never before been obtained; and this contribution to knowledge may be regarded as one of the most important of the present day. In the published tables we have the predictions of the height and times of high and low water for over 250 points on the Atlantic coast. On the Pacific coast predictions have been made with equal success for a great number of stations, and these are annually increasing in number. Prof. William Ferrell has developed a new method of calculating tides, of a purely dynamical kind.

The method hitherto in use has consisted in supposing the water to be in a state of equilibrium under the attractions of the earth, moon, and sun, and then applying purely empirical corrections to the results so obtained. Prof. Ferrell has taken account of the fact that the water is in motion and has momentum. This was first done by Laplace, but unsuccessfully, because friction was neglected. Ferrell has taken account of this. His theory has been applied by himself, at the desire of the present superintendent of the coast survey, to the case of Boston harbor; and its superior accuracy has thus been demonstrated, as well as its great value in saving laborious calculations of empirical corrections. Prof. Peirce has given much study to the calculation of the effects of friction on tidal currents; and his results, combined with the original observations and researches of Mr. H. Mitchell, have produced a great advance in the theory of this subject, and important practical rules for draining tide lands, etc. - Figure of the Earth. The geodetic system of surveying originated in the efforts of philosophers to determine the precise figure and size of the earth.

It is well known that the earth is not exactly spherical in shape, but is flattened slightly at the poles of the axis about which it revolves, this axis being about 26 miles shorter than the equatorial axis. The determination of the relative lengths of the earth's axes has been one of the most important physical problems of all ages. The dimensions of the earth are of course essential elements in the mathematical investigations connected with astronomy, and in the computations of trigonometrical surveys. The measurement of extended arcs of meridian and parallel furnish the best means of determining these lengths; and the problem has been considered of so much importance, that expensive expeditions have been fitted out, and surveys made in different parts of the world, for this object alone. But, although approximate determinations have been made, it cannot be said that the dimensions of the earth are definitely settled. The primary triangulation of the coast survey furnishes incidentally valuable contributions to science in this respect.

An arc of the meridian 1,500 m. in length has been measured in India, one of 1,800 m. through Russia, extending from the Black sea to the Arctic ocean, and another of 900 m. in France, from Dunkirk to the island of Formentera in the Mediterranean. Several arcs have also been measured in Germany; and in fact there is hardly a civilized nation that has not contributed its share to our knowledge of this subject. It was in the first attempts to measure the French arc that the science of geodesy originated. In the United States, an arc of the meridian has been measured by the coast survey, between the years 1844 and 1867. It extends from Nantucket in Massachusetts to Farmington in Maine, and is 3° 23' in length. A second arc is in process of measurement between Ocracoke inlet in North Carolina and the head of Chesapeake bay. The northern part, which extends over Chesapeake bay, was completed in 1871, and is 2° 40' in length. The total extent of the whole arc when completed will be about 4° 32'. Other arcs will be measured as the geodetic work advances. - Variation of the Compass. It is well known that every navigator determines his course and direction by means of an instrument called the mariner's compass, which depends solely upon the direction which a small needle or bar of steel assumes when magnetized and left free to move in any direction.

This direction is nearly north and south; and it was formerly supposed that the north end of the needle pointed directly to the north pole of the earth, to which it was attracted by some powerful agent in the polar regions. Continued observation and study of the subject, however, disclosed the fact that this was not true. The real direction of the needle at any point between the equator and the poles is inclined to the horizon, and also to the true meridian; or, in other words, the needle has a dip and a variation or declination. At Key West, for instance, in 1858, the dip of the needle was 55°; at Cape Hatte-ras, 68°; at New York, 73°; at Halifax, 76°; while the declination was 5° E. at Key West, and 6° W. at New York; and between these places there is a line where there is no variation from the true meridian. This line passes near Wilmington, N. C, Charlotteville, Va., and Pittsburgh, Penn. Going westward from this line, the declination of the north end of the needle to the east of the true meridian increases rapidly until the Pacific coast is reached, when it is from 15° to 20° E. It is found also that the direction at any one place is not constant, but that it changes not only during each day, but from year to year.

In surveyors' and mariners' compasses the dip of the needle is overcome by suspending it from a point above its centre of gravity; but the declination still exists, and gives rise to what is popularly called the variation of the needle. Surveyors on land have generally the means of as-certaining the variation by astronomical observations, by which very great errors in their maps may be avoided; but the common mariner has no such resource. In sailing from the gulf of Mexico to Portland. Maine, his compass would pass through all points from 5° E. to 13°

W. How is he to know this, unless it be put down on his chart? And how will a chart for one year answer for another, when the variation is constantly changing? It is plain that the laws which govern these changes must be found out, so that the changes may be predicted. The determination of these laws, and the actual direction of the needle at various points of the coast at particular times, have occupied the attention of the superintendents of the coast survey. It is impossible to explain here the delicate and laborious nature of the observations necessary for determining the direction and intensity of the magnetic force. The results published by the coast survey have been obtained by comparing the observations of many years with the deductions of theory, and may be said to exceed in importance and usefulness all that had previously been done in this country. From the results of observations made not only on the Atlantic and Pacific coasts, but also in the interior of the continent, a map has been constructed giving the lines across the continent along which the dip is the same, and along which the declination is the same, and corresponding lines for the intensity. From such results the laws are obtained for predicting future changes.

From these facts the importance of a full investigation of a subject of such vital interest to navigation may be appreciated. As it forms a part of the duties of the coast survey to furnish the mariner with all the information possible on this subject, it ought not to be neglected even in a brief account of the work. - Office Work. The observations and charts made in the field are at the close of each season's work sent to the coast survey office in Washington, where they are combined to form the charts. The trian-gulation and astronomical observations are subjected to a double computation, first by the observers, and next by the computers in the office, in order to insure perfect accuracy and faithfulness. The topographical and hydro-graphical sheets are combined, and reduced drawings are made on scales suitable for publication. A connected series of charts of the whole coast is projected on a scale of 1/80,000. Besides these, local charts of harbors and bays are published on larger scales, adapted to the importance of the locality and amount of detail to be shown.

General const charts are also published on a scale of 1/400,000.

When the reduced charts are drawn and verified, they pass into the hands of the engraving division of the office, where they are executed on copper. When the plates are completed, electrotype copies are taken of them, which serve for printing the charts, the original plates being preserved in the archives. The electrotyping establishment of the coast survey is very extensive, and one of the most successful in the world. It was in practical operation several years before the process came into general use, and considerable advances were made in the art at this establishment. Photography is also employed to reduce the original charts to the scale of the intended publications, and a photographic establishment has long been a part of the office. For reducing maps from one scale to another and transferring their outlines to the engraving plate, an instrument called a pantograph has been for some years employed. This is a repeating machine composed of a number of arms acting upon each other as levers, with points for tracing and engraving, and mounted upon traverse wheels, for ease and accuracy of movement.

This instrument can be set to any desired scale, representing the proportion which the map to be engraved bears to the original; and when so set, with the tracing point resting upon the original map and the engraving point upon the plate, if the former be moved over the map, the latter will reproduce upon the plate an absolutely exact copy of the original on the required scale. The advantage gained by dispensing with the old methods of reduction, which required an experienced draughtsman, at great expense, together with the greater accuracy resulting from but one operation in reducing from the original to the plate, is apparent when we consider the usual process of drawing, tracing, transferring, and entering by hand. Here are four distinct operations, each liable to more error than the one operation performed by the pantograph. The charts are finally printed at the office, and distributed for sale to agents in the principal seaports. The prices are fixed at very low rates, so as to place a complete set of charts within the reach of every navigator.

Provision has been made by congress for the publication of the observations made in the progress of the survey, so as to place the data on which the correctness of the charts depends beyond the possibility of loss, and to submit them to the criticism of the world. - Organization. The operations of field work which have been described are carried on simultaneously at many points on the coast. The Atlantic and gulf coasts are divided into nine, and the Pacific coast into two sections, each having its triangulation, astronomical, topographical, and hydrographical parties, all working independently, but upon the same system; so that, in the end, the whole will form a connected survey from Maine to Texas, and from San Diego to the 49th parallel on the Pacific. Besides these sections, since the acquisition of the territory of Alaska, the coast survey has added that large extent of coast to its already extensive field of operations; and parties have been at work there regularly, carrying on reconnois-sance, triangulation, topography, and hydrography, whenever the weather of that stormy region would permit.

For conducting these operations there are employed in the coast survey, exclusive of hands and seamen, 94 civilians of different grades, and 11 officers of the navy, a number of the latter being required for vessels engaged in hydrography, which are under naval discipline. This force does not include computers, draughtsman, engravers, and clerks employed in the office, all of whom number 93. The whole work is under the control of the United States treasury department; while the superintendent directs all the details of the work, governs the movements of the parties, and controls the expenditures. The expense is defrayed from annual appropriations by congress, made upon estimates submitted by the superintendent, which from 1853 to 1858 amounted to about $200,000 for the Atlantic and gulf coasts, and about $150,-000 for the western coast. Of late years, however, the work has become so much extended, and the labors of the survey so much increased, as to necessitate a much larger expenditure, not a small item in which is the appropriations for new vessels to replace those captured and destroyed during the war, and those which have become worn out by long and arduous service. The progress of the work from year to year is given to the public in the annual reports of the superintendent.

In these reports not only the results of the year's operations are given, but also the ways and means by which they are obtained. The liberality of congress in publishing and largely distributing these reports has tended greatly to increase the public interest in the work. - The investigations of the tides, the Gulf stream, the magnetic force of the earth, and the meteorological conditions of the atmosphere, have an equal bearing upon the interests of navigation and commerce and the sciences connected with the physical condition of the globe. But there are other practical results of the coast survey which have a more direct influence in protecting our commerce from the dangers by which it was formerly attended. A consideration of these results will exhibit the advantage of an intelligent application of true scientific principles in all works of this character. Previous to the year 1844, 300 vessels were wrecked annually on our coast, attended with a great loss of life. Of these vessels one sixth were destroyed on the Florida reefs. To illustrate the causes which led to this great loss of life and property, it will only be necessary to mention a few of the discoveries made in the survey of the coast.

The position of the entrance to Delaware bay, between Cape May and Cape Henlopen, was found to be eight miles in error. Six dangerous shoals were discovered in one year in the vicinity of Nantucket, lying directly in the track of our European commerce, and of the heavy coast trade between the eastern and southern states. A new channel, with two feet more water than any other, was discovered in the entrance to New York harbor. Dangerous shoals were discovered at the entrance to Chesapeake bay, and along the coasts of Virginia and North Carolina. Innumerable other discoveries of no less importance have been made, but space forbids other mention of them. The few above given are sufficient to show the inaccuracies of all our charts previous to the investigations of the coast survey. The means that have been applied to correct these great evils have not been incommensurate with the end. It may be said that advantage in economy is not the least of the practical results of the scientific methods of the survey. Compared with foreign surveys, it is not only more accurate in detail, but its results have been produced with a rapidity and economy altogether unprecedented. The English survey was commenced in 1791, and is still unfinished, the land work being as yet unconnected with the hydrography.

The cost of that survey is more than four times the cost of ours. During the ten years previous to 1848, Great Britain expended for hydrography alone $7,500,000. The total cost of the United States coast survey up to that time was only $800,000, including land work and hydrography. At the present time, while the survey has extended its operations across the whole continent, and even included the distant domain of Alaska, its expenditures, including the cost of building a number of new vessels, have been comparatively small. With this small expense the survey has been extended so as to embrace the whole of our Atlantic, Pacific, and gulf coasts. During the year 1872 12 triangulation parties, 2 astronomical parties, 12 hydrographical parties, and 14 topographical parties were in the field on the Atlantic and gulf coasts, and 13 parties on the Pacific, besides the computers, draughtsmen, engravers, etc, employed in the office. Up to the present time (18V3) 1,282 original topographical and 1,144 hydrographical sheets have been surveyed, and charts of 240 harbors on the Atlantic and gulf coasts, and of 100 harbors on the Pacific, have been published, besides 209 coast and sailing charts, great numbers of copies of which have been issued.

An elaborate and careful "Coast Pilot" of the Atlantic coast is in process of preparation, and one has already been completed and published for Alaska and the Pacific coast.