(1) Another name for nomogram, from the French "abaque". (2) A nomogram used in aerial navigation. (1) (astronomy) The deviation of the apparent (observed) direction of a light source from its true direction (the direction of a line from observer to source at the instant of observation) caused by the velocity of light from the source and the velocity of the observer relative to the source. Aberration does not occur if source and observer are moving directly towards or away from each other. Such motion affects the frequency but not the direction of the light received. See also Doppler shift. In astronomy and geodesy, aberration can usually be separated into two parts: that which results from the motion of the observer alone and that which results from the motion of the source alone. That part attributable to the motion of the observer is given by

sin (q - qo) = (| o| / ||) sin q o

where q is the true direction to the light source, q o is the observed direction, o is the velocity of the observer, and is speed of light. The directions are measured from the vector o. Only two kinds of motion of geodetic importance affect o: the rotation of the Earth which causes diurnal aberration, and the revolution of the Earth, which causes annual aberration. The part of the aberration attributable to motion of the source alone is known as planetary aberration. (2) (optical system) Any failure of an optical system to image a point in object space as a point in image space or to preserve a uniform scale over the image. An aberration therefore causes either a blurring or a distortion of the image. Seven basic varieties of optical aberration are recognized. Five kinds (called seidel aberrations) affect monochromatic light: spherical aberration, coma, astigmatism, curvature of field, and distortion. Two kinds (called chromatic aberrations) affect polychromatic light: aberration. The first three aberrations cause points to appear as blurs. In the next two, points are resolved as points, but the object point and its matching image point do not lie on a straight line through the center of perspective. The two chromatic aberrations cause an object seen in white light to become a set of blurred, multicolored images. The apparent change in direction of stars, planets, and other celestial bodies, caused principally by the changing direction in which the Earth is moving, in its revolution about the Sun, with respect to the line connecting the Earth to the celestial object. During the course of a year, a star on the ecliptic appears to move from one end of a straight line and back again; the length of the line is twice the constant of aberration. () A star at the pole of the ecliptic appears to move in a circle whose diameter is twice the constant of aberration. Stars between the ecliptic and the pole appear to move in ellipses of major diameter twice the constant of aberration and with minor axes increasing with angular distance from the ecliptic. The ellipticity of the Earth's orbit causes the apparent paths of stars not in the ecliptic to vary slightly from the elliptical. Because the Earth revolves also about the common center of gravity of the Earth and the Moon, a small component (0."01) of aberration with monthly periodicity is induced. The separation, by an optical system, of a single ray of polychromatic light in object space into a number of monochromatic rays in image space that do not refocus to a single point. In the absence of other kinds of aberration, chromatic aberration causes the separation of a white point in object space into a sequence of overlapping monochromatic points in image space, with the violets closest to the lens and the reds farthest from the lens. The two kinds of chromatic aberration are: longitudinal and transverse. Longitudinal chromatic aberration produces a sequence of overlapping differently colored points parallel to the optical axis; transverse chromatic aberration produces a similar sequence of points along a line across (transverse to) the axis. The maximum, theoretical value k of the annual aberration. It is given by the formula

k = 2p a/[c T(1 - e2)1/2 ]

in which a is the mean distance of the Earth from the Sun, c is the speed of Light, T the length of the sidereal year, and e is the eccentricity of the For the epoch 2000 A.D., k has the value 20."49552 (Seidelmann 1977). The quantity k is given by

k = (2p R cos f')/ cT

where R is the radius of the Earth at the observer's geocentric latitude , T is the length of the sidereal day, and c is the speed of light. Because k is a function of f, the term "constant" is not well taken. Another definition of k omits the factor cos f (See Woolard and Clemence 1966, p. 129), yielding k =0."32. The difference in apparent directions of moving sources of light having the same true direction. Differential aberration results when the angular velocities of the sources, as seen by the observer, are different, and is a form of planetary aberration; also called parallactic aberration. Photographs of artificial satellites against a stellar background show differential aberration. The apparent change in direction to a star or other celestial object caused by the combination of the velocity of light and the velocity of the observer on the rotating Earth. Diurnal aberration is taken into account in first-order determinations of astronomical azimuth and longitude; it is not considered in determinations of astronomical latitude because an observer has practically no latitudinal motion. The change in apparent direction of a light source, such as a planet or other astronomical body, caused by the movement source while the light travels to the observer. Stars do not show planetary aberration because they are so far away that light emitted at a particular time reaches the observer before the star has moved an appreciable angular distance with respect to the Earth. Planets and other bodies within the Solar System may, however, move through an appreciable angle during the time the light is traveling to the observer. When the body is an artificial satellite of the Earth, the aberration is called differential aberration by geodesists. Any one of five different aberrations that can prevent an optical system from imaging a point or straight line in object space into a point or straight line in image space. (2) for a list of Seidel aberrations. The focusing of rays emanating from a point source on the optical axis closer to the focal plane if they enter the optical system close to the optical axis than rays from the same source which enter the system far from the optical axis. The envelope of the converging rays is called the "caustic" of the system. The amount of spherical aberration varies with the location of the object point and, for any particular point, is approximately proportional to the square of the distance of the outermost rays from the optical axis. The adjective "absolute" as used in science and in geodesy in particular has several meanings. Examples are given below. (1) Defined in terms of standards and of measurements using those standards, without reference to any theory about the nature of the quantity measured. For example, an absolute coordinate system is one whose position and scales are specified with respect to real, identifiable points and distances and directions with respect to these points. The points and the distances and directions are the standards by which the coordinate system is defined. (2) Defined in terms of naturally occurring things or phenomena. For example, an absolute coordinate system in this sense could be one using the Earth's axis of rotation and the direction of gravity to establish directions, and the Earth's gravity potential to establish vertical scales. (3) Measurable (or measured) directly in terms of length, mass, and time. For example, measurement of the acceleration of gravity by measuring the acceleration of a falling object would be an absolute measurement, while measurement of the relative extension of a weighted spring at various places would be a relative measurement. (4) Defined with respect to some natural base or unit. For example, the "absolute zero" of temperature is the lowest (theoretically) attainable temperature. (of temperature) The quantity - 273.16oC on the Celsius (formerly centigrade) temperature scale. By definition, the triple-point of water is at +273.16K on the Kelvin (absolute) temperature scale. Absolute zero is the theoretical condition of complete absence of heat; all molecular motion ceases. (field survey). A list of values of a certain quantity made for a survey, derived directly from measurements of that quantity and recorded in the field book. Specifically, one of the following lists. (a) In triangulation, a list of angles or (most commonly) directions, of differences of elevation along a base line, or of zenith angles. The measurements may be copied directly into the abstract from the field book or may be changed slightly: this is done, for example, in the case of an abstract of directions, in which a constant value is added to the measured value to make a particular direction equal to zero. (b) In leveling, a list of measured differences in elevation, with corresponding distances and other pertinent information. A list of all courses and distances made good, together with all data to be used in plotting and adjusting the dead-reckoning line. A complete summary of all information on public record relating to ownership (title) of a piece of land. An abstract of title customarily cites the surveys delimiting the land, shows plats made from the surveys, and lists changes of ownership, mortgages, liens, etc.; often referred to simply as "abstract". The common practice of referring to the abstract of title as the title should be discontinued because, legally, they are entirely different things. The boundary of land described in terms of the other pieces of land, highways, etc., adjoining and bounding that land. For example, "abutted on the west by lot number 36." This term has also been used to denote the boundaries on the ends as distinguished from those on the sides, as "buttings and sidings." Also called buttal or butting. The rate, , of change of velocity,

= d /dt

where is the vector of velocity, and t the time. A device for measuring acceleration. A common design of such a device is a pendulum suspended from a pivot fixed to an accelerating body. As the body accelerates, the pendulum is deflected through an angle which is a function of the acceleration. Another common design embodies a mass held in the equilibrium position by springs or other elastic members; acceleration is then determined from the distortion of the elastic members. Masses resting on strain gauges have also been used as accelerometers. A particularly sensitive accelerometer embodies a mass suspended by electrostatic or electromagnetic forces; the acceleration is measured by the amount of force that must be used to keep the mass in a fixed position. An accelerometer that detects differential accelerations by measuring changes in capacitance has been used in satellites. One conducting sphere is centered within another and the pair are placed in free-fall. The relative motions of the inner and outer spheres indicate the presence of nongravitational forces on the outer sphere - principally air-drag or radiational pressure. The force used by the balancing system to keep the inner sphere centered is measured to provide an indication of the acceleration. (1) The ability of the eye to see sharp images of objects at different distances. (2) The ability of the eyes to bring two separate images into superposition. The gradual accumulation of land by natural causes, as out of the Sea or a river. Accretion occurs principally by actions of water of which there are two kinds: the deposition of solids and the receding of the edge of the water. The first kind is called alluvion and its result, alluvium; the second kind is called reliction or dereliction. Note that the term "accretion" applies only to the accumulation of land; the accumulation of solid matter under water is referred to as batture, as is the result of such accumulation. (1) Closeness of an estimated (e.g., measured or computed) value to a standard or accepted value of a particular quantity. Accuracy is commonly referred to as "high" or "low" depending on the size of the differences between the estimated and the standard values. (2) The square root of the average value of the sum of the squares of the differences between the values in a set and the corresponding values that have been accepted as correct or standard. (3) The reciprocal of the quantity defined in (2). Accuracy cannot be calculated solely from values based on measurements. A standard value or set of standard values must be available for comparison somewhere in the chain of calculations. The standard of reference may be: (a) an exact value, such as the sum of the three angles of a plane triangle being exactly 180o; (b) a value of a conventional unit as defined by a physical representation thereof, such as the international meter, defined by the orange line of Kr30 86; (c) a value determined by refined methods and deemed sufficiently near the ideal or true value to be held constant, such as the adjusted elevation of a permanent bench mark or the graticule of a map projection. (4) Applied to the numbers in a mathematical table or to the numbers produced by a digital computer, the term "accuracy" may mean (a) the number of significant digits in the numbers, (b) the order of magnitude of the least significant digit, or (c) the number of correct places in computations made with a mathematical table. Applied to numbers produced by an analog computer, the term has meaning (1) above, where the "measured" quantities are the computations made by the computer and the correct values are those that would have been obtained by exact calculation. A unit of area in the English system of measure, defined as 10 square chains (l chain equals 4 rods or 66 feet). An acre is exactly equal to 43,560 square feet or 4,840 square yards, and is approximately equal to 4047 square meters. There are 640 acres in a square mile. By an ordinance of Edward I in 1303, the acre was defined as the area contained in a rectangle 40 rods long and 4 rods wide. With the rod defined as 5 1/2 ulnae (yards), as defined by the Edward I iron standard for the ulna, the acre is again 4,840 square yards. The term "square acre" is meaningless and should not be used. Lying near or close to. "Adjacent" implies that two objects or parcels of land are not widely separated, although they may not actually touch, while "adjoining" implies that no third object or piece of land lies between them. Touching, as distinguished from being merely close to or adjacent. "Adjoining" and "abutting" are at present often used as synonyms. However, there is an old, useful distinction: two parcels adjoin if they have a common side; they abut if they have a common end. (1) The process of changing the values of a given set of quantities so that results calculated using the changed set will be better than those calculated using the original set. The concept "better" is vague. The most common interpretation is that the sum of the squares of differences between results obtained by measurement and results obtained by calculation shall be a minimum. With this criterion, the method of least squares is the required process. (2) The result of an adjustment in the above sense. Synonymous in this sense with "results". (3) The process of finding, from a set of redundant observations, a set of "best" values, in some prescribed sense, for the observed quantities or for quantities functionally related to them. For example, if each angle of a plane triangle is measured, it is likely that the three values will not add up exactly to the 180o required by geometry. The mathematical process of calculating three angles which do satisfy the requirement is called the adjustment. The three resulting angles are then called adjusted values. In general, there will be N given (observed) values and N equations relating them to unknowns. Adjustment is the process of reducing the N equations in M unknowns to M equations in M unknowns and solving this set of equations. The M equations are sometimes called the reduced equations. (4) Geological changes in the Earth, under the influence of gravity, that occur because of a change in the distribution of matter on the Earth's surface. Such changes create a shift from static equilibrium of the Earth's masses, and displacements called adjustments occur in the crust (and probably in the mantle) to compensate for the surface changes and to maintain static equilibrium. See also isostatic compensation. (1) The determination of corrections to the coordinates of a set of points extending over a large area, the solution being obtained simultaneously for all the points. The term block adjustment is used to distinguish this process from that in which the points are arranged along strips or arcs and corrections are obtained first for coordinates of points within each strip or arc and the results for these strips or arcs are then modified so that they fit together without any inconsistency. See also aerotriangulation adjustment, block; aerotriangulation adjustment, bundle; triangulation adjustment, Bowie method of; and Helmert blocking. (2) The same as definition (1), except that the adjustment need not be done for all points simultaneously. A process of calculating a set of values so that the largest difference between any of these and the corresponding observations is smallest in absolute value. An adjustment in which the number of independent constraints (a priori conditions among the quantities to be adjusted) is minimal, that is, just sufficient to ensure a unique solution. Such an adjustment is "free" of distortion that may be introduced by redundant constraints. A free adjustment produces residual and adjusted observables that are not dependent on the particular minimal constraints used and is preferred for statistical evaluation. Also called "adjustment using minimal constraints" or "inner adjustment". The adjustment of the values of geodetic quantities, such as lengths, angles, directions, coordinates, etc., that characterize a geodetic network. The adjustment of a horizontal geodetic network. An adjustment satisfying the condition that the sum of the squares of the differences between the given and changed quantities be a minimum. The adjustment of a vertical geodetic network. The process of adjustment applied to observed values; the process of calculating, from observed values of quantities, values (of these quantities) that are better in some specified sense. Either the observed or the theoretical values may be considered the true values of the quantities. When the term "adjustment of observations" is used, the theoretical values are commonly considered the true values. The numbers resulting from an adjustment are called the "adjusted values", and the differences between observed and adjusted values are called the errors in or the corrections to the observed values. The above terminology is not universal, and there has been criticism directed at use of the term "adjustment of observations" on the ground that an observation (i.e., its value) is an established fact and cannot be changed or adjusted. See also traverse adjustment, triangulation ad justment, leveling adjustment, and gravity adjustment. Determination of the bz values during orientation of the successive models on a stereoplotter using barometric measurements of the altitudes of the air stations (recorded during photography). Only differences in altitude are required; these are provided by the statoscope. Phototriangulation using aerial photographs. Aerotriangulation is also called aerial triangulation. Radial aerotriangulation (see aerotriangulation, radial ) in which the unknown coordinates of ground points are determined mathematically from measured coordinates, on the image, of radial centers and directions to the images of the unknown points. Determining the coordinates of ground points in a strip of aerial photographs when coordinates are known for ground points at only one end of the strip. Commonly contrasted to bridging, in which ground control is known at both ends of a strip. A graphic radial aerotriangulation done by tracing the directions from successive radial centers directly onto a transparent plotting sheet rather than by transferring the directions to templets. Also called direct radial plot. A radial aerotriangulation done by other than analytical means. Graphic radial aerotriangulation is usually done directly, incorporating the ground control plotted on a map, map graticule, or map grid, but may first be done independently of such control and later adjusted to it as a unit. In the latter case, the scale and azimuth of the resulting network are not known until the network is adjusted to the ground control. A graphic radial aerotriangulation may be made by several methods: slotted-templet, spider-templet, and hand-templet. Aerotriangulation in which horizontal control extension is accomplished by a combination of resection and intersection using directions of images from the radial centers of overlapping photographs. Radial aerotriangulation can be done graphically or analytically, but it is assumed to be grahical unless otherwised specified. A radial aerotriangulation is also termed a "radial plot" or a "minor control plot" or, inappropriately, "radial triangulation". The radial center for near-vertical photographs may be the principal point, the nadir, or the isocenter. A radial aerotriangulation is assumed to be made with the principal points as radial centers unless the modifying term designates otherwise, or unless the context states that a radial center other than the principal point was used. A form of graphic radial aerotriangulation using stereotemplets prepared from stereoscopic models. The method permits doing an aerotriangulation for a whole area at once and is not restricted to aerotriangulation along strips of photography. A direct radial aerotriangulation in which the photographs are plotted in flight strips without reference to ground control and the strips are later adjusted to each other and to the ground control. A method of computing the horizontal coordinates of the ground points corresponding to the principal points of overlapping aerial photographs by resecting on three horizontal control points appearing in the overlap. (1) An aerotriangulation adjustment in which the ground points whose coordinates are to be determined are not necessarily imaged on a single strip of photographs but mutually consistent corrections are determined without regard to the possible occurrence of the photographs in strips. The photographs, when assembled, generally form a rectangular (block-like) an array. (2) The same as (1), except that the corrections are determined simultaneously for all the photographs. Also called bundle aerotriangulation adjustment. (3) The same as (1), except that the photographs occur in strips and the coordinates of points imaged in each strip are determined first for each strip and then adjustments are made between coordinates of points in different strips. (1) An aerotriangulation adjustment based on the principle of collinearity, i.e, the geometry underlying this adjustment is that of bundles of rays passing through perspective centers and joining ground points to image points. A method of orienting a strip of photographs by using the Bz-curve to find the difference between the true photographic nadir point and that indicated by a multiplex type of stereoscopic plotting instrument. The strip can also be leveled by this method if the aircraft's altimeter altitude is used. An aerotriangulation adjustment in which the corrections to coordinates of ground points are determined separately for each pair of overlapping photographs and the inconsistencies between coordinates from different pairs are removed in a second or third series of computations. An aerotriangulation adjustment in which the photographs are arranged in strips and the corrections are determined simultaneously only to the coordinates of ground points appearing on each strip; a second set of computations is then made to minimize the disagreements between coordinates obtained for points common to two or more strips. The time elapsed since the preceding new moon. It is usually expressed in days. (1) The line joining two air stations from which overlapping photographs have been taken. (2) The length of the line in (1) above. (3) The distance, in a stereoscopic model, between adjacent perspective centers as reconstructed in the stereoscopic plotting instrument. Also called model base or base. The analog, in the model, of the line or distance between adjacent locations of the camera. A system that constantly measures and records the altitude of an aircraft by combining the outputs of a precise radar altimeter and a very sensitive barometric altimeter. At the same time, the point from which the altitude was measured is determined by means of a camera synchronized with the pulses from the altimeter. Also called APR, TPR, and Terrain Profile Recorder. The point occupied by the perspective center of an aerial camera at the instant a photograph is taken. One of the two points on which a bar of standard length rests when in use; these points are equidistant from the ends of the bar and separated by 1/square root of 3 the length of the bar. Such a suspension produces least deformation of the bar by its own weight. The ratio of the total amount of radiation (power) reflected or scattered by a body to the total amount of radiation incident on the body. In practice, albedo is measured and calculated only for the observable portion of a body. For example, the albedo of the Moon is calculated for the visible face only, although this is not stated when giving the Moon's albedo. The albedo of the Moon is 0.07, the albedo of the Earth is 0.39, the albedo of Jupiter is 0.51. A set of instructions for solving certain types of problems, particularly calculations. Eratosthenes' algorithm for finding all the primes less than a given number is an example. Most instructions (programs) for digital computers are algorithms. (1) The compensation, by changes in amplitude of terms in a finite Fourier series, for frequencies present in the data but not represented in the series. (2) More generally, the differences between the values of the constants in a mathematical representation of data and the values the constants would have if the representation were improved by adding more terms. The part of a surveying instrument which consists of a sighting device, with index, and accessories for reading or recording data. The alidade of a theodolite or surveyor's transit is the upper part of the instrument, it includes the telescope, the micrometer microscopes or verniers, and accessories, all mounted on what is called the "upper motion" of the instrument. It is used in observing a direction or angle on a graduated circle which is mounted on the "lower motion". The alidade used in topographic surveying consists of a straightedge carrying a telescope or other sighting device, and used in recording a direction on the plane table sheet. The movable arm of a sextant is an alidade. An alidade consisting of a peepsight mounted on a straight edge so that the edge of the straight edge is parallel to the vertical plane in which the line of sight rotates. A telescopic alidade containing a pendulum instead of a level for establishing the direction of the horizontal line of reference for vertical angles. An alidade containing a damped pendulum that automatically brings the index mark of the vertical arc to the correct reading on the scale even if the base of the alidade is not quite level. An instrument composed of a telescope mounted on a straight edge ruler, and used with a plane table in topographic surveying. Also called a telescope alidade. (1) (alinement) The placing of points along a straight line or in a common vertical plane. (2) The location of points with reference to a straight line or to a system of straight lines. The use of the term in surveying should be limited to operations associated with straight lines. (3) In astronomic geodesy, the placement of the optical axes of a telescope in proper relation to the index marks on the horizontal and vertical, or the right ascension and declination circles. It should not be confused with collimation, which is the bringing of the optical elements of a telescope into proper relation with each other. The angle between the actual line of sight of a telescope and the direction in which the horizontal or vertical circles on the telescope or on an auxiliary telescope indicate that the line of sight should lie. (1) The formation of land from the bed of a river or body of water by the gradual, natural accumulation of matter on the bed or by the gradual, natural recession of the water. It is differentiated from batture in that the latter occurs beneath the water surface and does not form land. (2) The land formed by the gradual, natural accumulation of matter on the bed of a river or by the gradual, natural recession of the water. The solid material (sand, silt, gravel and other solids) deposited by running water. This material may accumulate to form land, the process (and sometimes the result) being referred to as alluvion, or it may remain beneath the surface of the water to raise the level of the bed (the result being referred to as batture ). An astronomical almanac prepared particularly for the use of aerial navigators. An annual publication containing, for each day or other suitable fraction of the year, information on the locations of celestial bodies, together with the times and circumstances of various astronomical events such as sunset and sunrise, of particular use for navigation. In 1980 the titles, The American Ephemeris and Nautical Almanac, prepared by the U.S. Naval Observatory, and The Astronomical Ephemeris, published by H.M. Nautical Almanac Office, were changed to The Astronomical Almanac. An astronomical almanac prepared particularly for use on ocean-going ships. Any small circle on the celestial sphere parallel to the horizon. Also called parallel of altitude and circle of equal altitude. (adjective) Rotatable in altitude and azimuth. Most geodetic transits, theodolites, and satellite-tracking instruments are usually alt-azimuth mounted. An instrument on an alt-azimuth mounting equipped with both horizontal and vertical graduated circles, for the simultaneous observation of horizontal and vertical directions or angles. The alt-azimuth instrument derives its name from the terms altitude and azimuth. Many theodolites and engineer's and surveyor's transits are alt-azimuth instruments. An instrument that determines its distance above a particular surface. This distance is usually referred to as the altitude of the instrument. There are two common types of altimeter: the barometric altimeter, which determines altitude above a surface of constant atmospheric pressure, and the radar (or laser) altimeter, which determines altitude above the physical surface of the Earth or other celestial body. An aneroid barometer whose scale is graduated in feet, yards, or meters as well as (or instead of) in units of atmospheric pressure. It indicates the distance of the barometer above a previously selected surface of constant pressure. The instrument measures air pressure and its scale is graduated to show altitude as a function of pressure. A barometric altimeter is calibrated by adjusting the instrument to read the correct elevation at a point of known elevation. Altitudes are then measured with respect to the surface of current constant pressure through this point. An instrument that determines altitude by measuring the length of time needed for a pulse of coherent light to travel from the instrument to the surface and back, and multiplies half this time by the speed of light to get the straight-line distance to the surface. The pulses are usually sent out in a narrow beam that may not illuminate the surface directly below the instrument. The beam's direction must therefore be known, or controlled. An altimeter which emits pulses at radio frequenceies, measures the time of transit to-and-from the surface below and converts this to a one-way distance by multiplying the time of transit by half the speed of radio waves in the atmosphere. A barometric altimeter used to determine approximate differences of altitude or elevation between points. Determining distances above the physical surface of the Earth or other celestial body, or above a level of specified (reference) air pressure. The usual instruments are radar altimeters or barometric altimeters. However, an aneroid barometer that indicates air pressure only may be used the pressures measured, and the results converted to altitudes by calculation. See also hypsometry. Altimetry differs from hypsometry in that the latter refers specifically to determining surface elevations; i.e., distances of a physical surface above the geoid. A method of determining differences of altitude from differences of atmospheric pressure observed with a barometer. By the application of certain corrections and the use of what is sometimes called the hypsometric equation, a difference of atmospheric pressure at two places is transformed into a difference of elevations of those places. If the elevation of one station above a reference surface (such as the geoid) is known, the approximate altitudes of other stations connected with it by barometric altimetry can be computed. By using barometers of special design, and including several stations of known altitude in a series of occupied stations, the accuracy of the altitudes determined for the new stations is increased. Corrections are applied for temperature, latitude, index of barometer, closure of circuit, diurnal variation in atmospheric pressure, etc. A method of determining approximate altitudes in regions where extremely rugged terrain exists. The method is identical to the two-base method of barometric altimetry, except that the roving barometers are carried by air and read in the aircraft as it passes on a level with the topographic feature whose altitude is to be determined. A method for quickly obtaining altitudes of points along a route between two points of known altitude by using four barometric altimeters in pairs. One pair of altimeters remains at the starting point while the other pair is advanced to the first point at which altitude is to be determined. At this point, the altimeters and weather instruments are read and the values are recorded. The pair at the starting point is now moved to the second point at which the altitude is to be determined, and the foregoing procedure is repeated. The pairs are advanced alternately, one past the other, until the last point of known altitude (which may be the starting point) is reached. (1) Determining the distance of a radar altimeter above the physical surface of the Earth. The radar altimeter is usually carried in an aircraft, but has also has been used in spacecraft and artificial satellites. Altitudes obtained from artificial satellites are usually converted to the geodetic heights of the physical surface, most commonly over water. (2) Determining geodetic heights of points on the Earth's surface using data obtained from altimeters on aircraft or artificial satellities. This method requires knowledge of successive locations of the altimeter with respect to the reference ellipsoid. Determining the distance of a satellite above the surface of the Earth or other celestial body by using a radar or laser altimeter in the satellite. A method of barometric altimetry using two barometers. One, designated the "base barometer", is left at a central point of known altitude and the other, called the "roving barometer", is moved from point to point of unknown altitude. At each point occupied by the roving barometer, the pressure, weather conditions, and time of observation are recorded; the same quantities are measured and recorded once every five minutes at the central (base) point. Data are later reduced to altitudes. Determining altitudes by measuring the temperatures at which water boils at points of unknown altitude. The temperature at which water boils at any point on the Earth depends on the atmospheric pressure at that point, which in turn depends in part on the altitude of the point. Factors other than altitude also affect atmospheric pressure, and factors other than atmospheric pressure affect the boiling point. Hence, thermometric altimetry is less precise than barometric altimetry. A method of altimetry using three barometers, two of which are placed at separate points of known altitude chosen so that the altitudes of all points occupied by the third barometer lie between those altitudes. The barometers and weather instruments at the two points of known altitude are read and recorded every 5 minutes. The third barometer and associated weather instruments are read as each point is occupied. Data for these points are later reduced to altitudes. (1) The distance of a location above a reference surface. The most usual reference surface is sea level. (2) The distance of a location above the physical surface of the Earth. "Altitude" is a generic term that defies exact technical definition. It is evident that distance must be determined along some suitable line. "Suitable" connotes a line whose direction closely approximates a perpendicular to the surface and passes through the location in question. See also elevation, height, and altitude, barometric (3) (1) The vertical angle between the plane of the horizontal (at the point of observation) and the line connecting the point of observation with the observed (or defined) object or point. The angular altitude is the complement of the zenith angle; it is also known as the altitude, the elevation, or the angular elevation. In surveying, the angular altitude is positive if the object is above the plane of the horizon and negative if below it. A positive angular altitude is also called the angle of elevation; a negative angular altitude is then called an angle of depression. The observed angular altitude corrected for instrumental errors, personal errors, and errors in the surface from which the angle is measured, but not for refraction, parallax, or semidiameter. Also called rectified altitude. (1) The distance between two surfaces of constant atmospheric pressure, one of which is the reference surface. The distance between two such isobaric surfaces is not constant in either space or time. This kind of altitude therefore depends on the theory or assumptions used for locating the surfaces as well as on the data themselves. (2) The difference in pressure between two surfaces of constant atmospheric pressure, with the lower surface taken as referent. The angular altitude of a celestial body near but not on the celestial meridian. A correction is applied to the ex-meridian altitude to obtain the meridian altitude. Dynamic height. This term is employed in the U.S. Standard Atmosphere Tables . The angular altitude of a celestial body measured on the meridian of the observer. A boundary line thought of as enclosing and going around a place. A space at least 2.5 feet in width, between neighboring buildings, left for the convenience of going between them. A point at which the variation of the tides is zero and from which the cotidal lines radiate, progressing through all phases of the tidal cycle. Also known as a nodal point. A region surrounding an amphidromic point. The set of cotidal lines in an amphidromic region. A system of cotidal lines whose amphidromic point appears to be located on land rather than on the open ocean. A composite picture made by superposing one picture of a stereoscopic pair in one color on the other picture in a complementary color. The colors chosen are generally red and blue-green. When viewed through spectacles with a red filter as one lens and a blue-green filter as the other lens, the anaglyph provides a three-dimensional effect. Anaglyphs are used in photogrammetric plotting instruments. (2) A stereoscopic pictures side by side, one of which is printed in one color and the other in the complementary color. A figure-eight shaped diagram showing the declination of the Sun throughout the year and also the equation of time. It may be shown on a plane or curved surface, such as on an analemmatic sundial, but is most commonly shown near the Equator on a terrestrial globe. A variant spelling of anallactic. (1) In general, a geometric figure formed by (a) a pair of intersecting, straight lines terminated at the point of intersection (the two lines are called sides; the point of intersection is called the vertex); (b) a pair of intersecting planes terminated at the line of intersection (called the axis); or (c) the surface generated by moving a straight half-line about its end point (called the apex), the line returning upon itself once and only once. The figure defined by (a) is a plane angle; the figure defined by (b) is a dihedral angle; the figure defined by (c) is a solid angle or cone; if the surfaces generated by the straight half-line of (c) are planes, it is a polyhedral angle. The angle between two intersecting curves is the plane angle between the tangents to the curves at the point of inter section. The size, or measure, of an angle is the rate of separation of the lines or surfaces forming the angle. The following methods are used to obtain a measure of each of the three kinds of angle. (a) The size of a plane angle is determined by drawing a circle of arbitrary radius about the point of intersection. The ratio, times a specified constant, of the length of arc between the two lines to the entire circumference of the circle is the size of the angle. If the constant is 360o, the integral part of the size is in units of degrees. The fractional part is multiplied by 60 and the resulting integral part is in units of minutes. The fractional part of the second value is multiplied by 60 to transform that part in seconds. The scheme of degrees, minutes, and seconds denoted by o ' "is called the sexagesimal system and is said to be in arc measure. If the constant is 400, the unit of size is the centesimal degree, grad, or gon. If the constant is 2p, the unit is the radian. If the constant is 24, the integral part of the size is in units of hours, and the fractional part is broken down into minutes and seconds similar to the sexagesimal system. This system is known as the astronomical or time system, and is 15 times as large as the corresponding unit in the sexagesimal system. It is denoted by h m s. (b) The size of a dihedral angle is the size of the plane angle formed by a third plane perpendicular to the line of intersection (axis) of the two original half-planes. (c) The size of a solid angle (cone) is determined by drawing a sphere about the fixed point (apex). The ratio, times a specified constant, of the area inclosed by the solid angle to the area of the entire sphere is the size of the solid angle. The constant usually employed for solid angles is 4 p; the unit is the steradian. The unit square degree is also used in connection with more than one constant. (2) (astronomy) An angle is classified as topocentric if its vertex or apex is at the observer on the surface of the Earth (or other planetary body), geocentric if its vertex or apex is at the center of the Earth (or a representative ellipsoid), heliocentric if its vertex or apex is at the center of the Sun, and barycentric if the vertex or apex is at the center of the mass of the Solar System (or some subset thereof). Astronomical angles are expressed in the same units as angles in general. Where, however, the rotation of the Earth determines the angle, the size of the angle is usually expressed in units of time (hours, minutes and seconds) rather than in units of arc (degrees, minutes and seconds). (3) (geodesy) Angles in geodesy are usually classified according to the way they are measured. Those measured in a horizontal or nearly horizontal plane are called horizontal angles; those measured in a vertical or nearly vertical plane are called vertical angles. In the United States of America, the size of an angle is generally given in degrees, minutes, and seconds of arc. In other countries, particularly in Europe, sizes are often given in grads, centigrads, and centicentigrads. (4) (photogrammetry) Photogrammetric practice generally follows that of geodesy in its use of angles and angular measure. However, certain angles that occur frequently in aerial photogrammetry are given special names; the most common are: tilt (or pitch), roll, and swing (or yaw). Anadjusted value of an angle. An adjusted angle may be derived either from an observed angle or a concluded angle. (1) (astronomy) The angle less than 180o between the plane of the celestial meridian and the vertical plane containing the observed object, reckoned from the direction of the elevated pole. It is the spherical angle at the zenith in the astronomical triangle with vertices: pole, zenith, and star. (2) (geodesy) An angle, in triangulation or in a traverse, through which the computation of azimuth is carried. In a simple traverse, every angle may be an azimuth angle. Sometimes, in a traverse, to avoid carrying azimuths over very short lines, supplementary observations are made over comparatively long lines, the angles between these lines forming azimuth angles. In triangulation, certain angles, because of their size and position in the figure, are selected for use as azimuth angles and enter into the formation of the condition equation (azimuth equation) governing azimuths. (3) Synonymous with azimuth. Not to be confused with azimuth angle as used in triangulation and traverse. Use of azimuth is preferable to azimuth angle in order to avoid confusion with (2). One of a sequence of three angles (rotations) specifying the orientation of one (three-dimensional) coordinate system with respect to another, such that the successive rotations bringing them into coincidence are about three different axes. Let the system whose axes are x, y, z be rotated into the system with axes X, Y, Z. An example of a sequence of Cardan angles is given by a rotation about x yielding a coordinate system with axes x, y', z'; then a rotation about y' yielding x', y', Z; finally a rotation about Z yielding X, Y, Z. Five other sequences are possible satisfying the condition that the axes of rotation (i,j,k) are all distinct. This is in contrast to the Euler angles where the condition is i=k #j. Cardan angles are more practical for very small(differential) rotations than Euler angles. The photogrammetric rotations--roll, pitch, and yaw--are an example of a sequence of Cardan angles. An angle expressed in units that are related to the degree by 100 grads = 90o; a centesimal minute is 1/100 of a grad, and a centesimal second is 1/100 of a centesimal minute. See also gon and grad . An interior angle between adjacent sides of a closed figure, obtained by subtracting the sum of all the other (computed or observed) interior angles of the figure from the theoretical value of the sum of all the interior angles. The concluded angle is most frequently met with in triangulation, where it is obtained by subtracting the sum of two known angles of a triangle from 180o plus the spherical excess of the triangle. A horizontal angle measured from the prolongation of the preceding line, right or left to the following line. Only directed polygons, such as traverses, have deflection angles. The vertical angle, at the point of observation, between the geometric horizon and a line of sight to the apparent horizon. An angle in a triangle opposite a side used as a base in the solution of the triangle or a side whose length is to be computed. In a chain of single triangles, as the computation proceeds through the chain, two sides are used in each triangle: a known side and a side to be determined. The angles opposite these sides are the distance angles. An angle obtained by pointing the telescope of a transit at an object, reading the angle on the vertical circle, then reversing the instrument to put the vertical circle on the other side of the observer, redirecting the telescope at the object, and reading the new angle on the vertical circle. The difference of the two readings is the double-zenith angle and is twice the zenith angle. In trigonometric leveling and in astronomy, double-zenith angles are used because they are nearly free from effects of the inclination of the vertical axis of the instrument. One of a sequence of three angles (rotations) specifying the orientation of one (three-dimensional) coordinate system with respect to another, in which the first and third rotations are about the same axis, and the second is about a different axis. Let the system whose axes are x, y, z be rotated into the system w ith axis X, Y, Z. An example of a sequence of Euler angles is given by a rotation about z yielding x', y', z; then a rotation about x' yielding x', y", Z (finally a rotation about Z, yielding X, Y, Z). Five other sequences are possible satisfying the condition i= k $n jfor the axes of rotation (i,j, k). This is in contrast to the Cardan angles where the condition is that i, j, k are all distinct. The example can be called the z x z sequence. This and the z y z sequence are the most common instances of Euler angles. The angle between any side of a polygon and the adjacent side extended. "Exterior angle" is also used to designate the outside angles formed by a line intersecting two parallel lines. An angle between two directed lines in a horizontal plane. Equivalently, the dihedral angle between two planes intersecting in a vertical line. Angles measured on the horizontal circle of a theodolite are horizontal angles if the standing axis of the theodolite is vertical and the horizontal circle is perpendicular to the standing axis. An angle between adjacent sides of a closed figure, measured on the inside of the closed figure. The angle between the optical axes of any two rigidly connected cameras. Also, the angle between the optical axes of a vertical and an oblique camera, or the dihedral angle between the planes of a vertical and an oblique photograph. An angle obtained by direct instrumental observation. A measured angle which has been corrected for local conditions only at the point of observation is considered an observed angle. The angle, on the celestial sphere, between a great arc from a celestial body to the pole and a great arc from the celestial body to the observer's zenith. "Parallactic angle" should not be confused with or used for "parallax". The angle, measured eastward on the celestial sphere, from a line joining a specified point and the north celestial pole to a line joining the specified point and the point whose position angle is wanted. For example, the position angle of one star in a binary system is measured by placing the origin of a polar micrometer on the center of the other star and rotating the movable hairline from an initial direction through the north celestial pole to a final direction through the first star. A method of measuring angles in which the telescope is pointed at the initial point and the direction is read. The telescope is next aimed at the second point, the horizontal circle is clamped to the telescope, and telescope and circle are swung around together to point back at the initial point. The horizontal circle is then unclamped, the telescope pointed again at the second point, and this process repeated the desired number of times. The final reading on the circle is the sum of the individual measurements. The average is obtained by dividing this sum by the number of measurements. An angle between great circles on a sphere. A spherical angle is measured by (a) the dihedral angle between the planes of great circles, (b) the plane angle between tangents to great circles at their intersection, or (c) the arc intercepted by these great circles on the great circle 90o from the point of intersection. An angle between two curves on a spheroid. By definition, its size is that of the angle between the tangents to the two curves at the point of intersection. An angle between two directed lines in a vertical plane. In surveying, one of the sides of a vertical angle is usually either (a) a horizontal line in the vertical plane (the angle is then called the angle of elevation or depression, or (b) a vertical line (the angle is then called a zenith angle). The angle measured positively from the observer's zenith to the object observed. Also called zenith distance. (1) The angle, at the rear nodal point of an optical system, between the two rays to two points that determine a characteristic dimension of the image formed by the optical system. Also called field of view, or angle of coverage. Characteristic dimensions are the length of a side or the length of the diagonal of a square image, or the length of the longer or shorter side of a rectangular image, etc. (2) (photogrammetry) Twice the angle whose tangent is half the length of the diagonal of the image, divided by the calibrated focal length. The angle, measured clockwise, from the preceding leg of a traverse to the following leg. Cngstrom (C) 10-10 meter. Invented for designating wavelengths of radiation in the optical and shorter-wavelength parts of the spectrum. The optical part of the spectrum lies approximately between 4,000 and 7,500 Cngstroms. The Cngstrom is not an accepted part of SI, but is still used in books and papers on spectroscopy. Current units used in SI for visible light are the nanometer (nm), or 10-9 meter. The product of the moment of inertia of a body by its angular velocity. The process of obtaining differences of elevation by means of observed vertical angles, combined with lengths of lines. In geodesy, vertical angulation is called trigonometric leveling. In general, any quantity whose values differ from those expected or predicted by simple theory. The following usages are examples. (a) (astronomy) True anomaly; mean anomaly; eccentric anomaly. These quantities are angles which pertain to elliptic orbits. The term "anomaly" was applied because ancient astronomers expected orbits to be circular. (b) (geodesy) (c) (geophysics) (d) (oceanography) The difference between some particular characteristic of seawater and the corresponding characteristic either of seawater under standard conditions or of a standard sample of seawater. The angle from the line of apsides of an elliptical orbit to a radius vector drawn from the center of the ellipse to a point Q on the circle having the line of apsides as its diameter, such that Q is on the perpendicular from the line of apsides through the center of mass of the orbiting body. The eccentric anomaly is related to the mean anomaly by Kepler's equation . The angle from the line of apsides of an elliptical orbit to the radius vector from the attracting focus to a hypothetical point moving with angular velocity equal to the average angular velocity of the actual orbiting body. The mean anomaly is related to the eccentric anomaly by Kepler's equation. The angle from the line of apsides of an elliptical orbit to the radius vector from the attracting focus to the center of mass of the orbiting body. The parallel of latitude, in the Southern Hemisphere, at which the latitude is equal to the complement of the declination of the winter solstice. Because the obliquity of the ecliptic is steadily changing, the winter solstice is not fixed in declination; thus, the Antarctic Circle, as defined above, is not a line of fixed position. On a map, the Antarctic Circle is customarily at latitude 66o33'S. This is the complement of 23o27'S used for the latitude of the Tropic of Capricorn . The antenna, in a set of antennas engaged in radio interferometry, used as a referent in establishing an epoch for the time of arrival of signals. The term is used in particular in very long baseline interferometry with a pair of antennas. Fluid flow in the atmosphere or oceans with a clockwise rotation about the local vertical in the Northern Hemisphere and a counterclockwise rotation in the Southern Hemisphere. (1) Any material part of an optical system specifically intended and designed to allow some light to pass through and to stop the rest of the light. Equivalent, in this sense, to stop. (2) In particular, the part (element) which determines the amount of light (power) reaching the detector. Also called the aperture stop. (3) A measure of the light-gathering power of an optical system. In simple refracting optical systems, the aperture is approximately the diameter of the front (objective) lens. More exactly, it is the diameter of the aperture stop that determines the angular size of the axial cone of rays from the object. In reflecting optical systems, the diameter of the primary mirror is usually considered the aperture. If the mirror is small, the square-root of the unobscured area of the primary mirror is often used. In catadioptric systems, the diameter of either the primary mirror or the lens may be used. Note that aperture is not the same as numerical aperture . The product of the index of refraction of the medium in image space and the sine of the half-angle of the cone of illumination there. In microscope optics, the definition above is used with "object space" substituted for "image space". The ratio of the effective focal length of an optical system to the diameter of the entrance pupil. Also called "f-number" or "f-stop". When objects other than point sources, such as stars, are viewed or photographed, the illumination in the image is determined by the relative aperture, rather than by the aperture alone. The diameter of the entrance pupil limits the power arriving at an element of the image, while the focal length determines the area over which this power is spread. The point, in the elliptical orbit of a planet or a comet, most remote from the Sun. A prefix meaning farthest from (the attracting body). E.g.; apogee, the point, in the elliptical orbit of a satellite of the Earth, at which the satellite is farthest from the Earth. Note: aphelion, not "apohelion", is used. The point, in an elliptical orbit, at which the body is farthest from the focus where the attracting mass is located. Also called apoapsis , and apofocus. The point, in the elliptical orbit of a satellite of the Earth, at which the satellite is farthest from the Earth's center of mass. A surface of rotation whose meridional section is defined by the the equation: r' = a sech [b ( t + c)], where a, b, and c are constants, t is the isometric latitude, and r' is the perpendicular distance from the axis of rotation to the surface. The constants are chosen so that the aposphere touches the ellipsoid with which it has a common axis of rotation along some parallel that passes through the center of the area for which the transformation is required. An atmospheric layer characterized by high ion density: the F -layer of the ionosphere. It occurs in the general region between 150 and 300 km. All the air space lying within the boundaries and above the floor of the approach-zone district at an airport. All of the region outward from the end of a runway in which the heights of structures or other hazards to aircraft are restricted. The slope and dimensions of the approach zone district are usually fixed by zoning commissions. The surface defining maximum heights is the "floor" of the district. (1) A value close to, but not exactly, the correct value for a quantity. (2) The process of obtaining approximations. Two different methods are used: direct, in which an approximation is calculated only once; and successive, in which a value, called the first approximation, is calculated and then used in repetitions of the calculation to get values called "second approximation", "third approximation", etc., each of which is closer and closer to the correct value. This process is repeated until either a satisfactory value is obtained or no change in value results. This method is also known as the "iterative process of approximation". (1) (pl. apsides) A point, on a curve, at which the radius vector is a maximum or a minimum. (2) Either of the two points in an orbit at which the distance of the body from the center of attraction is an extremum. Also called "apse". For an elliptical orbit, these two points lie on the major axis of the ellipse and the center of attraction lies on a focus of the ellipse. The point closest to that focus is called "peri-apsis" and that farthest is called "apo-apsis". The line joining the two points is the line of apsides or line of apse. The Earth, as a satellite of the Sun, passes closest to the Sun at perihelion, farthest from the Sun at aphelion. Correspondingly, a satellite of the Earth passes through perigee and apogee. (1) (mathematics) A portion of a mathematically defined curve. A circular arc is part of a circle; an elliptical arc, part of an ellipse; etc. A Jordan arc, also called a simple arc or simple curve, is a one-to-one continuous map of a straight line. (2) (triangulation) (3) A curved piece of metal graduated to indicate angles. See, e.g., Beaman arc; quadrant. An arc of a great circle. A method for the determination of the size and figure of the Earth by the measurement of lengths of arcs of triangulation and the astronomic coordinates of the ends of the arc. Also called grade measurement. It is customary to differentiate between meridional- and latitudinal-arc measurements. A chain of single, connected figures (triangles, quadrilaterals, etc.) which follows, approximately, an arc on the reference ellipsoid. The best known arcs of triangulation follow meridians or parallels, but some, such as the Eastern Oblique Arc in the United States of America, which runs from Maine to Louisiana, do not. One-sixtieth of a minute of arc. 1/3600 of a degree. More properly, "second of arc." Also written as "arcsecond" or "arc second". The parallel of latitude, in the Northern Hemisphere, at which the latitude is equal to the complement of the declination of the summer solstice. Because the obliquity of the ecliptic is steadily changing, the summer solstice is not fixed in declination; thus, the Arctic Circle, as defined above, is not a line of fixed position. On a map, the Arctic Circle is customarily shown at latitude 66o33'N. This is the complement of the 23o27'N used for the latitude of the Tropic of Cancer. (1) The extent of a surface, or an appropriately defined portion of a surface. (2) A numerical measure of (1) expressed in units of length squared. For example: the area of a sphere is 4 p times the length squared of the radius of the sphere. The area of the portion of a sphere within a small circle drawn on the sphere is 2pr[r - (r2 - s2)1/2] The two units of area in almost universal use today are the square meter and the hectare. Corresponding units in the English system, still used in the United States of America, are the square foot and the acre. For any aerial photograph that is one of a series in a flight strip, the central part of the photograph delimited by the bisectors of overlaps with adjacent photographs. On a vertical photograph, all images within the effective area have less displacement than their conjugate images on adjacent photographs. (1) (astronomy) Synonym for angle. (2) (mathematics) An independent variable. This usage is found principally in works on celestial mechanics or tides. It is also used for the discrete values indexing rows or columns in tables of functions. (3) (tides) The angular variable in the representation of tidal variation by Fourier series. The theoretical phase of a constituent of the equilibrium tide. It is usually represented as the sum of two angles V and u, in which V is uniformly and rapidly changing and involves multiples of the hour angle of the mean Sun, mean longitudes of the Sun and Moon, and mean longitude of the lunar or solar perigee; and u is slowly changing and depends on the longitude of the ascending node of the Moon's orbit. The (tidal) equilibrium argument computed for the Greenwich meridian. The angle, at the center of attraction, from the ascending node to the orbiting object measured in the direction of motion of the orbiting body. The sum of the argument of perigee and the true anomaly. The angle, at the center of attraction, from the ascending node to perigee, measured in the direction of motion of the orbiting body. (1) A unit of area approximately 0.85 acre. It originated in France and was used in surveys of land, now part of the United States of America, granted by the French crown. The size of the arpent depends on its origin and local custom. For surveys in Arkansas and Missouri, the value 0.8507 acre has been used. For surveys in Louisiana, Mississippi, Alabama, and northwestern Florida, the value 0.84725 acre has been used. (2) A unit of distance equal to the square root of an arpent as defined in (1). Its values corresponding to those given in (1) for area are 1 arpent = 192.500 feet or 58.674 m, and 1 arpent = 191.995 feet or 58.5198 m. In Canada, the arpent is exactly 180 French feet. () (1) A subsidiary station established between principal stations of a traverse, for convenience in measuring the distance between the principal stations. A-stations are established along a curved route, as along a curved section of a railroad, where the measured lengths must be carried through a series of short, straight lines, even though azimuth control may be carried through widely spaced stations. The A-stations form a loop with the (main) line connecting the principal stations, the distance between which is obtained by projecting the measured lengths of the short lines onto the main line. See equation, perpendicular. A-stations are so-called because, in a given series, they are designated by the name of a principal station followed by the letters A, B, C, etc., in order of distance from that station. They are sometimes called "A, B, C stations". (2) (1) A region of the solid Earth, composed of the lower portion of the crust and the plastic upper portion of the mantle, that allows continental drift. Conjectures as to the depth and thickness of the asthenosphere vary greatly. (2) A region, in the upper mantle, characterized by low velocity and and high attenuation of seismic waves. The difference in focus between two fans of rays coming from common point in object space; one fan passes through a line perpendicular to the optical axis at the front nodal point; the other passes through a line perpendicular to the first line at the nodal point. Astigmatism is one of the five Seidel aberrations. It is zero if the point source is on the optical axis (in symmetrical optical systems) and increases with the distance of the source from the optical axis. A single, off-axis point source is astigmatically imaged as two short, mutually perpendicular lines at different distances from the lens. A lens which introduces astigmatism into an optical system. An astigmatizer is mounted so it can be moved into or out of the optical path at will. In a sextant, an astigmatizer may be used to elongate the image of a celestial body into a horizontal line. A fictitious star assumed to move along the celestial Equator at a uniform rate corresponding to the frequency of one of the several harmonic constituents of the tide-producing force. Each astre fictif crosses the meridian at a time corresponding to the maximum of the constituent it represents. An adjective indicating that the combined methods or data of astronomy and geodesy apply. For example astrogeodetic leveling or astrogeodetic coordinates. (1) (astronomy) (2) (navigation) A device used for optically projecting a set of curves showing stellar or solar angular altitudes onto a chart or plotting sheet; the curves vary with time so they will remain in the correct position on the chart or plotting sheet. An instrument for measuring angular altitudes of celestial objects. See astrolabe, pendulum; astrolabe, planispheric; astrolabe, prismatic; etc. The term, derived from Greek words meaning "to take a star", has been used to designate a great variety of instruments; the three referred to above are of especial interest to surveyors and mapmakers. An astrolabe designed by A. Danjon and based on the double-image astrolabe of Claude and Driencourt, but with a side-by-side relationship of the images and with a motor-driven prism. The Claude and Driencourt astrolabe splits light from an incoming star at about 30o zenith distance to give two images in the focal plane. As the star approaches 30o zenith distance, the two images approach each other along diagonal lines intersecting on the optical axis, and coincide when the zenith distance is exactly 30o. In the Danjon astrolabe, a double Wollaston prism is introduced at the focus. This, together with some screens, produces two images side by side if the prism is placed at the proper distance on the optical axis from the focal plane. This side-by-side relationship is maintained by a motor that moves the prism uniformly along the optical axis, so the zenith distance over a short interval on either side of 30o is measured by the displacement of the prism. The observer merely needs to make small corrections to the displacement from time to time. An astrolabe whose distinctive feature is a mirror suspended on top of a pendulum to form the artificial horizon; its telescope is placed so that observations are made at a constant angular altitude. One form of this instrument consists of a V-shaped casting carrying the objective and eyepiece lenses at the ends of the arms. The mirror, which rests on top of the pendulum and forms the level surface (artificial horizon), is located at the intersection of the V. The pendulum is suspended so that it is free to swing in either of two planes at right angles to each other, such as the north-south and the east-west planes. The pendulum is highly damped so that the mirror comes to rest quickly and remains steady under normal observing conditions. An astrolabe of ancient origin, consisting of a full graduated circle with a centrally mounted alidade, and accessory adjustable plates on which are engraved graticules of the stereographic projection of the heavens and of the sphere for local latitudes. See map projection, stereographic. The instrument is held suspended in a vertical plane, and the angular altitude of a star is observed with the alidade. The projection-bearing plates are adjusted so that, in essence, graphical solutions of astronomical problems are obtained. An astrolabe, consisting of a telescope with a prism and artificial horizon attached at its objective end, used for determining astronomic positions. In its usual form, this instrument consists of a horizontal telescope which contains a 60o prism; the face of the prism nearest the objective is perpendicular to the line of collimation of the telescope; and a small mercurial horizon is attached to the instrument beneath the prism. In observing, two images of an observed star are seen, one reflected directly into the telescope by the lower face of the prism, the other reflected first by the mercurial horizon, then by the upper face of the prism into the telescope. The two images of the star move in opposite directions either toward or away from coincidence. At the instant of coincidence, the star is at the apparent angular altitude of the prism angle. Prismatic astrolabes may be made with the angle between the lower face of the prism and the mercurial horizon inclined at other than 60o. See also astrolabe, Danjon. The term is sometimes restricted to mean the positional astronomy of stars. One of a set of constants of an astronomical nature that are needed for the calculation of ephemerides. The set is sometimes referred to as a "system of astronomical constants". Not all astronomical constants are geodetically significant. Those of particular importance and the values adopted for them in 1976 by the International Astronomical Union are listed below. (The values are not necessarily the same as the values adopted or recommended by the International Association of Geodesy for the same constants.) For constants and values used before 1976, consult the national ephemerides in use before that time.

k Gaussian gravitational constant 0.017 202 098 95 L3/2M-1/2 T-1 (where the dimensions L, M, and T stand for astronomical unit, mass of the Sun, and ephemeris day, respectively)

c speed of light in vacuo 299,792.458 km s-1

ae equatorial radius of earth 6,378,140 m

G constant of gravitation 6.672 x 10-11 m3 kg-1 s-2

GMe geocentric gravitational constant 3.986 005 x 1014 m3 s-2

J 2 dynamical form-factor for Earth 0.001 082 63

mmass of Moon/mass of Earth 0.012 300 02

P general precession in longitude per Julian century, at epoch 2000 5 029."096 6

N constant of nutation at epoch 2000 9."210 9

e obliquity of the ecliptic at epoch 2000 AD 23o 26."21."448

p u solar parallax 8."794 148

k constant of aberration at epoch 2000 20."495 52

A length of astronomical unit 1.495 978 70 x 1011 m

See Seidelman (1977) for further details about the above values. A conventional unit of distance in astronomy roughly equal to the semimajor axis of the Earth's orbit. Abbreviated as "a.u". It is determined from Kepler's third law:

(a.u.)3 = K2T2Ms(1 + M)/4p 2

where T = the period of revolution in ephemeris days, Ms = the mass of the Sun, taken as the unit of mass. m = the ratio of the mass of the Earth to the mass of the Sunk = the Gaussian gravitational constant, 0.017 202 098 950 000. Initially, Gauss applied m, T, and the mean distance of the E arth to the Sun, r, to determine k. Although better values of r, m and T are now available, k has been employed in so many computations and tables that it was found easier to use the above equation for defining the astronomical unit than for defining k. The distance in kilometers equivalent to the astronomical unit is 149,597,870 km, as calculated from the constants adopted by the International Astronomical Union in 1976. The science dealing with bodies and phenomena occurring in regions outside the Earth's atmosphere, and with meteors and cosmic rays within the Earth's atmosphere. Astronomy can be divided into (a) positional astronomy, which deals with the locations and motions of celestial bodies, and (b) astrophysics, which deals with intrinsic physical characteristics of the bodies, such as radiation, temperature, constitution, evolution, etc. Some astronomers call "positional astronomy" simply "astronomy" and limit use of the term "positional astronomy" to describing only the positions and kinematics (but not the dynamics) of celestial bodies. Astronomy is also divided into disciplines according to the wavelengths of the radiation by which the bodies are observed. Astronomy is related to geodesy principally through the use of observations of the Sun, Moon, stars, and recently, quasars for determining locations on the Earth's surface and for determining the rotation of the Earth. The determination of longitudes, latitudes, and azimuths by observations of the directions of stars, planets, the Moon, or other celestial bodies. Coordinates so determined are called astronomic coordinates or astrogeodetic coordinates. The part of astronomy dealing with the locations and motions of celestial bodies such as planets, comets, stars, and groups of stars. Often referred to simply as "astronomy". Astrometry is sometimes used as a synonym for positional astronomy but is more often considered to deal only with the locations and kinematics of celestial bodies, and in particular with the locations and kinematics of stars. Celestial mechanics deals with the dynamics of changes in location of celestial bodies and is generally considered as being purely theoretical. Statistical astronomy deals with statistical descriptions of location and changes of location and hence deals less with locations and motions of individual bodies but rather with the locations and motions of aggregates of bodies. The branch of astronomy in which observations are made by using radio wavelengths, i.e., wavelengths longer than 300 micrometers. Sometimes taken to apply only to astronomy involving radio waves originating at the object observed. In contrast, astronomy involving radio waves generated at an observatory and reflected or scattered by the astronomical object is then called "radar" astronomy. Properly, radio astronomy includes both kinds. Radar astronomy currently is limited to observation of bodies within the Solar System. A lack of symmetry in the appearance of an object as seen from a particular point of observation and caused by an actual asymmetry in the object or its aspect. Asymmetry of object causes an object to change appearance when observed from different locations and can result in different points on the object being sighted at from different points of observation. A square or rectangular pole may face the observer in such a way that a line bisecting the angle made by lines of sight tangent to the edges of the pole does not pass through the center of the pole. If a square cupola or tower is sighted on, resulting errors may be quite large. The errors caused by observing on such objects are of the same character as those caused by observing an eccentric signal. Asymmetry of object differs from phase (surveying) in that the former is caused by an actual asymmetry of the geometry of the object as viewed; the latter is caused by asymmetric illumination of the object. (1) The envelope of gas surrounding a planet or other celestial body. (2) The envelope of gas (air) surrounding the Earth. The Earth's atmosphere is generally divided into a sequence of layers having different properties, the kind of division depending upon its purpose. Meteorologists divide the atmosphere into: the troposphere, extending from the surface of the Earth to about ll km; the stratosphere, extending from there to about 50 km; the mesosphere, continuing from the top of the stratosphere to about 80 km; and the thermosphere, extending from there up to about 500 km. The outermost region, where molecules easily escape from the Earth's attraction, is called the exosphere and may or may not be considered part of the atmosphere. Geodesists and radio engineers consider the atmosphere to be divided into troposphere and stratosphere, as above, but place the ionosphere next. The ionosphere continues from the top of the stratosphere to 300 or 400 km and is characterized by the presence of enough ions and electrons to detectably affect radio waves. The air in the immediate vicinity of a survey instrument or surveying station. The temperature and pressure of the ambient atmosphere are referred to as the ambient temperature and the ambient pressure, respectively. atmosphere, refractive index of ">The ratio of wavelength of radiation of given type in the atmosphere to the corresponding wavelength in vacuum. Formulas for the refractive index of the atmosphere for unmodulated monochromatic light, modulated light, and for microwaves were adopted at the 12th General Assembly of the International Union of Geodesy and Geophysics in 1963. (No. 70, 1963, p. 390, or Bomford 1980: pp. 44-47.) A hypothetical vertical distribution of atmospheric temperature, pressure, and density (and sometimes height) which is generally accepted as satisfactorily representing actual conditions in the atmosphere. The standard atmospheres of most geodetic importance are (a) the ICAO (International Civil Aviation Organization) Standard Atmosphere (1964), (b) the ISO (International Standards Organization) Standard Atmosphere (1973), and (c) The U.S. Standard Atmosphere (1976). Atmosphere (c) agrees with the ICAO Standard Atmosphere (1964) up to 32 km and with the ISO Standard Atmosphere (1973) up to 50 km. Above 50 km and up to 1000 km, atmosphere (c) is based on data from rockets and artificial satellites. Also of geodetic importance is (d) Table 51, Geopotential Meters to Geometric Meters, Smithsonian Meteorological Tables (6th edition, 1958). The position of a body defined by the angles between the axes of the coordinate system of the body and the axes of an external coordinate system. In particular, in photogrammetry, the orientation of a camera, or of the photograph taken with that camera, with respect to some external reference system. Usually expressed as tilt, swing, and azimuth, or as roll, pitch, and yaw. The difference between the apparent topocentric angular diameter of a celestial body and its geocentric angular diameter. A factor used in connection with the harmonic analysis of tides or tidal currents to allow for the fact that the tabulated hourly heights or speeds used in the summation for any constituent other than a solar one do not in general occur on the exact constituent hours to which they are assigned, but may differ from the assigned times by as much as a half-hour. A telescope containing illuminated cross hairs placed so that they are imaged by the objective lens system at infinity. When a reflecting plane is placed approximately perpendicular to the optical axis of the telescope, the cross hairs and their reflected image can be viewed simultaneously through the ocular of the telescope. The image will be displaced by twice the angle between the optical axis and the perpendicular to the reflecting surface. (adjective) True scale. (1) The breaking of a stream through its banks in a sudden and unexpected manner in such a way as to form another channel. The term is of legal significance when the avulsion results in cutting off a large amount of land from one owner and adding it to another's land. (2) The rapid erosion of a shore by waves during a storm. The legal status of this definition is uncertain, some courts assign only definition (1), above to it. (1) Any line along which measurements are made in determining the coordinates of a point, or any line from which angles are measured for the same purpose. An axis usually same as a line of reference such that one of the coordinates of a point lying on the axis is zero. (2) A line with respect to which a geometric figure is symmetrical. (3) Any line about which a body rotates or revolves. In geodetic and astronomic instruments, the line usually coincides with the axis (sense 2 above) of a cylindrical rod or tube carried in a bearing, so the term "axis" is also applied to this cylinder. (4) A line connecting two distinguished points. E.g., the magnetic poles of the Earth are joined by the magnetic axis. The line joining two opposite fiducial marks on a photograph. The axis about which the telescope or alidade of an instrument rotates when moved vertically. For an instrument in perfect adjustment, the horizontal axis is perpendicular to the vertical axis of the instrument and to the collimation axis of the telescope. It should coincide with the line through the centers of the pivots that support the telescope. For an instrument in perfect adjustment and properly leveled, this axis is horizontal with respect to the surface and when the telescope is rotated around it, the collimation axis will define a vertical plane. Deviations from proper instrumental adjustment are measured with a striding level or a hanging level. The ray path through the focal points of an optical system that has the shortest geometric length. Equivalently, the ray path from object space to image space with the least angular deviation along the path. Applied to lens systems that contain only spherical surfaces, the definition becomes "a line connecting the centers of curvature of all the surfaces in a lens system". (1) One of the three (two) perpendicular axes through the center of an ellipsoid (ellipse) having, among them, the shortest length and the longest lengths of all axes of the figure. (2) (3) The line about which the telescope or alidade of an instrument rotates when moved horizontally. For an instrument in perfect adjustment and properly leveled, this axis occupies a vertical position, passes through the center of the horizontal circle, and is perpendicular to its plane. A synonym for line of collimation. Since this term can be confused with the term collimation axis, it is best to avoid its use altogether. The intersection of the plane of a photograph with the horizontal plane of reference at the ground or with the plane of a horizontal map. Corresponding lines in the photograph plane and the map plane intersect on the axis of homology. Also called axis of perspective, map parallel, or perspective axis. A line through the perspective center of a photograph and perpendicular to the principal plane of a photograph. A horizontal angle reckoned clockwise from the meridian. In the basic control surveys of the United States of America and in those of many other countries, azimuths are currently reckoned clockwise from south. In military control surveys of most countries, including the U.S.A., azimuths are reckoned clockwise from north. In 1986, when the U.S. National Geodetic Survey begins publishing geodetic data on the North American Datum of 1983 (NAD 83), the measurement of azimuths will be referenced from the north for basic control surveys in the U.S.A. At the point of observation, the angle measured from the vertical plane through the celestial pole to the vertical plane through the observed object. The astronomic azimuth is established directly from observations on a celestial body and is measured in the plane of the horizon. It differs in value from the geodetic azimuth because of the deflection of the vertical which can be as much as a minute of arc, or more, in extreme cases. Astronomic azimuths may also be reckoned clockwise from north. In navigation, they are sometimes reckoned either clockwise or counterclockwise through 180o, from the south in the southern hemisphere, and from the north in the northern hemisphere. In recording an astronomic azimuth it is essential that both the initial direction and the direction of reckoning be indicated. The angle at a point A between the tangent to the meridian at A and the tangent to the geodesic from A to the point B whose geodetic azimuth is wanted. Until 1985 the U.S. National Geodetic Survey had considered a geodetic azimuth to be positive clockwise starting from south. The azimuth is called the "forward azimuth" for the line AB. The angle at B between the tangents to the meridian and to the geodesic is called the "back azimuth" or "reverse azimuth"for the line AB. Because of the convergence of the meridians, the forward and back azimuths of a line do not differ by exactly 180o, except where the two end points have the same geodetic longitude or where the geodetic latitudes of both points are 0o. The angle in the plane of projection between a straight line and the central meridian of a plane-rectangular coordinate system. In the State plane coordinate systems established by the former U.S. Coast and Geodetic Survey, grid azimuths are reckoned from south (0o) clockwise through 360 degree. While essentially a map related quantity, a grid azimuth may, by a mathematical process, be transformed into a survey or ground related quantity. A geodetic azimuth derived from an astronomic azimuth by means of the Laplace equation. (qv) At the point of observation, the angle between the vertical plane through the observed object and the vertical plane in which a freely suspended symmetrically magnetized needle, influenced by no transient artificial magnetic disturbance, will come to rest. Magnetic azimuth is generally reckoned from magnetic north (0 degree) clockwise through 360o. Such an azimuth should be marked as magnetic, and its date of establishment given. The angle at a point between the meridian plane through that point and the normal section which passes through that point and another point. The determination of astronomic azimuth. Although the term properly should include the determination of geodetic azimuths, it is not used with that meaning. The determination of the astronomic azimuth of a line by measuring, with a direction-theodolite, the horizontal angle between a selected star and a suitable mark, and applying that angle to the azimuth of the star computed for the epoch of the observation. In the horizontal control surveys of continental United States, azimuth determination by the astronomic-direction method is preferred over other methods. A circumpolar star is observed at any hour angle, the mark being a signal light on a main-scheme station or at a station (called an azimuth mark) established for the purpose. A correction for inclination of the horizontal axis, depending upon the angular altitudes of the star and of the mark, is applied to the observed angle, and corrections for curvature of the apparent path of the star, for variation of the pole, and for diurnal aberration are also used in the computation. Determination of azimuth by the astronomic-direction method or by the micrometer method, using Polaris as the observed star. A method of determining astronomic azimuth by measuring the angle between the azimuth mark and the vertical plane through the point at which a star, whose angular altitude is the same as the latitude of the observer, crosses the almucantar. The time of crossing is observed and the azimuth of the point of crossing is calculated. The determination of azimuth by measuring horizontal angles from a star to the desired direction at two different times--when the star first reaches a specified angular altitude and when the same star next reaches that same angular altitude. The average of the two angles is the azimuth of the direction. In determining azimuths in the Northern Hemisphere, the direction should be generally south of the observer, while if the point is in the Southern Hemisphere, the direction should be generally north of the observer. If the Sun is used, a correction must be made for the change in declination of the Sun between the morning and afternoon observations. It is also important to remember to make all observations on the same limb. Except in the case of the Sun, a knowledge of the star's coordinates or the time is not necessary. The determination of the astronomic azimuth of a line by measuring indirectly, with an ocular micrometer attached to a theodolite or transit, a horizontal angle mark (light) located on the ground close to the vertical plane which passes through the star, and applying that angle to the azimuth of the star computed for the epoch of the observation. At elongation, the apparent motion in azimuth of a close circumpolar star, such as Polaris, is very small for an appreciable period of time, so a series of observations can be made by the micrometer method without reorienting the instrument. A correction for inclination of the horizontal axis, depending on the altitudes of the star and of the mark, is applied to the observed angle, and corrections for curvature of the apparent path of the star, for variation of the pole and for diurnal aberration are also used in the computations. The determination of the astronomic azimuth of a line by accumulating on the horizontal circle of a repeating theodolite the sum of a series of measures of the horizontal angle between a selected star and a suitable mark, and then applying the average of such measures to the azimuth of the star computed for the mean epoch of the observations. This method is very precise and accurate theoretically, but in practice is not as satisfactory as the direction method of azimuth determination. A correction for inclination of the horizontal axis, depending on the altitudes of the star and of the mark, is applied to the observed angle, and corrections for curvature of the apparent path of the star, variation of the pole, and for diurnal aberration are also used in the computations. A variant of the astronomic-direction method of determining astronomic azimuth, in which the azimuth of the star is calculated from the rate of change of zenith distance with time. (1) The angle from the meridian through a meridian telescope to a plane perpendicular to the telescope's horizontal axis. (2) The angle defined similarly for any telescope with an alt-azimuth mounting when the horizontal axis should be perpendicular to the meridian. (3) For any instrument for which a nearly vertical plane can be defined, the difference between the azimuth of that plane and the azimuth in which it is supposed to lie. This definition is often used for the calibration of radio telescopes. A radial line from the principal point, isocenter, or nadir point of a photograph, representing the direction to a similar point of an adjacent photograph in the same flight line. The line is used extensively in radial triangulation. A geodetic monument carrying a mark whose azimuth from a given point is known either by measurement or by definition. A signal lamp or a target whose astronomic azimuth from a survey station is determined by direct observations on a celestial body. The mark may be a lamp or illuminated target placed especially for the purpose or may be a signal lamp at another survey station. A marked point established in connection with a triangulation (or traverse) station to provide a starting azimuth for dependent surveys. The geodetic azimuth to the azimuth mark is determined instrumentally. Historically, azimuth marks consisting of bronze tablets set in concrete or stone have been established in connection with the basic horizontal control survey of the United States. These marks are usually located so they can be easily used, without special construction to elevate either instrument or target. At a station having an established azimuth mark, both the geodetic azimuth and the grid azimuth of the mark on the State plane coordinate system are computed and published. A mark whose astronomic azimuth from a Laplace station is known are computed and published.