# Error Definitions for Land Surveyors

**error—**The difference between an observed or computed value of a quantity and the ideal or true value of that quantity. Because the ideal or true value of a quantity, with few exceptions, cannot be known with exactness, the term error is applied to a difference between an observed or computed value of a quantity and some standard or accepted value used in lieu of the ideal or true value. Exceptions: The ideal or true value of a quantity can be known with exactness when it is (a) mathematically determinable, independent of observation—as for example, the sum of the three angles of a plane triangle is 180°; (b) a conventional value established by authority—as for example, the length of the meter (unit) defined by the International Prototype Meter at the International Bureau of Weights and Measures. Errors are of various kinds, depending on how and where they originate. The term error with appropriate adjective or qualifying clause is used to designate the type of error, e.g., accidental error, error of observation, etc. See also *error, actual.*

**error, accidental—**An error which does not always recur when a measurement is repeated under the same conditions. See also *error, random.*

**error, accumulative—**A systematic error which is the same in both magnitude and sign through a given series of observations. A number of readings under these conditions will have an accumulated error equal to the number of readings multiplied by the error in one reading. See also *error, **constant.*

**error, actual—**The difference between the accepted or standard value and the measured value of a physical quantity. See also *error.*

**error, average—**The arithmetic mean of all the errors of a set taken without regard to sign. See also error, *mean.*

**error, centering—**An error caused by inaccurate pivoting in an instrument. Also called eccentric error.

**error, compensating—**An error that tends to offset a companion error and thus obscure or reduce the effect of each.

**error, constant—**A systematic error which is the same in both magnitude and sign through a given series of observations. An example of a constant error is the index error of a precision instrument. See also *error, **accumulative.*

**error, external—**A systematic error arising from natural physical conditions outside the observer. Examples of external errors are the effect of atmospheric refraction on spirit leveling, the changes in the length of a surveyor’s tape because of thermal expansion, and the effects of atmospheric pressure on barometric altitudes.

**error, index—**A constant instrumental error due to the displacement of the zero or index mark or vernier of an instrument or scale.

**error, instrumental—**A systematic error resulting from imperfections in, or faulty adjustment of, instruments or devices used. Also called “calibration error.”

**error, instrument centering—**The error caused by the instrument not being positioned directly over the center of the point of observation.

**error, mean—**An ambiguous term sometimes used to denote average error, error of the mean, or mean-square error. Its use is not recommended. See also *error, average.*

**error, mean-square–**See *standard deviation.*

**error, natural—**An error arising from variations in natural phenomena such as geomagnetism, gravity, humidity, refraction, atmospheric pressure, temperature, or wind.

**error, orthometric—**That part of the difference between a measured elevation and the true elevation point caused by the non-parallelism of the various equipotential level surfaces along the route which the leveling was done. Alternatively, the negative of the orthometric correction. Level surfaces at different elevations are not exactly parallel. A lake at a high elevation in latitude 45°N would be nearer the geoid at its northern end than it would at its southern end. This would cause an apparent error in a level line which rose from the geoid to the south end of the lake, then followed the lake’s surface to the northern end, then dropped down to the geoid again, and finally followed the geoid back to the starting point.

**error, periodic—**An error whose amplitude and direction vary systematically with time.

**error, personal—**An error caused by an observer’s personal habits, mental or physical reactions, or inability to perceive dimensional values exactly. It may be accidental or systematic. See also *equation, personal.*

**error, position—**See *position error.*

**error, positional—**See *positional error *[CARTOGRAPHY].

**error, probable—**An indication of the precision of any single observation in a series of measurements. It is a function of the accidental errors attending the individual observations in the series. An error of such magnitude that the likelihood of its being exceeded in a set of observations is equal to the likelihood of its not being exceeded; its value is that of the mean-square error multiplied by 0.6745.

**error, random—**An error produced by irregular causes whose effects upon individual measurements are governed by no known law connecting them with circumstances and which therefore can never be subjected to computation a priori; accidental error. Characteristics of random error: **(1)** small errors occur more frequently than large errors; and **(2) **there are as many negative errors as positive errors. With these assumptions, probabilities can be associated with the results of the method of least squares, and it is to the elimination of random errors only that the method of least squares may be applied.

**E****rror, residual—**The difference between any value of a quantity in a series of observations, corrected for known systematic errors, and the value of the quantity obtained from the mean or other adjustment of that series.

**error, standard—**The standard deviation of the errors associated with physical measurements of an unknown quantity, or statistical estimates of an unknown quantity or of a random variable.

**error, systematic—**An error whose algebraic sign and, to some extent, magnitude bear a fixed relation to some condition or set of conditions; regular error. Systemic errors always follow some definite mathematical or physical law, and they are generally eliminated from a series of observations by computation or by systematic field methods.

**error, target centering—**The error caused by the target not being positioned directly over the center of the point being observed.

**error ellipse—**A region of some statistical certainty (95 percent is very common). If the same measurements were re-performed under the same conditions using the same equipment, and the same control was used, one would be 95 percent certain that the coordinates from the re-survey would be within the error ellipse defined by the original adjustment. It is derived from the post-adjustment variance-covariance matrix.

**error equation—**See *equation, error.*

**error of closure-**^{1}The difference between a value of a quantity determined by surveying and the fixed or theoretical value of the same quantity.** ^{2} **The difference between the sum of a series of angles and the theoretically correct answer.

^{3}The amount by which two values of the azimuth of a line, derived by different surveys or along different routes, fail to be exactly equal to each other.

^{4}[LEVELING] The amount by which two values of the elevation of the same bench mark, derived by different surveys or through different survey routes or by independent observations, fail to be exactly equal to each other.

^{5}[TRAVERSE] The amount by which a value of the position of a traverse station, as obtained by computation through a traverse, fails to agree with another value of the same station as determined by a different set of observations or route of survey.

**error of collimation—**See *collimation, error of*

**error propagation—**Computation of error in a computed quantity based on a mathematical law and error estimates of measured values.

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Source: NSPS “Definitions of Surveying and Related Terms“, used with permission.

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