errors of observation and measurement caused by the imperfection of instruments (such as the inevitable differences between the real instrument and the “ideal,” which is represented by its geometric scheme) and by the inaccurate installation of the instrument in operating position. Instrument errors must be taken into account in measurements requiring high accuracy; if they are disregarded, systematic errors result, which may make the measurement data largely worthless.
Calculations of instrument errors are of particular importance in astronomy, geodesy, and other sciences in which extremely precise measurements are required. In view of this, the development of research methods on instrument errors and the elimination of their effects on observational and measurement data is one of the principal tasks of the theory of measuring instruments. Instrument errors may be subdivided into three categories.
Errors related to imperfections in the manufacture of individual instrument parts may not be eliminated or changed by the observer, but they are carefully studied, and the errors caused by them are eliminated by the introduction of the required corrections or by rationally devised measurement methods that eliminate their effect on the final results. Instrument errors belonging to this category include errors of the scale divisions on divided circles, according to which the direction to an object under observation is read; errors of the scale divisions of measuring instruments; eccentricity errors, which arise from a discrepancy between the center of rotation of a divided circle or alidade and the center of the circle’s divisions; periodic and running errors of micrometer screws, caused by imperfections in their threading or assembly; errors caused by flexure of instrument parts; and errors associated with optical instruments, such as distortion, astigmatism, and coma.
Errors related to faulty assembly and adjustment of instruments and to insufficient accuracy in installation in the position required by the theory of a particular method of observation include collimation error, which is a deviation from the 90° angle between the line of sight and the transit axis; errors associated with the inclination of an instrument’s horizontal axis to the horizon and its inaccurate installation (setting) at the required azimuth; inaccurate centering of objective lenses; and some errors of recording equipment. Instrument errors of this category, which may be detected by instrument control tests, may be reduced to a minimum by adjustment of certain parts of the instrument, for which provision is made in their design. The small fractions of these errors that remain uncorrected are determined by means of auxiliary devices, such as levels, nadir-horizons, and collimators, or are inferred from the observations (for example, azimuthal error) and their effect is taken into consideration during the processing of the observational data.
The category of errors associated with a change in the properties of an instrument with time, particularly those caused by temperature changes, also includes the overall effect of all other errors that are not accounted for by the theory of the instrument. These instrument errors are the most complex. They are especially detrimental, since they develop systematically and are not clearly detectable during observations and measurements. They become apparent only upon measurement of the same quantity with different instruments. Thus, systematic differences that usually exceed the random errors inherent in the methods and instruments by a factor of 1.5–2.0 (sometimes 5–6) are always detected in the comparison of star coordinates obtained from observations at different observatories or of precisely timed radio-signal corrections determined by different time services. One of the important tasks is the detection, thorough investigation, and if possible, elimination of the sources of instrument errors of this category.
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