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Über die Exzentrizität von Teilkreisen / G. Schell (1955)

Public Titre : Über die Exzentrizität von Teilkreisen Titre original : [Sur l'excentricité du Cercle gradué] Type de document : Thèse/HDR Auteurs : G. Schell, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1955 Collection : DGK - C Sous-collection : Dissertationen num. 015 Importance : 90 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] cercle horizontal Index. décimale : 30.03 Instruments de géodésie Résumé : (Auteur) In the present paper the author has undertaken to study the influence of eccentricity hitherto only occasionally dealt with in publications, and particularly to investigate to what extent the procedure applied in modern instrument production of renouncing the second reading point with small sized instruments, may be permissible with regard to its lesser precision. Assuming that the centre of rotation of the horizontal limb does not coincide with the geo-metrically defined centre of graduation nor with the centre of rotation of the alidade, a derivation of general validity is established regarding the effective eccentricity as a function of the alidade direction and the position of the circle. Beside a description of the general measuring arrangement for the horizontal circle the author shows and explains by a numerical example that it is possible to unequivocally determine the vectors of eccentricity by inverting the values of measurement, as resulting from the investigating procedure with axis strain in theodolites realized by Rannie and Dennis. He compares the very clear graphical adjustment with a strictly numerical procedure and an approximate solution resulting directly from the measuring scheme of Rannie and Dennis. Experiments with several instruments have shown, that the eccentricity between the center of rotation of the limb and the centre of the graduation circle was greater than the eccentricity between the rotation centres of alidade and circle. Hence follows that the position of the circle does influence the eccentricity-error to the same degree as the alidade direction itself. Therefore the observation by half rounds must be avoided, as possible, with all instruments provided with only one reading place. The influence of errors due to eccentricity, occurring with observations by half rounds is shown by a numerical example. When checking instruments it was hitherto customary to indicate but one value depending on the alidade direction. But this single value is not sufficient for determination of the conditions of eccentricity. For this purpose two values will be necessary: the vector of eccentricity between the rotation centres of alidade and limb, and moreover the vector of eccentricity between centre of rotation of the limb and centre of the graduation circle. The author shows that a second, diametrical reading place is indispensable with measurements of vertical angles, since the influences of eccentricity in contradiction to the measurement of horizontal angles are not eliminated by observing in both the telescope positions. Starting from the general equation of eccentricity established in the first part, the author derives formulae, pertaining to the different systems of numbering and giving a relation between the inclination of the axis of collimation and the residual error due to eccentricity. From these formulae follows that the error in reading due to eccentricity becomes a maximum particularly with approximately horizontal vision. Moreover the author treats the variation of the index error, due to eccentricity and depending on the inclination of the axis of collimation. This study proves that the effective eccentricity, with respect to its influence on vertical angles and index errors, is defined by the appropriate orthogonal components of the linear eccentricity. Several measuring procedures applicable to determine the important parameters of eccentricity are examined and critically compared with each other. Thereby it is shown that considerable instrumental requirements are necessary for an exact investigation. In many cases the short distances have to be excluded from measurement of eccentricity-errors, because a superposition with three other sources of error would arise thereby. By means of examples the procedures applied are. explained in detail, and the errors due to eccentricity are demonstrated numerically. If the variation in position of the spindle with respect to its shell, caused by the free play of axis, is also considered, the necessity of providing a diametrically opposed reading point will result to a still higher degree than with the pure errors due to eccentricity. When treating the errors due to axial run there is a difference occurring between systematic portions i. e. which may be defined analytically and accidental irregularities in axial running, caused by a shaky motion of the spindle in its shell. Regarding the systematic motion of the axis the author assumes a hypo-cycloidal rolling in its bearing with the vertical axis, and a uniform lifting out of its bearings with the transverse axis. These reflections prove that with instruments having only one reading place the direction, even when observed in two positions of the telescope, still involves systematic axial defects in the form of apparent eccentricity-errors, whereas the zenith distance observed in two positions of the telescope is free from such influences. The irregular axial defects influence both the direction and inclination measurements. The means taken from diametrically opposed readings are free from systematic and accidental errors due to axial run. The eccentricity-errors due to the free play of the axis are demonstrated qualitatively with two instruments with respect to both the horizontal and vertical circles. Hence follows that the amount of these errors exceeds the magnitude of errors due to defects of circle graduation. With instruments having only one reading place it is a damage that the eccentricity-errors due to irregular axial run cannot be controlled. In conclusion, the author generally states that instruments without a second reading device in many cases do not profit by the accuracy obtainable in pointing and reading-off. Numéro de notice : 37446 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63764

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
37446-01	30.03	Livre	Centre de documentation	En réserve M-103	Disponible