| Résumé : |
(Auteur) An important factor in national and international triangulations is represented by the determination of scale. Such determination results from two essentially different component parts, i.e., (a) the measurement proper of a given base line, and (b) the enlargement or transportation of this base to a main triangulation side by means of observing a base net.
In connection with M. GASSER's article on the Development of Base Apparatus and Measuring Procedures the apparatus, procedures and standardizations with regard to base measurement had been treated in Chapter 1, as far as they have been in use since 1900. In accordance with the procedure indicated by HADERT, the Bessel constants were recom-puted for all German bases of a more recent date, that is from the year 1880 onwards. The lengths thus found, together with values resulting from measurements made with other base equipment, were confronted with the values resulting from SCHREIBERS's standardization of 1880; the irreliablity of the Bessel apparatus could be proven, even through the Hadert corrections had been applied. In consequence of recent technical development G. FORSTER's suggestion of a modern rigid apparatus was supplemented.
This was followed up by a discussion of advantages and disadvantages of the non-rigid wire and tape apparatus having a length of from 24 to 50 metres as well as of the customary base measuring accessories and methods. L. BENES had indicated a proposal according to which conclusions should be made from the result of the partial lengths (portees) to the behavior of the wires during the measuring process. This proposal has been discussed and extended. So possibilities are shown for the determination of wire constants on the individual measuring days, values which are more plausible than the mean values hitherto in use which result from the two standardizations or the values intercalated between them in a linear manner.
A discussion was made of the errors exercised by measuring equipment, standardiza-tion and measuring procedure. The results supplied a full justification of the customary measuring order found empirically. In the same manner the classical error computations were checked as to furnishing reliable criteria on the precision and accuracy of a base mea-surement. The reasons have been explained why the 24 meter standards and short standard bases (having, like that of Potsdam, a length of 240 m) were bound to fail in the fields. These investigations had been based on the results obtained in connection with studies, extended over a period of several years, on the 24-meter standard line at the pavilion of the "Bureau international des Poids et Mesures". Thus the interrelationship has been shown between a minimum length of 700 meters which, for reasons of practical requirements, had been adopted, during the last years, for a base or reference, and the periodical changes of a 24-meter line observed by GUILLAUME (19091913). After a study of the methods used in the determination of the lengths of standardization with respect to the standard bases of reference of Nummela (Finland) and that of Potsdam (new) the proposal has been made to standardize the standard base of reference with a modern bar apparatus, since the customary procedure of standardization by wires will supply satisfactory results only after a number of years have elapsed. The customary procedure of determining the coefficients of thermal expansion but one time and in an overall fashion scarcely appears tolerable inasmuch as changes of that coefficients have been found out which supposedly occur in connection with progressing age of the wires. A current control of the coefficient of thermal expansion may best be obtained by using the interference comparator or in water, since relative measuring is concerned.
Chapter 2 deals with the problem of enlarging base lines. A total of 110 European bases supplied the mean length as of 6.7 km, where as the length of a main side of triangulation varies from 24 to 35 km. For transporting the base line to a main side, base nets are made use of. Since the configuration of such a net greatly differs from that of the main triangulation net, specific procedures are in use for the observation. In Germany the method developed by SCHREIBER in 1880 is still regarded as the best. Other nations, such as Finland, however, have never made any use of this method, or have performed a successive modification, such as USSR, Sweden, and Norway. Therefore it was felt necessary to closely consider the reasons given by SCHREIBER for his method.
An investigation of 22 single angles in SCHREIBER nets made it clear that, according to this method, part of the angles were observed too often so that systematic errors exercised a domineering influence, whereas another part, owing to too small an amount of sets (24) possesses too less a degree of probability. The assignement of weights, based on the number of sets, does not appear tolerable. An error computation, performed for 11 angles measured in from 24 to 72 sets shows considerable deviations of the accuracy of SCHREIBER angles having the same weight. For SCHREIBER failed to establish a relationship between weight and mean unreliability. An investigation into the Base Nets of Meppen and Vienna shows that some observations were canceled in an almost arbitrary manner, which was done in order to stick to the prescribed number of sets on one hand, and, on the other hand, to keep the error of the triangle closure below the i 1 limit as usual in the main triangulation.
Based on ,,angle diagramms" (Winkelbilder), i. e., graphs of the course of the mean value as resulting from the current observations in half sets, the results obtained from the angle observations have been shown up. It has furthermore been demonstrated that employment of the SCHREIBER method of observation and the SCHREIBER configuration of net entails all the detrimental effects of the periodical and permanent local fields of side refraction.
An investigation into reciprocal coefficients of weight ("strength of the net, Q") for ideal figures, such as isosceles and one-sided rhombus, a combination of two similar triangles, isosceles and onesided double rhombus, resulted into an interesting diagram. It shows how the "strenght of the net" varies with the ratio of enlargement and with the shape of base nets.
Subsequently the Q values, computed for 42 European nets, were entered into the diagrams. The position of the values of Q with reference to the curves of the ideal figures now admits of conclusions to the respective advantages or disadvantages of the net configurations occuring in practice. To this end the diagrams of the base nets treated have been represented in a uniform scale for the enlarged side Sv. These model nets together with the diagram then permit to find good values of approximation for Q, the strength of the net, of any net.
Summing up it may be stated that the SCHREIBER Method based merely on the theory of accidental errors and on purely statical requirements, does not take fully account of the true physical conditions and is therefore not entirely satisfying. |
Kritische Betrachtungen zur Messung und Vergrößerung von Grundlinien (1953)
