engleski

Application of Bošković Geometric Adjustment Method on Five Meridian Degrees

Josip Ruđer Bošković (Dubrovnik, 18th May 1711 – Milan, 13th February 1787) from his early scientific days began to publish theses on the issues of Earth’s shape and size which represented a major scientific problem of the 18th century. During the 18th century scientists were having a great discussion around the question whether the Earth was flattened or bulging at the poles. In the late 17th century, Newton proved that the Earth should be flattened at the poles because of its rotation. Domenico Cassini assumed the opposite, that Earth had the shape of an egg so, at the end of 17th and in the beginning of 18th century he conducted comprehensive geodetic observations to prove his assumption. There existed two basic methods for determining the Earth’s figure: pendulum experiments and the determination of the meridian arc length. The idea of the second method was to determine the length of the meridian arc that corresponded to one degree of latitude. French Academy carried out the measurements during 1730s to test theoretical interpretations of the Earth’s figure. Bošković came to the idea of confirming his assumption on meridians inequality by measuring the length of the meridian arc. To accurately determine the figure of the Earth, in his first attempt to determine ellipticity Boˇskovi´c compared five arc lengths of one meridian degree, which he considered to be sufficiently accurate. Those were the measurements, of the meridian degrees, carried out in South America (Quito), South Africa (the Cape of Good Hope), France (Paris), Finland (the province of Lapland), and his own, carried out in Rome, Italy. Whereas astronomical and geodetic measurements are liable with errors caused by various sources, Boˇskovi´c was aware that the causes of errors can not be fully eliminated during the construction of instruments and measurements. When comparing mentioned five degrees of meridian, Bošković could not determine such an ellipsoid consistent with all the measurements. He decided to determine corrections that would fix all degrees and get a better estimate of true values. In 1755 Bošković and Christopher Maire published the first results of those measurements and analysis of measured data in the book De Litteraria Expeditione per Pontificiam ditionem ad dimentiendas duas Meridiani gradus et corrigendam mappam geographicam (A scientific journey through the Papal State with the purpose of measuring two degrees of meridian and correcting a geographical map) on more than 500 pages. According to Bošković, data should be fixed in such a way that: 1. The differences of the meridian degrees are proportional to the differences of the versed sines of double latitudes 2. The sum of the positive corrections is equal to the sum of the negative ones (by their absolute values) and 3. The absolute sum of all the corrections, positive as well as negative, is the least possible one. In his works Bošković gave geometric description of solutions for the mentioned conditions. In the paper we describe in detail the example with five meridian degrees. Data have been taken from Bošković original book. Geometric solution, described by Bošković himself, is not easy to understand at first, as it is noted by other authors who have studied the Bošković method as well. Today, by software for interactive geometry, his method can be analytically defined and visualized in a way which provides better understanding. For this purpose, GeoGebra has been used, a free mathematics software which joins geometry, algebra, statistics and calculus in one easy-to-use package.

Josip Ruđer Bošković; geometric adjustment method; GeoGebra

nije evidentirano