Les instruments du calcul savant > Instruments d'intégration conservés au musée des arts et métiers |
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Orthogonal Planimeter Orthogonal planimeter with disk-and-wheel mechanism, Wetli-Hansen type
Orthogonal planimeter by H. Ausfeld, Wetli-Hansen type (CNAM 06340-0000) The invention of the orthogonal planimeter by Johann Martin Hermann (1785[?]-1841) and Tito Gonnella (1794-1867) remained almost unnoticed, notwithstanding the publications by Gonnella in 1825 and 1841. Thus it became possible to reinvent these devices or parts thereof. Although Tito Gonnella in his 1825 publication had already described the disk-and-wheel mechanism that later was named after him, this integrating mechanism soon became unknown or forgotten, which made possible its reinvention in 1849/50 by the Swiss engineer Kaspar Wetli (1822-1889). Wetli type instruments were manufactured, incorporating several modifications by Simon Stampfer (1790-1864), by the polytechnic workshop of Georg Christoph Starke (1794-1865; later Starke & Kammerer) in Vienna. Their instruments made the possibility of theoretically exact mechanical integration a widely known fact. Only a short time after the first Wetli-Starke planimeters appeared on the market (c1850), several people tried to make the instrument even more useful and precise. One of these persons was the astronomer Peter Andreas Hansen (1795-1874) in Seeberg/Gotha. His successful modifications became known as Wetli-Hansen type planimeters, sometimes also known as Hansen-Ausfeld planimeters, by adding the maker's name. While Gonnella probably had initially used, in his first prototypes, the cone-and-wheel mechanism also used by Herrmann, he had realised at least when he prepared his 1825 publication that the cone might be replaced by a disk, with the additional advantage that negative ordinates, too, would then pose no problem to his instrument. (Today it is obvious to see a disk as being the limiting case of a cone whose angle at the summit approaches 180°, but in 1825 this must have been quite an abstraction.) But regardless of whether a cone or a disk is used, the resulting integrating mechanism is an immediate translation of mathematical integration into mechanics. Because mathematical integration may be considered as being continuous multiplication combined with simultaneous accumulation, it was no problem for contemporary engineers to see that the cone-and-wheel or disk-and-wheel mechanisms simply do this. Thus the correctness of the instrument was immediately accepted - quite in contrast to what happened to Jakob Amsler's polar planimeter in 1856. |
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