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I. Mechanik.</strong> <i>(German)</i> <a class="label nowrap" href="/08.0542.01">JFM 08.0542.01</a> </h2> <div class="source"> Leipzig. Teubner (1876). </div> <div class="abstract">Der Verfasser erkl盲rt in der ersten Vorlesung, abweichend von der gew枚hnlichen Erkl盲rung, die Mechanik als die Wissenschaft von der Bewegung, und stellt als Aufgabe derselben hin, die in der Natur vor sich gehenden Bewegungen vollst盲ndig und auf die einfachste Weise zu beschreiben. Vollst盲ndig, d. h. es soll keine Frage, die in Betreff der Bewegungen gestellt werden kann, unbeantwortet bleiben. Darin liegt eine Eischr盲nkung gegen眉ber der gew枚hnlichen Definition. Diese Eischr盲nkung hat der Verfasser acceptirt, um damit die Unklarheiten und Dunkelheiten zu vermeiden, wie sie durch die hergebrachte Definition der Mechanik als Wissenschaft von den Kr盲ften hervorgebracht wurden. Der Verfasser wendet sich sodann zu den weiteren Erkl盲rungen. Indem er sich zun盲chstauf den K枚rper mit unendlich kleinen Dimensionen, den materiallen Punkt, beschr盲nkt, wekl盲rt er, was unter Componenten der Geschwindigkeit, Componenten der Beschleunigung zu verstehen sei. Zur Erl盲uterung der Begriffe dient der Fall eines schweren Punktes und die Planetenbewegung. Nachdem er sodann den Satz vom Parallelogramm der Kr盲fte besprochen, stellt er die Gleichungen der Problems der drei K枚rper auf. In der zweiten Vorlesung geht er dann zur Bewegung eines unfreien Punktes mit Anwendung auf das einfache Pendel 眉ber und wendet sich dann, nachdem der Begriff der Masse beleuchtet ist, zu den Lagrange’schen Gleichungen. Es folgen dann in den weiteren Abschnitten die S盲tze 眉ber Gleichwicht, Schwerpunkt, Drehungsmomente und die Bewegung eines starren K枚rpers. In der achten Vorlesung wird das Pendel und der Einfluss der H枚he und der geographischen Breite auf die Schwere besprochen. Die neunte Vorlesung ist dem Einfluss der Drehung der Erde gewidmet.<br class="zbmathjax-paragraph">Nachdem so in den neun ersten Vorlesungen nur materielle Punkte und starre K枚rper behandelt sind, werden nunmehr die relativen Verschiebungen nicht starrer K枚rper untersucht. Den Ausgangspunkt bildet die Annahme, dass die K枚rper stetig ausgedehnte Materie sind, und dass die Bewegung in ihnen sich stetig mit dem Orte 盲ndert. Daraus ergeben sich dann die Druckcomponenten bei Fl眉ssigkeiten und elastischen festen K枚rpern. Es folgt die Hydrostatik, Gleichgewicht rotirender Fl眉ssigkeiten, Archimedisches Princip, dann die Theorie der Capillarerscheinungen. Die Grundlage bildet hier das Gausse’sche Princip: Wenn zwei verschiedenartige K枚rper in einer Fl盲che sich ber眉hren, so wirken in Golge hiervon Kr盲fte, die ein Potential haben, welches gleich der Gr枚sse der Ber眉hrungsfl盲che, multiplicirt mit einer von der Natur der beiden K枚rper abh盲ngigen Constanten ist. Das Princip selbst wird nicht abgeleitet, sondern in dieser Hinsicht auf Gauss verwiesen. Die Differentialgleichungen der capillaren Fl盲chen, sowie die Grenzbedingungen werden aufgestellt. Die Differentialgleichung f眉r die Ber眉hrungsfl盲che zweier schwerer Fl眉ssigkeiten wird f眉r den Fall angen盲hert integrirt, dass sie eine Rotationsfl盲chen ist und die Abst盲nde der betrachteten Punkte von der Rotationsaxe sehr gross sind. Nun folgen die Differentialgleichungen der Hydrodynamik in der Euler’schen und Lagrange’schen Form. Daran schliesst sich eine Darstellung der neueren hydrodynamischen Untersuchungen, der von Helmholtz 眉ber Wirbelbewegungen, der von Helmholtz un d Kirchhoff 眉ber freie Fl眉ssigkeitsstrahlen, der Bewegungen eines K枚rpers in einer Fl眉ssigkeit, namentlich der Ellipsoids verificirt, die Potentialgleichung transformirt.<br class="zbmathjax-paragraph">Es folgen die Schallbewegungen der Luft, wobei die von Helmholtz in seiner “Theorie der Luftschwingungen in R枚hren” (Crelle LVII.) entwickelten Resultate abgeleitet werden, sowie die Theorie der cubischen Pfeifen. Nachdem weiter noch der Ausfluss schwerer Fl眉ssigkeiten, sowie einige andere hydrodynamische Problemem ohne Ber眉cksichtigung der Reibung behandelt sind, z. B. die Wellenbewegung, folgen die hydrodynamischen Gleichungen mit Ber眉cksichtigung der Reibung, sowie einige Anwendungen derselben. Den Schluss bilden Abschnitte der Elasticit盲tstheorie. Diese Abschnitte enthalten haupts盲chlich die Resultate fr眉herer Arbeiten von Herrn Kirchoff selbst, n盲mlich ausser der Ableitung der allgemeinen Elasticit盲tsgleichungen die Theorie des unendlich d眉nnen elastischen Stabes und der unendlich d眉nnen Platte.<div class="reviewer"> Reviewer: <a href="/authors/?q=Orthmann+Wangerin">Orthmann, Dr. (Berlin) Wangerin, Prof. (Berlin)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A2714548">Cited in <strong>5</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A2714548">Cited in <strong>876</strong> Documents</a></div></div> <div class="keywords"> <h3>JFM Section:</h3><a href="/?q=ut%3A%22Zehnter+Abschnitt.+Mechanik.+Capitel+1.+Allgemeines.+%28Lehrb%C3%BCcher.%29."">Zehnter Abschnitt. Mechanik. Capitel 1. Allgemeines. 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