Repertorium der literarischen arbeiten aus dem gebiete der reinen und angewandten mathematik: "Originalberichte der verfasser," gesammelt und hrsg, Band 2Leo Koenigsberger, Gustav Zeuner B.G. Teubner, 1879 |
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Häufige Begriffe und Wortgruppen
Abel'schen Abhandlung algebraischen allgemeinen beiden bekannten beliebig bestimmt bezeichnet Büschel Capitel Coefficienten Conductor constant Curve oder Fläche Differential Differentialquotienten Doppelbelegung drei Ebene eindeutig einfach elliptische Integrale elliptischen Functionen endlich entsprechen equation equilibrium ergiebt Ernst Schröder F₁ Fall folgende Form Formeln gegebenen Curve Geometrie Geometrie der Lage Geraden giebt gleich Gleichung Gleichungen fünften Grades Grades Green'schen Sätze Grössen Hülfe hyperelliptischen Integrale Ikosaeder Integration irgend Jacobi'schen Kegelschnitte Leo Koenigsberger letzten liche lineare Logarithmischen Lösungen Massen Math Methode million number Ordnung P₁ Pappus partielle Differentialgleichungen phases Polyeder polygone positiv Potential projectivische punti reine und angewandte Repertorium für reine resp Resultate sämmtliche Satz singulären Punkte Sophus Lie speciellen superficie surface System Systems Tangenten theils Theoreme Theorie Transformation Ueber unendlich unserer Untersuchungen variables Veränderlichen Verf verschiedenen vollständige vorgeschriebenen Werthe VR(t Weise Werthe x₁ Y₁ Y₂ Zahl zwei zweiten
Beliebte Passagen
Seite 301 - For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy, the variation of its entropy shall either vanish or be negative.
Seite 312 - The second part of the paper* commences with a discussion of the conditions of internal and external equilibrium for solids in contact with fluids with regard to all possible states of strain of the solids.
Seite 318 - It follows from the general relations given above that, when a film has more than one component, those components which diminish the tension will be found in greater proportion on the surfaces. When the film is extended, there will not be enough of these substances to keep up the same volume- and surface-densities as before, and the deficiency will cause a certain increase of tension. It does not follow that a thinner film has always a greater tension than a thicker formed of the same liquid. When...
Seite 311 - When the proximate components of a gas-mixture are so related that some of them can be formed out of others, although not necessarily in the gas-mixture itself at the temperatures considered, there are certain phases of the gas-mixture which deserve especial attention. These are the phases of dissipated energy, ie, those phases in which the energy of the mass has the least value consistent with its entropy and volume. An atmosphere of such a phase could not furnish a source of mechanical power to...
Seite 304 - These are all that exist, for of these variables ; n -\- 2 are evidently independent. Now upon these relations depend a very large class of the properties of the compound considered? — we may say in general? all its thermal, mechanical; and chemical properties; so far as active tendencies are concerned; in cases in which the form of the mass does not require consideration.
Seite 307 - ... (14) in which the values of the accented letters are to be determined by the phase or system of phases of which the stability is in question, and the values of the unaccented letters by any other phase of the same components, the possible formation of which is in question. We may call the former constants, and the latter variables. Now if the value of the expression, thus determined, is always positive for any possible values of the variables, the phase or system of phases will be stable with...
Seite 315 - Beside this condition, which relates to the nature of the surface of discontinuity, there are other conditions of stability, which relate to the possible motion of such surfaces. One of these is that the tension shall be positive. The others are of a less simple nature, depending upon the extent and form of the surface of discontinuity, and in general upon the whole system of which it is a part. The most simple case of a system with a surface of discontinuity is that of two coexistent phases separated...
Seite 311 - Gas-mixtures with convertible components. — The theory of the phases of dissipated energy of an ideal gas-mixture derives an especial interest from its possible application to the case of those gas-mixtures in which the chemical composition and resolution of the components can take place in the gas-mixture itself, and actually does take place, so that the quantities of the proximate components are entirely determined by the quantities of a smaller number of ultimate components, with the temperature...
Seite 311 - For this end, we first form the equation in p, t, fir //j, etc. for the gas-mixture, regarding its proximate components as not convertible. This equation will contain a potential for every proximate component of the gas-mixture. We then eliminate one (or more) of these potentials by means of the relations which exist between them in virtue of the convertibility of the components to which they relate, leaving the potentials which relate to those substances which naturally express the ultimate composition...
Seite 314 - ... (24) There are terms relating to variations of the curvatures of the surface which might be added, but it is shown that we can give the dividing surface such a position as to make these terms vanish, and it is found convenient to regard its position as thus determined. It is always sensibly coincident with the physical surface of discontinuity. (Yet in treating of plane surfaces, this supposition in regard to the position of the dividing surface is unnecessary, and it is sometimes convenient...