This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1888 Excerpt: ...the expression (155) calculate all those terms in the mean Lagrangian function which involve such coordinates. There may however be some terms in the Lagrangian function which do not involve these quantities and if we require these we must determine them by other considerations; a large number of problems can however ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1888 Excerpt: ...the expression (155) calculate all those terms in the mean Lagrangian function which involve such coordinates. There may however be some terms in the Lagrangian function which do not involve these quantities and if we require these we must determine them by other considerations; a large number of problems can however be solved even though we do not know the values of these terms. To get some idea of the different kinds of terms which may exist in the Lagrangian function let us consider the energy of a system consisting of a large number of molecules. In the expression for the energy we can calculate all the terms involving the coordinates which fix the electric, magnetic or elastic configuration of the system, and in the terms depending upon the strain coordinates we may include those terms which involve the.average distance between the molecules. There may however be some terms left which each molecule contributes independently of its neighbours and which do not involve any of the controllable coordinates. The sum of these contributions will be proportional to the number of the molecules and must also be a function of the temperature, because the mean state of the system is fixed by the controllable coordinates and the temperature, and the mean kinetic energy must therefore be a function of these quantities. By hypothesis the terms we are considering do not involve the controllable coordinates, so that the only quantity they can depend upon is the temperature. The potential energy of the molecules may also contribute terms to the Lagrangian function which do not involve the controllable coordinates and which therefore we cannot calculate by equation (155). For the purposes for which we use the Lagrangian function all that we require to know about it-is the...
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