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. 1906 Excerpt: ...from point to point in composition and state of strain in a given state of reference (x," y," z"), and if the body is fully described in that state of reference, both in respect to its composition and to the displacement which it would be necessary to give to a homogeneous solid of the same composition, for which ey is ...
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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. 1906 Excerpt: ...from point to point in composition and state of strain in a given state of reference (x," y," z"), and if the body is fully described in that state of reference, both in respect to its composition and to the displacement which it would be necessary to give to a homogeneous solid of the same composition, for which ey is known in terms of dx dz...-jp, and the quantities which express its composition, to bring it from the state of reference (x', y', z) into a similar and similarly situated state of strain with that of the element of the nondx" dz" homogeneous body, we may evidently regard, ... as known for each element of the body, that is, as known in terms of x," y," z." We shall then have ev, in terms of tjy, ... J.j, x," y," z"; and since the composition of the body is known in terms of x," y," z," and the density, if not given directly, can be determined from the density of the homogeneous body in its state of reference (x', y', z'), this is sufficient for determining the equilibrium of any given state of the non-homogeneous solid. An equation, therefore, which expresses for any kind of solid, and with reference to any determined state of reference, the relation between the quantities denoted by ev., Jjv., ... $7, involving also the quantities which express the composition of the body, when that is capable of continuous variation, or any other equation from which the same relations may be deduced, may be called a fundamental equation for that kind of solid. It will be observed that the sense in which this term is here used, is entirely analogous to that in which we have already applied the term to fluids and solids which are subject only to hydrostatic pressure. dec dz When the fun...
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