Elements of Vector Analysis: Arranged for the Use of Students in Physics (Classic Reprint)

Excerpt from Elements of Vector Analysis: Arranged for the Use of Students in PhysicsAny vector may be regarded as the product of a positive scalar (the magnitude of t e vector) and a unit vector.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Science & Math

Josiah Willard Gibbs

Mathematics

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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: ...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 e, tjT,, „... p, 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. When the fundamental equation between eT, J?v'. j-y is known, we may obtain by differentiation the values of t, X,... Zv in terms of the former quantities, which will give eleven independent relations between the twenty-one quantities Cv ' 'v' die" ' ' ' Ez" ' "x ' " z' (415) which are all that exist, since ten of these quantities are independent. All these equations may also involve variables which express the composition of the body, when that is capable of continuous variation. If we use the symbol //T to denote the value of i/r (as defined on page 89) for any element of a solid divided by the volume of the element in the state of reference, we shall have T=er--ttiT. (416) The equation (356) may be reduced to the form 8Y=-t,v'St+(xx.S). (417) Therefore, if we know the value of yfrv in terms of the variables ( doc ( i'-rp,...-rp, together with those which express the composition of the body, we may obtain by differentiation the values of Ijt, Xx,,... Zv in terms of the same variables. This will make ele...

Scientific Papers of J. Willard Gibbs Volume 1; Thermodynamics

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Excerpt from Elements of Vector Analysis: Arranged for the Use of Students in Physics(The three letters, i, j, k, will make an exception, to be mentioned more particularly hereafter.2. Def. - Vectors are said to be equal when they are the same both in direction and in magnitude. The reader will observe that this vector equation is the equivalent of three scalar equations.A vector is said to be equal to zero, when its magnitude is zero. Such vectors may be set equal to one another, irrespectively of any considerations relating to direction.3. Perhaps the most simple example of a vector is afforded by a directed straight line, as the line drawn from A to B. We may use the notation AB to denote this line as a vector, i. e., to denote its length and direction without regard to its position in other respects. The points A and B may be distinguished as the origin and the terminus of the vector. Since any magnitude may be represented by a length, any vector may be represented by a directed line; and it will often be convenient to use language relating to vectors, which refers to them as thus represented.Reversal of Direction, Scalar Multiplication and Division.4. The negative sign (-) reverses the direction of a vector. (Sometimes the sign + may be used to call attention to the fact that the vector has not the negative sign.)Def. - A vector is said to be multiplied or divided by a scalar when its magnitude is multiplied or divided by the numerical value of the scalar and its direction is either unchanged or reversed according as the scalar is positive or negative. These operations are represented by the same methods as multiplication and division in algebra, and are to be regarded as substantially identical with them. The terms scalar multiplication and scalar division are used to denote multiplication and division by scalars, whether the quantity multiplied or divided is a scalar or a vector.5. Def. - A un…

Excerpt from The Collected Works of J. Willard Gibbs, Vol. 2 of 2: Part One: Elementary Principles in Statistical Mechanics; Part Two: Dynamics; Vector Analysis and Multiple Algebra; Electromagnetic Theory of Light The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or. More precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results. The laws of statistical mechanics apply to conservative systems of any number of degrees of freedom. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The Collected Works of J. Willard Gibbs, Vol. 2 of 2: Part One: Elementary Principles in Statistical Mechanics; Part Two: Dynamics; Vector Analysis and Multiple Algebra; Electromagnetic Theory of Ligh

Excerpt from Manual Hebrew and English Lexicon: Including the Biblical Chaldee; Designed Particularly for Beginners Aphel. Apocopated. Article or articles. Common gender. Causative. Chaldaic. Collective or collectively. Common gender. Compare conjunction. Conjugation. Construct state. Conversive denominative. Derivative or derivatives. For example. Emphatic state. Feminine. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Manual Hebrew and English Lexicon: Including the Biblical Chaldee; Designed Particularly for Beginners (Classic Reprint)

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Excerpt from The Collected Works of J. Willard Gibbs, Vol. 2 of 2: Part One: Elementary Principles in Statistical Mechanics; Part Two: Dynamics; Vector Analysis and Multiple Algebra; Electromagnetic Theory of LightThe laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or. More precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results. The laws of statistical mechanics apply to conservative systems of any number of degrees of freedom.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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Books by Josiah Willard Gibbs

See the best price to sell, buy, or rent books by Josiah Willard Gibbs. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Elements of Vector Analysis: Arranged for the Use of Students in Physics (Classic Reprint)

Scientific Papers of J. Willard Gibbs Volume 1; Thermodynamics

Elements of Vector Analysis: Arranged for the Use of Students in Physics (Classic Reprint)

The Collected Works of J. Willard Gibbs, Vol. 2 of 2: Part One: Elementary Principles in Statistical Mechanics; Part Two: Dynamics; Vector Analysis and Multiple Algebra; Electromagnetic Theory of Ligh

Manual Hebrew and English Lexicon: Including the Biblical Chaldee; Designed Particularly for Beginners (Classic Reprint)

The Collected Works of J. Willard Gibbs, Vol. 2 of 2: Part One: Elementary Principles in Statistical Mechanics; Part Two: Dynamics; Vector Analysis and Multiple Algebra; Electromagnetic Theory of Ligh