Yale's Sloane Physical Laboratory, as it stood between 1882 and 1931 at the current location of Jonathan Edwards College. Gibbs's office was on the second floor, to the right of the tower in the picture.
Gallery of Josiah Gibbs
Building housing the Josiah Willard Gibbs Laboratories, at Yale University's Science Hill
Yale's Sloane Physical Laboratory, as it stood between 1882 and 1931 at the current location of Jonathan Edwards College. Gibbs's office was on the second floor, to the right of the tower in the picture.
Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics (Cambridge Library Collection - Mathematics)
(Josiah Willard Gibbs (1839-1903) was the greatest America...)
Josiah Willard Gibbs (1839-1903) was the greatest American mathematician and physicist of the nineteenth century. He played a key role in the development of vector analysis (his book on this topic is also reissued in this series), but his deepest work was in the development of thermodynamics and statistical physics. This book, Elementary Principles in Statistical Mechanics, first published in 1902, gives his mature vision of these subjects. Mathematicians, physicists and engineers familiar with such things as Gibbs entropy, Gibbs inequality and the Gibbs distribution will find them here discussed in Gibbs' own words.
Vector Analysis: A Text-Book for the Use of Students of Mathematics and Physics, Founded Upon the Lectures of J. Willard Gibbs ... 1901
(Originally published in 1901. This volume from the Cornel...)
Originally published in 1901. This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies. All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume.
Elements of Vector Analysis: Arranged for the Use of Students in Physics (Classic Reprint)
(Excerpt from Elements of Vector Analysis: Arranged for th...)
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
The Scientific Papers of J. Willard Gibbs, Vol. 2 (Classic Reprint)
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JjuJKM.. A Permission for the preserU reprvni of the different papers contained in these volumes has in every case been obtained from the proper authorities.
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Josiah Willard Gibbs was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics.
Background
Gibbs was born on February 11, 1839 in New Haven, Connecticut, the fourth of five children and the only son of Josiah Willard Gibbs and his wife Mary Anna, née Van Cleve. On his father's side, he was descended from Samuel Willard, who served as acting President of Harvard College from 1701 to 1707. On his mother's side, one of his ancestors was the Rev. Jonathan Dickinson, the first president of the College of New Jersey (later Princeton University).
Education
Gibbs was educated at the Hopkins School and entered Yale College in 1854 at the age of 15. At Yale, Gibbs received prizes for excellence in mathematics and Latin, and he graduated in 1858, near the top of his class. He remained at Yale as a graduate student at the Sheffield Scientific School. At age 19, soon after his graduation from college, Gibbs was inducted into the Connecticut Academy of Arts and Sciences, a scholarly institution composed primarily of members of the Yale faculty. In 1863, Gibbs received the first Doctorate of Philosophy (Ph.D.) in engineering granted in the US.
Gibbs was appointed tutor at Yale in 1863. He taught Latin in the first two years, and natural philosophy in the third. He then went to Europe, studying in Paris in 1866-1867, in Berlin in 1867 and in Heidelberg in 1868. Returning to New Haven in 1869, he was appointed professor of mathematical physics in Yale College in 1871, and held that position till his death.
His first contributions to mathematical physics were two papers published in 1873 in the Transactions of the Connecticut Academy on "Graphical Methods in the Thermodynamics of Fluids," and "Method of Geometrical Representation of the Thermodynamic Properties of Substances by means of Surfaces." His next and most important publication was his famous paper "On the Equilibrium of Heterogeneous Substances," which, it has been said, founded a new department of chemical science that is becoming comparable in importance to that created by Lavoisier.
Gibbs's lecture notes on vector calculus were privately printed in 1881 and 1884 for the use of his students, and were later adapted by Edwin Bidwell Wilson into a textbook, Vector Analysis, published in 1901. From 1882 to 1889, Gibbs wrote five papers on physical optics, in which he investigated birefringence and other optical phenomena and defended Maxwell's electromagnetic theory of light against the mechanical theories of Lord Kelvin and others.
Gibbs coined the term statistical mechanics and introduced key concepts in the corresponding mathematical description of physical systems, including the notions of chemical potential (1876), and statistical ensemble (1902). His derivation of the laws of thermodynamics from the statistical properties of systems consisting of many particles was presented in his highly influential textbook Elementary Principles in Statistical Mechanics, published in 1902, a year before his death. Gibbs died in New Haven on April 28, 1903, at the age of 64, the victim of an acute intestinal obstruction.
Gibbs joined Yale's College Church (a Congregational church) at the end of his freshman year and remained a regular attendant for the rest of his life.
Politics
Gibbs generally voted for the Republican candidate in presidential elections but, like other "Mugwumps", his concern over the growing corruption associated with machine politics led him to support Grover Cleveland, a conservative Democrat, in the election of 1884. Little else is known of his religious or political views, which he mostly kept to himself.
Views
Quotations:
"One of the principal objects of theoretical research in my department of knowledge is to find the point of view from which the subject appears in its greatest simplicity."
"A mathematician may say anything he pleases, but a physicist must be at least partially sane."
"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."
"Mathematics is a language."
"We avoid the gravest difficulties when, giving up the attempt to frame hypotheses concerning the constitution of matter, we pursue statistical inquiries as a branch of rational mechanics."
Membership
Honorary Member of the London Mathematical Society (1892), Foreign Members of the Royal Society (1897)
Personality
Gibbs was always neatly dressed, usually wore a felt hat on the street, and never exhibited any of the physical mannerisms or eccentricities sometimes thought to be inseparable from genius. His manner was cordial without being effusive and conveyed clearly the innate simplicity and sincerity of his nature.
The esoteric nature of his work made him practically unintelligible to students. Shy and retiring by nature, he made no effort to attract followers or to communicate to a wider audience.
Quotes from others about the person
In Edward Bidwell Wilson's view: "Gibbs was not an advertiser for personal renown nor a propagandist for science; he was a scholar, scion of an old scholarly family, living before the days when research had become research . .. Gibbs was not a freak, he had no striking ways, he was a kindly dignified gentleman."
In an obituary published in the American Journal of Science, Gibbs's former student Henry A. Bumstead referred to Gibbs's personal character: "Unassuming in manner, genial and kindly in his intercourse with his fellow-men, never showing impatience or irritation, devoid of personal ambition of the baser sort or of the slightest desire to exalt himself, he went far toward realizing the ideal of the unselfish, Christian gentleman. In the minds of those who knew him, the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life."
In 1954, a year before his death, Albert Einstein was asked by an interviewer who were the greatest thinkers that he had known. Einstein replied: "Lorentz", adding "I never met Willard Gibbs; perhaps, had I done so, I might have placed him beside Lorentz."
Connections
Gibbs never married, living all his life in his childhood home with his sister Julia and her husband Addison Van Name, who was the Yale librarian.
The Royal Society honored Gibbs in 1901 with the Copley Medal, then regarded as the highest international award in the natural sciences, noting that he had been "the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical and thermal energy and capacity for external work."
The Royal Society honored Gibbs in 1901 with the Copley Medal, then regarded as the highest international award in the natural sciences, noting that he had been "the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical and thermal energy and capacity for external work."