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Second Essay on a general Method in Dynamics. Received October 29, 1834, - Read January 15, 1835. (2 Memoirs).
London, Richard Taylor, 1834-35. 4to. No wrappers as extracted from ""Philosophical Transactions"", 1835 - Part I. Titlepages to the volume present. (2),95-144. Both papers clean and fine.
First appearance of this groundbreaking paper in which Hamilton develops the whole of theoretical dynamics by the aid of one function only, his 'Characteristic' or 'Principal' Function. He applies his method to a case of planetary motion, using a system of canonical elements"" (Introduction, The Mathematical Paper of Sir William Rowan Hamilton, xiii). Hamilton then argues that the ""tool of the characteristic function could also be applied to reformulate the fundamental laws of dynamics"" thus the actual motion of mass point in a field of forces, e.g., is found to be governed by equations that are the analogues of those determining the propagation of the rays of light. Hamilton's optical-mechanical analogy, not only provided a new and more powerful formulation of classical mechanics but also, came to form the foundation of the Schrödinger scheme of quantum mechanics, e.g., wave mechanics. "" (Mehra The Historical Development of Quantum Theory)
HAMILTON, WILLIAM ROWAN. - THE GENERAL PRINCIPLE OF LEAST ACTION - HAMILTON' S PRINCIPLE.
Reference : 42329
(1834)
On a general Method in Dynamics" by which the Study of the Motions of all free Systems of attracting or repelling Points is reduced to the Search and Differentiation of one central Relation, or characteristic Function. Received April 1, - Read April 1...
London, Richard Taylor, 1834-35. 4to. No wrappers as extracted from ""Philosophical Transactions"" 1834 - Part II. and 1835 - Part I. Both titlepages to the volumes present.Pp. (2),247-308 a. (2),95-144. Both papers clean and fine.
First appearance of these two groundbreaking papers in which Hamilton carries further the dynamics of Lagrange by expressing the kinetic energy in terms of the momenta and the co-ordinates of a system, and discovers how to transform the Lagrangian equations into a set of differential equations of the first order for the determination of of the motion. The Hamilton principle is also called The Principle of ""Least Action"". The Hamilton Principle as stated in the papers offered here ""was the first of his two great ""discoveries"". he second was the quaternions, which he discovered...1843 nd towhich he devoted most of his efforts during the remaining 22 years of his life.""(DSB).Maupertouis, Euler, and Lagrange introduced the principle of ""Least Action"" covering the science of dynamics, and now Hamilton brought the principle into a form which was capable of expressing all the laws of Newtonian science in a representation as minimum-problems, that is, all gravitational, dynamical and electrical laws could be represented as minimum problems. In 1925 Heisenberg, Born and Jordan showed, that the Hamilton equations are still valid in quantum theoryAlthough formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and has even been extended to quantum mechanics, quantum field theory, relativity and criticality theories. Its influence is so profound and far reaching that many scientists regard it as the most powerful single principle in mathematocal physics and place it at the pinnacle of physical science.
On Quaternions" or on a new System of Imaginaries in Algebra. - [MAKING THE GENERAL THEORY OF RELATIVITY POSSIBLE]
London, Richard and John Taylor, 1844. Contemp. hcalf. Gilt lettering to spine ""Philosophical Magazine"" - Vol. XXV. In: ""The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. Conducted by David Brewster et al."". Vol. XXV. A stamp to titlepage and a few other pages. Entire volume offered (July-December 1844). VIII,552 pp., textillustr. Hamilton's paper: pp. 10-13, 141-145 and 241-246.
![On Quaternions" or on a new System of Imaginaries in Algebra. - [MAKING THE GENERAL THEORY OF RELATIVITY POSSIBLE]. HAMILTON, WILLIAM ROWAN.](https://static.livre-rare-book.com/pictures/LLX/46875_1_thumb.jpg)
![On Quaternions" or on a new System of Imaginaries in Algebra. - [MAKING THE GENERAL THEORY OF RELATIVITY POSSIBLE]. HAMILTON, WILLIAM ROWAN.](https://static.livre-rare-book.com/pictures/LLX/46875_2_thumb.jpg)
![On Quaternions" or on a new System of Imaginaries in Algebra. - [MAKING THE GENERAL THEORY OF RELATIVITY POSSIBLE]. HAMILTON, WILLIAM ROWAN.](https://static.livre-rare-book.com/pictures/LLX/46875_3_thumb.jpg)
First printing of this landmark paper in which Hamilton published his creation of a new algebra of quaternions (a noncommunicative algebra), a turning point in the development of mathematics and a discovery which made possible the creation of the general theory of relativity. His algebra was later to form the basis of quantum mechanics and for the proper understanding of the atom.""Gauss had treated imaginary numbers in combination with real ones as representing points on a plane and showed the methods by which such complex numbers could be manipulated. Hamilton tried to extend this to threee dimensions and found himself unable to work out a self-consistent method of multiplication, until it occurred to him that the cummutative law of multiplication need not necessarily hold. It is taken for granted that A times B is equal to B times A... and this is an example of what seems to be an eternal and inescapable truth. Hamilton, however, showed that he could built up a logical algebra for his quaternions only when B times A was not made to equal - A times B. This seems against common sense but, like Lobachevski, Hamilton showed that the truth is relative and depends on the axioms you choose to accept.""(Asimov).The creation of quaternions is one of the famous moments in the history of mathematics. ""The quaternions came to Hamilton in one of those flashes of understanding that occasionally occur after long deliberation on a problem. He was walking into Dublin on 16 October 1843 along the Royal Canal to preside at a meeting of the Royal Irish Academy, when the discovery came to him. As he described it, ""An electric circuit seemed to close.""18 He immediately scratched the formula for quaternion multiplication on the stone of a bridge over the canal. His reaction must have been in part a desire to commemorate a discovery of capital importance, but it was also a reflection of his working habits. Hamilton was an inveterate scribbler. His manuscripts are full of jottings made on walks and in carriages. He carried books, pencils, and paper everywhere he went. According to his son he would scribble on his fingernails and even on his hard-boiled egg at breakfast if there was no paper handy.""(DSB).Hamilton later developed his invention in his book from 1853 ""Lectures on Quaternions"" - see PMM: 334 and Grattan-Guiness ""Landmark Writings in Western Mathematics 1640-1940"", pp. 460 ff.In this volume other importent papers by Gassiot, Sylvester, Joule, Draper.
