Mathematical Papers

George Green, N. M. Ferrers

• Publisher: Dover Publications
• Year: 2013
• Print ISBN: 9780486442679
• eBook ISBN: 9780486155142
• Topic: Mathematics
• Subtopic: History & Philosophy of Mathematics
• Index: Mathematics

An almost entirely self-taught mathematical genius, George Green (1793 –1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works.
The first paper, "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism," which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as designating the result obtained by adding together the masses of all the particles of a system, each divided by its distance from a given point. Its three-part treatment first considers the properties of this function and then applies them, in the second and third parts, to the theories of magnetism and electricity.
The following paper, "Mathematical Investigations concerning the Laws of the Equilibrium of Fluids analogous to the Electric Fluid," exhibits great analytical power, as does the next, "On the Determination of the Exterior and Interior Attractions of Ellipsoids of Variable Densities." Other highlights include the brief but absorbing paper, "On the Motion of Waves in a variable canal of small depth and width," and two of his most valuable memoirs, "On the Laws of Reflexlon and Refraction of Sound" and "On the Reflexlon and Refraction of Light at the common surface of two non-crystallized Media," which should be studied together.

AN ESSAY ON THE APPLICATION OF MATHEMATICAL ANALYSIS TO THE THEORIES OF ELECTRICITY AND MAGNETISM.

* Published at Nottingham, in 1828.

PREFACE.

AFTER I had composed the following Essay, I naturally felt anxious to become acquainted with what had been effected by former writers on the same subject, and, had it been practicable, I should have been glad to have given, in this place, an historical sketch of its progress; my limited sources of information, however, will by no means permit me to do so; but probably I may here be allowed to make one or two observations on the few works which have fallen in my way, more particularly as an opportunity will thus offer itself, of noticing an excellent paper, presented to the Royal Society by one of the most illustrious members of that learned body, which appears to have attracted little attention, but which, on examination, will be found not unworthy the man who was able to lay the foundations of pneumatic chymistry, and to discover that water, far from being according to the opinions then received, an elementary substance, was a compound of two of the most important gases in nature.

It is almost needless to say the author just alluded to is the celebrated CAVENDISH, who, having confined himself to such simple methods, as may readily be understood by any one possessed of an elementary knowledge of geometry and fluxions, has rendered his paper accessible to a great number of readers; and although, from subsequent remarks, he appears dissatisfied with an hypothesis which enabled him to draw some important conclusions, it will readily be perceived, on an attentive perusal of his paper, that a trifling alteration will suffice to render the whole perfectly legitimate².

Little appears to have been effected in the mathematical theory of electricity, except immediate deductions from known formulae, that first presented themselves in researches on the figure of the earth, of which the principal are, – the determination of the law of the electric density on the surfaces of conducting bodies differing little from a sphere, and on those of ellipsoids, from 1771, the date of CAVENDISH’S paper, until about 1812, when M. POISSON presented to the French Institute two memoirs of singular elegance, relative to the distribution of electricity on the surfaces of conducting spheres, previously electrified and put in presence of each other. It would be quite impossible to give any idea. of them here: to be duly appretiated they must be read. It will therefore only be remarked, that they are in fact founded upon the consideration of what have, in this Essay, been termed potential functions, and by means of an equation in variable differences, which may immediately be obtained from the one given in our tenth article, serving to express the relation between the two potential functions arising from any spherical surface, the author deduces the values of these functions belonging to each of the two spheres under consideration, and thence the general expression of the electric density on the surface of either, together with their actions on any exterior point.

I am not aware of any material accessions to the theory of electricity, strictly so called, except those before noticed; but since the electric and magnetic fluids are subject to one common law of action, and their theory, considered in a mathematical point of view, consists merely in developing the consequences which flow from this law, modified only by considerations arising from the peculiar constitution of natural bodies with respect to these two kinds of fluid, it is evident the mathematical theory of the latt...

Table of contents

• Title Page
• Copyright Page
• PREFACE.
• Table of Contents
• AN ESSAY ON THE APPLICATION OF MATHEMATICAL ANALYSIS TO THE THEORIES OF ELECTRICITY AND MAGNETISM.
• MATHEMATICAL INVESTIGATIONS CONCERNING THE LAWS OF THE EQUILIBRIUM OF FLUIDS ANALOGOUS TO THE ELECTRIC FLUID, WITH OTHER SIMILAR RESEARCHES.
• ON THE DETERMINATION OF THE EXTERIOR AND INTERIOR ATTRACTIONS OF ELLIPSOIDS OF VARIABLE DENSITIES.
• ON THE MOTION OF WAVES IN A VARIABLE CANAL OF SMALL DEPTH AND WIDTH.
• ON THE REFLEXION AND REFRACTION OF SOUND.
• ON THE LAWS OF REFLEXION AND REFRACTION OF LIGHT AT THE COMMON SURFACE OF TWO NON-CRYSTALLIZED MEDIA.
• NOTE ON THE MOTION OF WAVES IN CANALS.
• SUPPLEMENT TO A MEMOIR ON THE REFLEXION AND REFRACTION OF LIGHT.
• ON THE PROPAGATION OF LIGHT IN CRYSTALLIZED MEDIA.
• RESEARCHES ON THE VIBRATION OF PENDULUMS IN FLUID MEDIA.
• APPENDIX.
• DOVER PHOENIX EDITIONS
• DOVER PHOENIX EDITIONS