history-of-physics

"Newton’s glory was to fulfil, in his Principia of 1687, Galileo's hope of geometrizing gravitation. The ingredients of his solution were Descartes' first law of motion (the principle of inertia), Galileo's rules of and composition of velocities, and Kepler's rules of planetary orbiting. Newton showed that Kepler's rules following form Galileo's, the principle of inertia, and the assumption that a planet falls towards the Sun along the line joining their centres. Since Kepler's rules allowed the substitution of an area for a time, Newton could reduce the problem of the magnitude of gravitational acceleration to a problem in geometry."

"Only around the end of the nineteenth century did scientists come across a few observations that did not fit well with Newton's laws, and these led to the net revolution in physics - the theory of relativity and quantum mechanics."

"Lex I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressi cogitur statum illum mutare. Lex II. Mutationem motus proportionalem esse vi motrici impressa; & fieri secundum lineam rectam qua vis illa imprimatur. Lex III. Actioni contrariam semper & aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales & in partes contrarias dirigi. (English translation: Law I. Every body perseveres in its state of rest or of uniform motion in a straight line, except in so far as it is compelled to change that state by the forces impressed upon it. Law II. The change of motion is proportional to the motive force impressed upon it; and takes place along the straight line on which that force is impressed. Law III. To an action there is always an opposite and equal reaction: or the actions of two bodies on each other are always equal and directed in opposite directions.)"

"The proper or interior conducibility of a body expresses the facility with which heat is propagated in passing from one internal molecule to another."

"The problem consists in expressing, by one equation, the variable form of this curve, and in thus including in a single formula all the successive [temperature] states of the solid."

"[I]f two bodies of the same volume and of different nature have equal temperatures, and if the same quantity of heat be added to them, the increments of temperature are not the same; the ratio of these increments is the, ratio of their capacities for heat."

"The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory... is to demonstrate these laws; it reduces... researches on the propagation of heat, to problems of the integral calculus whose elements are given by experiment."

"I have deduced these laws... in the course of several years with the most exact instruments..."

"[T]he same expression whose abstract properties geometers had considered, and which... belongs to general analysis, represents... the motion of light in the atmosphere... determines the laws of diffusion of heat in solid matter, and enters into... the theory of probability."

"The new theories explained in our work are united for ever to the mathematical sciences, and rest like them on invariable foundations; all the elements... they... possess they will preserve, and... acquire greater extent. Instruments will be perfected and experiments multiplied. The analysis which we have formed will be deduced from more general, ...[i.e,] more simple and more fertile methods... For all substances... determinations will be made of all... qualities relating to heat, and of the variations of the coefficients which express them. At different stations on the earth observations will be made, of the temperatures of the ground at... depths, of the intensity of the solar heat and its effects... in the atmosphere, in the ocean and in lakes; and the constant temperature of the heavens proper to the planetary regions will become known. The theory... will direct... these measures, and assign their precision. No considerable progress can... be made... not founded on experiments... for mathematical analysis can deduce from general and simple phenomena the expression of the laws of nature; but... application of these laws... demands... exact observations."

"If now the source be suppressed, heat will continue to be propagated in the [ring's] interior... but that... lost in the... void, will no longer be compensated... by the... source, so that all... temperatures will... diminish... until... equal to the temperatures of the surrounding medium."

"When the [heat] source is removed, the line which bounds the ordinates... at the different points will change its form continually."

"If we place a solid homogeneous... sphere or cube, in a medium... [of] constant temperature... for a... long time, it will acquire at all its points... [the] temperature... of the fluid. Suppose the mass to be withdrawn... to transfer... to a cooler medium, heat will begin to be dissipated at its surface; the temperatures at different points of the mass will not be... the same, and if we suppose it divided into an infinity of layers by surfaces parallel to its external surface, each of those layers will transmit, at each instant, a certain quantity of heat to the layer which surrounds it. If... each molecule carries a separate thermometer... the state of the solid will from time to time be represented by the variable system of... these thermometric heights. It is required to express the successive states by analytical formulae, so that we may know at any... instant the temperatures... and compare the quantities of heat which flow during the same instant, between two adjacent layers, or into the surrounding medium."

"[T]he effects of the propagation of heat depend in... every solid substance, on three elementary qualities... its capacity for heat, its own conducibility, and the exterior conducibility."

"The external or relative conducibility of a solid body depends on the facility with which heat penetrates the surface, and passes from this body into a given medium, or... from the medium into the solid. The last property is modified by the... polished state of the surface... also according to the medium in which... immersed; but the interior conducibility can change only with the nature of the solid."

"To found the theory, it was... necessary to distinguish and define... the elementary properties which determine the action of heat... a very small number of general and simple facts; whereby every... problem... is brought back to... mathematical analysis."

"The successors of these philosophers have extended these theories, and given them an admirable perfection: they have taught us that the most diverse phenomena are subject to a small number of fundamental laws..."

"We have... instruments adapted to measure many of these effects... but... not the mathematical demonstration of the laws..."

"Radiant heat which escapes from the surface of all bodies, and traverses elastic media, or spaces void of air, has special laws... The mathematical theory... I... formed gives an exact measure of them. It consists... in a new which... serves to determine... effects... direct or reflected."

"The same theorems which have made known... the equations of... [heat] movement.., apply... to... problems of general analysis and dynamics whose solution has... long... been desired."

"If matter escapes us, as that of air and light, by its extreme tenuity, if bodies are placed far... in the immensity of space, if man wishes to know the... heavens at successive epochs... if the actions of gravity and of heat are exerted in the interior of the earth at depths... inaccessible, mathematical analysis can yet lay hold of the laws of these phenomena. It makes them present and measurable, and seems... a faculty of the... mind destined to supplement the shortness of life and... imperfection of... senses... more remarkable, it follows the same course in the study of all phenomena; it interprets... by the same language, as if to attest the unity and simplicity of the... the universe, and to make... evident that... order which presides over all natural causes."

"The subjects of these memoirs will be, the theory of radiant heat, the problem of the terrestrial temperatures, that of the temperature of dwellings, the comparison of theoretic results with... experiments, lastly the demonstrations of the differential equations of the movement of heat in fluids."

"The problem of the propagation of heat consists in determining what is the temperature at each point of a body at a given instant, supposing that the initial temperatures are known."

"When the temperatures have become permanent, the source... supplies, at each instant, a quantity of heat which... compensates for that... dissipated at all the points of the external surface of the ring."

"Whilst the temperatures are permanent and the source remains [continued and uniform], if at every point of the mean circumference of the ring an ordinate be raised perpendicular to the plane of the ring, whose length is... the fixed temperature at that point, the curved line which passes through the ends of these ordinates will represent the... state of the temperatures..."

"[T]he thickness of the ring is supposed... sufficiently small for the temperature to be... equal at all points of the same section perpendicular to the mean circumference."

"Let z be the constant temperature at point m [on] the mean circumference [of the ring], x the distance of this point from the [heat] source [point o], that is to say the length of the arc of the mean circumference, included between the point m and the point o... z is the highest temperature which the point m can attain by virtue of the constant action of the source, and this permanent temperature z is function f(x) of the distance x. The first part of the problem consists in determining the function f(x) which represents the permanent [temperature] state of the solid."

"Consider next the variable state... as soon as the [heat] source has been removed; denote by t the time... passed since the... source [removal], and by v the... temperature at... m after the time t. v will be a... function F(x, t) of the distance x and the time t; the object... is to discover this function F(x, t), of which we only know as yet that the initial value... f(x) = F(x, o)."

"If the mass is spherical, and we denote by x the distance... from the centre... t the time... cooling, and by v the variable temperature of the point m... all points... at the same distance x... have the same temperature v. This quantity v is a certain function F(x, t) of the radius x and... time t... such that it becomes constant whatever... value of x, when... [t=0]; for... the temperature at all points is the same at... emersion. The problem consists in determining... [F(x, t)]."

"[D]uring... cooling... heat escapes, at each instant, through the external surface, and passes into the medium... [and] this quantity is not constant; it is greatest at the beginning of... cooling. If... we consider the variable state of the internal spherical surface... [at] radius... x... there must be at each instant a... quantity of heat which traverses that surface, and passes through that part... more distant from the centre. This continuous flow of heat is variable like that through the external surface, and both are quantities comparable with each other; their ratios are numbers whose varying values are functions of the distance x, and of the time t... elapsed. It is required to determine these functions."

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy."

"[T]he action of heat is always present, it penetrates all bodies and spaces, it influences the processes of the arts, and occurs in all the phenomena of the universe."

"The notes marked R.L.E. are... from... memoranda on the margin of a copy of... Robert Leslie Ellis."

"In preparing this version in English of Fourier's celebrated treatise on Heat, the translator has followed faithfully the French original. He has, however, appended brief foot-notes, in which will be found references to other writings of Fourier and modern authors on the subject, distinguished by the initials [Alexander Freeman] A. F."

"Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics."

"Archimedes... explained the mathematical principles of the equilibrium of solids and fluids. ... Galileo, the originator of dynamical theories, discovered the laws of motion of heavy bodies. Within this new science Newton comprised the whole system of the universe."

"[T]he same principles regulate all the movements of the stars, their form, the inequalities of their courses, the equilibrium and the oscillations of the seas, the harmonic vibrations of air and sonorous bodies, the transmission of light, capillary actions, the undulations of fluids, in fine the most complex effects of all the natural forces, and thus has the thought of Newton been confirmed: quod tam paucis tam multa praestet geometria gloriatur [from so little to so much stands the glory of Geometry.]"

"[M]echanical theories... do not apply to the effects of heat... a special order of phenomena, which cannot be explained by the principles of motion and equilibrium."

"[T]o determine... movements of heat, it is sufficient to submit each substance to three fundamental observations. ...[B]odies ...do not possess in the same degree the power to contain heat, to receive or transmit it across their surfaces, nor to conduct it through the interior of their masses. These are the three... qualities... our theory... distinguishes and shews how to measure."

"No diurnal variation can be detected at the depth, of about three metres [ten feet]; and the annual variations cease to be appreciable at a depth much less than sixty metres."

"The principles of the theory are derived, as are those of rational mechanics, from a very small number of primary facts..."

"The differential equations of... heat [propagation] express the most general conditions, and reduce... physical questions to... pure analysis... not less rigorously established than... equations of equilibrium and motion. ...[W]e have always preferred demonstrations analogous to... the theorems... of statics and dynamics. These equations... receive a different form, when they express the distribution of luminous heat in transparent bodies, or the movements in the interior of fluids occasioned by changes of temperature and density. ...[I]n... natural problems which... most concerns us... the limits of temperature differ so little that we may omit... variations of... coefficients."

"The analytical equations... which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to... figures, and... rational mechanics; they extend to all general phenomena. There cannot be a language more universal and more simple, more free from errors and... obscurities, [i.e.,] more worthy to express the invariable relations of natural things."

"[[Mathematical analysis|[M]athematical analysis]] is as extensive as nature... it defines all perceptible relations, measures times, spaces, forces, temperatures; this... science is formed slowly, but it preserves every principle... acquired; it grows and strengthens... incessantly in the midst of... variations and errors of... mind. Its chief attribute is clearness; it has no marks to express confused notions. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them."

"The problems of the theory of heat present... simple and constant dispositions which spring from the general laws of nature; and if the order... in these phenomena could be grasped... it would produce... impression comparable to... musical sound."

"In this work we have demonstrated all the principles of the theory of heat, and solved all the fundamental problems... [W]e wished to shew the actual origin of the theory and its gradual progress."

"When heat is unequally distributed among the different parts of a solid mass, it tends to attain equilibrium, and passes slowly from the parts which are more heated to those which are less; and... it is dissipated at the surface, and lost in the medium or in the void."

"The tendency [of heat] to uniform distribution and the spontaneous emission which acts at the surface of bodies, change continually the temperature at their different points."

"If we expose to... continued... uniform... source of , the same part of a metallic ring, whose diameter is large, the molecules nearest... the source will be first heated, and, after a... time, every point of the solid will have... nearly the highest temperature... it can attain... not the same at different points... [and] less and less... [the] more distant from that [source] point..."

"These three elementary qualities are represented... by constant[s], and the theory... indicates experiments suitable for measuring their values. As soon as... determined... problems relating to the propagation of heat depend only on numerical analysis."