Mathematicians From France

"On January 16, 1793, the in Paris sentenced to death. Among those who took the fatal decision was... Lazare Carnot... [who] had a passion for the great Persian poet Saadi Shirazi... Carnot names his first son after Saadi. Sadi Carnot is thus born out of poetry and rebellion. As a young man, he develops a passion for those steam engines... beginning to transform the world... In 1824, he writes... "," in which he seeks to understand the theoretical basis of... these machines. The little treatise is packed with mistaken assumptions: he imagines that heat is a concrete entity... fluid that produces energy by "falling" from hot things to cold, just as... a waterfall... But it contains a key idea: that steam engines function... because the heat passes from hot to cold."

"Is heat the result of a vibratory motion of molecules? If... so, quantity of heat is simply quantity of motive power. As long as motive power is employed to produce vibratory movements, the quantity of heat must be unchangeable... but when it passes into movements of sensible extent, the quantity of heat can no longer remain constant."

"Could a motion (that of radiating heat) produce matter (caloric)? No, undoubtedly; it can only produce a motion. Heat is then the result of a motion. Then it is plain that it could be produced by the consumption of motive power, and that it could produce this power."

"Liquuefaction of bodies, solidification of liquids, crystallization—are they not forms of combinations of integrant molecules?"

"Nature, in providing us with combustibles on all sides, has given us the power to produce, at all times and in all places, heat and the impelling power which is the result of it. To develop this power, to appropriate it to our uses, is the object of heat-engines."

"We shall have [a complete theory] only when the laws of Physics shall be extended enough, generalized enough, to make known beforehand all the effects of heat acting in a determined manner on any body."

"Carnot considered that the steam engine was analogous to another prime mover, the water wheel. The analogy, and the upon which it was based, led Carnot to the incorrect conclusion that no heat was lost, or converted into mechanical energy during the operation of the steam engine. He thought that the same quantity of heat was given out by the boiler at the higher temperature as was received by the condenser at the lower temperature. However, the analogy led him also to the fruitful conception that the amount of energy produced... was solely dependent, in principle, upon the temperature difference between the boiler and the condenser and the amount of heat which passed from the one to the other. Thus it appeared that all heat engines in general, would have the same efficiency if they worked within the same temperature levels. He substantiated this... Carnot's principle, by pointing out that would be possible if it were not true. If two perfect heat engines operating between the same temperature levels did not have the same efficiency, it would be possible for the more efficient... to drive the less efficient engine backwards, pumping heat from the lower to the higher temperature, thus leaving the thermal conditions unchanged and yet generating a continuous excess of energy."

"Later, in 1830, Carnot appreciated that his comparison of... the waterwheel was not exact, and that some heat was converted into mechanical energy... Thereupon he abandoned the and adopted the view that heat was... motions of the particles of bodies, heat and mechanical energy being interconvertible... Carnot died... 1832, and his later views... were not published until 1878."

"Iron and heat are... the supporters, the bases, of the mechanic arts."

"To take away to-day from England her steam-engines would be to take away at the same time her coal and iron. It would be to dry up all her sources of wealth, to ruin all on which her prosperity depends, in short, to annihilate that colossal power."

"There is almost as great a distance between the first apparatus in which the expansive force of steam was displayed and the existing machine, as between the first raft that man ever made and the modern vessel."

"Savery, Newcomen, Smeaton, the famous Watt, Woolf, Trevithick, and some other English engineers, are the veritable creators of the steam-engine."

"[[Light|[L]ight]] is generally regarded as the result of a vibratory movement of the ethereal fluid. Light produces heat, or at least accompanies the radiating heat, and moves with the same velocity as heat. Radiating heat is then a vibratory movement. It would be ridiculous to suppose that it is an emission of matter while the light which accompanies it could be only a movement."

"When a hypothesis no longer suffices to explain phenomena, it should be abandoned. This is the case with... caloric as matter, as a subtile fluid. The experimental facts tending to destroy this theory are as follows: (1) The development of heat by percussion or the friction of bodies (experiments of Rumford, friction of wheels on... axles...). Here the elevation of temperature takes place at the same time in the body rubbing and the body rubbed. ...Thus heat is produced by motion. If... [caloric] is matter... matter is created by motion. (2) ...[A]ir compressed by the pumps must rise in temperature above the air outside, and it is expelled at a higher temperature. ...Thus heat has been created by motion."

"[T]here cannot be loss of living force, or, which is the same thing, of motive power, if the bodies act upon each other without directly touching each other, without actual collision. ...[T]he molecules of bodies are always separated from each other by some space ...they are never actually in contact. If they touched each other, they would remain united, and consequently change form. If the molecules of bodies are never in close contact with each other, whatever... forces... separate or attract them, there can never be either production or loss of motive power... This power must be as unchangeable in quantity as matter."

"[[Energy|[M]otive power]] is, in quantity, invariable in nature; that it is, correctly speaking, never either produced or destroyed. It is true that it changes form, that is, it produces sometimes one sort of motion, sometimes another, but it is never annihilated."

"The Collision of Bodies. ...[I]n the collision of bodies there is always expenditure of motive power. Perfectly elastic bodies only form an exception, and none such are found in nature."

"[C]hanges caused in the temperature of bodies by motion have been very little studied. This class of phenomena merits... attention... When bodies are in motion, especially when that motion disappears, or when it produces motive power, remarkable changes take place in the distribution of heat, and perhaps in its quantity."

"[A]lways in the collision of bodies there occurs... an elevation of temperature. We cannot, as did M. Berthollet, attribute the heat set free in this case to the reduction of the volume of the body..."

"What motives have influenced the writers who have rejected all religious systems? Is it the conviction that the ideas which they oppose are all injurious to society? Have they not rather included in the same proscription religion and the abuse of it?"

"The belief in an all-powerful Being, who loves us and watches over us, gives to the mind great strength to endure misfortune."

"It would seem... that heat set free should be attributed to the friction of the molecules of the metal, which change place relatively to each other, that is, the heat is set free just where the moving force is expended. ...We may also cite... the heat produced by the extension of a metallic rod just before it breaks... the greater the elongation before rupture, the more considerable is the elevation of temperature."

"Heat is simply motive power, or rather motion which has changed form. It is a movement among the particles of bodies. Wherever there is destruction of motive power there is, at the same time, production of heat in quantity exactly proportional to the quantity of motive power destroyed. Reciprocally, wherever there is destruction of heat, there is production of motive power."

"Carnot's work, Sur la Puissance Motrice du Feu, is the first in which any attempt is made to explain the production of work from heat. It is unfortunately marred by his assumption, that heat is a material substance, though it is only fair to say that he expresses grave doubts as to the truth of this hypothesis. ...He begins his investigation by premising the following correct principle, sadly neglected by many subsequent writers: 'If a body, after having experienced a certain number of transformations, be brought identically to its primitive state as to density, temperature, and molecular constitution, it must contain the same quantity of heat as that which it initially possessed.' Hence he concludes, that when heat produces work, it is in consequence of its being let down from a hot body to a cold one, as from the boiler to the condenser of a steam-engine. His investigation... forms the foundation of the modern theory."

"Science and technology are inseparable, in two senses. First, because and understanding of the laws of the universe is always implicit in technology. (Francis Bacon said, "Nature to be commanded must be obeyed.") Second, because, beyond a certain level in technology, the understanding tends to become explicit. Arguably the most profound scientific truth is the second law of thermodynamics, which notes the inexorability of universal chaos and thus... defines the current against which organic evolution and cultural evolution both swim. The earliest statement of the second law came in the nineteenth century from the Frenchman Sadi Carnot, who described himself as a "constructor of steam engines," the vocation that indeed had led him to see the gist of the second law."

"Taxes are a means of influencing production and commerce to give to them a direction which they would not naturally have taken. Such an influence may undoubtedly have disagreeable consequences if the taxes are imposed without discrimination or exclusively for a fiscal purpose, but it is entirely otherwise if wisdom and tact preside at their institution."

"The decadence of the Greeks and Romans... proves the influence of institutions upon customs."

"Men attribute to chance those events of the causes of which they are ignorant. If they succeed in divining these causes, chance disappears. To say that a thing has happened by chance, is to say that we have not been able to foresee it. I do not myself believe that any other acceptation can be given to this word. What to an ignorant man is chance, cannot be chance to one better instructed."

"If one could continually satisfy his desires, he would never have time to desire. Happiness then is necessarily composed of alternatives. It could not exist at a constant level."

"We say that man is an egotist, and nevertheless his sweetest pleasures come to him through others. He only tastes them on condition of sharing them."

"To each conqueror can be said, when he has ceased tormenting our poor globe, "Would you not have been able to tilt equally well against a little globe of pasteboard?""

"If human reason is incapable of discovering the mysteries of Divinity, why has not Divinity made human reason more clear-sighted?"

"Men desire nothing so much as to make themselves envied."

"Why try to be witty? I would rather be thought stupid and modest than witty and pretentious."

"Egotism is the most common and most hated of all vices. Properly speaking, it is the only one which should be hated."

"When discussion degenerates into dispute, be silent; this is not to declare yourself beaten."

"I rejoice for all the misfortunes which might have happened to me, and which I have escaped."

"Life is a short enough passage. I am half the journey. I will complete the remainder as I can."

"It must be that all honest people are in the galleys; only knaves are to be met with elsewhere."

"The strain of suffering causes the mind to decay."

"The laws of war, do they say? As if war were not the destruction of all laws."

"War has been represented as necessary to prevent the too rapid increase of the population, but war mows down the flower of the young men, while it spares the men disgraced by nature. Hence it tends to the degeneration of the species."

"According to the system of modern economists, it would be desirable that the government should interfere as little as possible in the commerce and industry of the country. Nevertheless we cannot deny that in certain circumstances this intervention is very useful."

"Taxes are regarded by economists as an evil, but as a necessary evil, since they provide for public expenses. Consequently, economists think that if the government possessed sufficient revenues, in domains for example, the suppression of all taxes would be a desirable measure."

"According to the doctrine of the church, God resembles a proposing enigmas, and devouring those who cannot guess them."

"The production of motion in steam-engines is always accompanied by... the re-establishing of equilibrium in the caloric; that is, its passage from a body in which the temperature is more or less elevated, to another in which it is lower."

"The church attributes to God all human passions—anger, desire for vengeance, curiosity, tyranny, partiality, idleness."

"If Christianity were pruned of all which is not Christ, this religion would be the simplest in the world."

"A religion suited to the soul and preached by men worthy of respect would exercise the most salutary influence upon society and customs."

"Employ only expressions of the most perfect propriety."