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Lazare and Sadi Carnot

Charles Coulston Gillispie and Raffaele Pisano
Publication Date: 
Number of Pages: 
History of Mechanism and Machine Science 19
[Reviewed by
Charles Ashbacher
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Lazare the father is far better known as a politician and soldier than as a scientist. His work in creating, organizing and equipping the massive army raised in France after the revolution demonstrates without question that he was an organizational genius. Napoleon is known as a military genius, but without the skills of Lazare Carnot, his victories would have been few and the history of what is known as the Napoleonic era would have been quite different. Trained as an engineer, Lazare Carnot made some original contributions to the development of the machines and the scientific principles that govern their behavior.

However, Lazare’s greatest contribution to machine science is his siring and nurturing of his son Sadi, the man considered the “father of thermodynamics.” This book only briefly covers the personal side of their history; the emphasis is on the mathematical and physical background of their work as well as some of the enormous number of applications.

Thermodynamics is the study of the ways where energy is converted from one form into another and explanations of the limits to the efficiency of the processes. Since this covers all mechanical and biological machines, a basic knowledge of thermodynamics is essential for the functioning of all scientists. Since this book takes you back to the creation of the area of thermodynamics, scientists in every field can learn from this book.

The authors do an excellent job of presenting the historical sequence of the work of the two Carnots. The mathematical and physical background of their results is put down before it is explained. For example, chapter 7 has the title “On Principles in Sadi Carnot’s Thermodynamics.” The text is well written, it would be possible for people that are not thoroughly schooled in mathematical principles such as integration to learn the principles of thermodynamics from reading this history.

The professor that I had for my courses in physical chemistry used to include exercises and other snippets into the instruction so that we would develop some appreciation for the “sweat, physical and mental effort and sometimes even blood” that researchers expended in developing the science of chemistry. From this book you will obtain an appreciation of the efforts of the Carnots’ in putting down the intellectual foundations for the rise of the machines that made the industrial revolution possible. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

Biographical Sketch of Lazare Carnot

The Science Of Machines:
Summary of Essai sur les machines en général
Geometric motions
Moment-of-Activity – The concept of work
Practical conclusions

The Development Of Carnot's Mechanics
Argument of the 1778 Memoir on theory of machines
Argument of the 1780 Memoir
Argument of the Principes fondamentaux de l'équilibre et du mouvement (1803)
Comparing the work of Sadi Carnot

The Carnot Approach And The Mechanics Of Work And Power, 1803–1829
Early engineering mechanics
Applied mechanics
The concept of work

An Engineering Justification Of Algebra And The Calculus
Geometric analysis and the problem of negative quantity
The compensation of error in infinitesimal analysis
Analysis and synthesis

History And Historiography Sadi Carnot’s Thermodynamics
A historical excursus
            On the science of Sadi Carnot’s time: the mechanics
            On the science of Sadi Carnot’s time: the theory of heat
            Toward physical mathematical theories
A Historiographycal excursus
            On Sadi Carnot’s historiography
On the methodology used to investigate Sadi Carnot’s science
            On specificity and scientificity in historical discourse
            On interpretation in historical discourse
            On categories in history of science
Biographical sketch of Sadi Carnot
            Notes on the philological aspects of Réflexions sur la puissance motrice du feu
            On Sadi Carnot’s studies at École Polytechnique
An index ad hoc of Réflexions sur la puissance motrice du feu

On Principles In Sadi Carnot’s Thermodynamics
An outline of the problem of history and logics
            On the mathematics
            On the physics
            On the physics mathematics
            On logics and structure
Sadi Carnot’s theory and its logical organization
            On DNSs and logical investigation
            The distribution of DNSs in Sadi Carnot’s book
            The possible theoretical roles played by a DNS
            Sadi Carnot’s arguments through his DNSs
Reconstruction of arguments and some cycles of reasoning expressed by DNSs
Sadi Carnot’s thermodynamics as PO theory. Its non–classical logic and its central problem
On Sadi Carnot’s theory: a case–study
Which and how many principles did Sadi Carnot express in his Réflexions sur la Puissance Motrice du Feu?
DNSs and mathematics in Sadi Carnot’s theory
Final remarks

What Are The Scientific Roots Of Sadi Carnot’s Cycle?
An outline of the problem
A comparative analysis: Volta’s battery and Sadi Carnot’s heat machine
            An analogy between heat fluid and electric fluid
            An analogy between the cycle of electric fluid and the cycle on heat states
            An analogy between heat work and electrical work
On the analogy between thermodynamics and electrostatics according to Mach’s investigations
Other kind of analogies
            On the birth of electricity and thermodynamic theories
            On the caloric and entropy
Final remarks

Historical Epistemology Of Thermodynamics. The Mathematics In Sadi Carnot’s Theory
An outline of the problem
A book of physics without mathematics?
The calculations and historical interpretation of the mathematical footnote
The “suppression” of adiabatic curves in Sadi Carnot’s cycle
            Why Sadi Carnot “supprime” the adiabatic curves?
            A possible solution. Lazare’s synthetic method
            The synthetic method in Réflexions sur la puissance motrice du feu
The mathematical character of the footnote
How did Sadi Carnot use his adiabatic equation? A possible calculation
A reflection on modern calculation of efficiency
Final Remarks

Studies And Heritage of Réflexions sur la Puissance Motrice du Feu
An outline of the problem
La théorie analytique de la chaleur, Reflections on Fourier and Lamé
            On Fourier’s Théorie analytique de la chaleur (1822)
            On Lamé’s Leçons sur la théorie analytique de la chaleur (1861)
            Final remarks on Fourier and Lamé’s theories
Theoretical advancements on caloric theory in Sadi Carnot’s work
            On dynamical effects of heat by Ferdnand Reech (1853)
            On cycles and equivalent mechanic of heat
On a comparative analyses between Paul de Saint–Robert’s Principes de Thermodynamique (1865) and Sadi Carnot’s Réflexions sur la puissance motrice du feu (1824)
            On Paul de Saint–Robert
            Historical analysis of Principes de Thermodynamique (1865)

Final Remarks On The Scientific Relationship between Père et Fils
An outline of the problem
A hypothesis on structure of scientific  parentage
On the lost Newtonian paradigm
On the constraints and production of work
On the machine en général and its working substance
On the analogy between hydraulic and heat machines
On the efficiency of a machine
On the impossibility of perpetual motion
On the synthetic method
On the principle of virtual work
On the principle of virtual work and the interactions
On the principle of virtual work and the state equations
Scholars, formulas, experiments and sources cited by Sadi Carnot in his Works
On the equivalence of work–heat
On the cycle and reversibility of a machine
Final remarks a mò of conclusions

Appendix to Chapter VII