# Calculation of the Effect of Machines

 Coverpage of Gustave Coriolis' 1829 textbook Calculation of the Effect of Machines.
In famous publications, Calculation of the Effect of Machines, or Considerations on the Use of Engines and their Evaluation is an 1829 textbook by French physicist Gustave Coriolis that introduced a number of fundamental modern concepts, such as the principle of the transmission of work, i.e. the standard definition of work as force times distance, the dynamode as a unit of work, and kinetic energy as one-half the mass times the squared velocity of an object. [1]

Overview
The following seems to be a circa 1844 posthumous abstract: [1]

Done at the Academy of Sciences, a book entitled From Veffet of Calculating Machines or remarks on the use of motors and their evaluation, to serve as an introduction to the study of special machines; Mr. Corious, Bridges and Roads engineer.

The theoretical considerations that govern the establishment and calculation of the effect of the machines are very worthy of the interest of the learned, either by themselves or by their influence on the progress of the arts. One of the main problems is proposed in construction machinery, is to replace, for the performance of useful work, our own forces by more powerful forces of natural agents. It is very important to use the most advantageous way as possible the considerable capital anjourd'hui which are devoted to this kind of companies.

The science of machines, considered in its full extent, is very large and almost entirely embraces all the arts. By merely part of the science that belongs to mathematics, we recognize that it borrows key concepts in geometry, the Static and Dynamic. Of these, the main one being the consideration of the action of machines and engines that are applied to them, in distinguishing elements of this action, and research proportions that must be established between these elements, to obtain natural agents the largest amount of work it is possible. These considerations have long since attracted the attention of surveyors. It was soon recognized that the effect of a machine, it was always easy to assimilate to the elevation of a weight was proportional to the high weight and the speed of the vertical ascent; Parent seems to have noticed, but the first in the Memoirs of Academy of Sciences for the year 1704, that given the motor to operate a job, the effect could be obtained was liable to vary within certain limits and the need to give so much to proportion the effort and speeds, this effect reached the highest value that the nature of the engine could contain. These ideas have been adopted by the learned and engineers have been busy this material. Theoretical and experimental research Daniel Bernoulli, Euler, Borda De Parcieux, Coulomb, Carnot, Belidor, Smeaton had generally intended to enjoy the action of the various engines, and learn to adjust to satisfy the maximum of conditions occurring in all matters of this kind, as well as in most sciences applications to the arts and natural philosophy.

Mr. Coriolis, in the work which the Academy has asked us to report to note that the theoretical concepts relating to the use of engines are item presented in the teaching of rational mechanics nor completely developed in treated special machines. These concepts are mainly in the application of the principle of conservation of kinetic energy, application specified by the illustrious Lagrange, in the last pages of the theory of analytic functions. Small, clever professor at École Polytechnique, whose untimely death has deeply distressed friends of science, gave a brief on this memory, printed in ...

To a good extent, Coriolis' 1829 textbook seems to be the main reference to German physicist Rudolf Clausius’ derivation of the energy U of a body or internal energy in the modern sense in the mathematical introduction to his 1875 textbook The Mechanical Theory of Heat, although, to note, he does not explicitly mention Coriolis.

References
1. (a) Coriolis, Gustave. (1829). Calculation of the Effect of Machines, or Considerations on the Use of Engines and their Evaluation (Du Calcul de l'effet des Machines, ou Considérations sur l'emploi des Moteurs et sur Leur Evaluation). Paris: Carilian-Goeury, Libraire.
(b) Coriolis, Gustave. (1844). Treatise on the Mechanics of Solid Bodies and Calculation of the Effect on Machines (Traité de la Mécanique des Corps Solides et du Calcul de l'effet des Machines) (section: Principle of the Transmission of Work in the Movement of a Material Point, pgs. 35-40). 2nd. Ed. Paris.