Dynamics, or kinetics, which treats of simple motion as an effect of the action of forces.

Energetics, which treats of modifications of energy under the action of forces, and of its transformation from one mode of manifestation to another, and from one body to another.

Under the latter of these four divisions of mechanical philosophy is comprehended that latest of the minor sciences, of which the heat-engines, and especially the steamengine, illustrate the most important applications-Thermodynamics. This science is simply a wider generalization of principles which, as we have seen, have been established one at a time, and by philosophers widely separated both geographically and historically, by both space and time, and which have been slowly aggregated to form one after another of the sciences, and out of which, as we now are beginning to see, we are slowly evolving wider generalizations, and thus tending toward a condition of scientific knowledge which renders more and more probable the truth of Cicero's declaration : "One eternal and immutable law embraces all things and all times." At the basis of the whole science of energetics lies a principle which was enunciated before Science had a birthplace or a name :

All that exists, whether matter or force, and in whatever form, is indestructible, except by the Infinite Power which has created it.

That matter is indestructible by finite power became admitted as soon as the chemists, led by their great teacher Lavoisier, began to apply the balance, and were thus able to show that in all chemical change there occurs only a modification of form or of combination of elements, and no loss of matter ever takes place. The "persistence" of energy was a later discovery, consequent largely upon the experimental determination of the convertibility of heatenergy into other forms and into mechanical work, for which we are indebted to Rumford and Davy, and to the

determination of the quantivalence anticipated by Newton, shown and calculated approximately by Colding and Mayer, and measured with great probable accuracy by Joule.

The great fact of the conservation of energy was loosely stated by Newton, who asserted that the work of friction

and the vis viva of the system or body arrested by friction were equivalent. In 1798, Benjamin Thompson, Count Rumford, an American who was then in the Bavarian service, presented a paper' to the Royal Society of Great Britain, in which he stated the results of an experiment which he had recently made, proving the immateriality of heat and the transformation of mechanical into heat energy.

1 "Philosophical Transactions," 1798.

This paper is of very great historical interest, as the now accepted doctrine of the persistence of energy is a generalization which arose out of a series of investigations, the most important of which are those which resulted in the determination of the existence of a definite quantivalent relation between these two forms of energy and a measurement of its value, now known as the "mechanical equivalent of heat." His experiment consisted in the determination of the quantity of heat produced by the boring of a cannon at the arsenal at Munich.

Rumford, after showing that this heat could not have been derived from any of the surrounding objects, or by compression of the materials employed or acted upon, says: "It appears to me extremely difficult, if not impossible, to form any distinct idea of anything capable of being excited and communicated in the manner that heat was excited and communicated in these experiments, except it be motion."1 He then goes on to urge a zealous and persistent investigation of the laws which govern this motion. He estimates the heat produced by a power which he states could easily be exerted by one horse, and makes it equal to the "combustion of nine wax candles, each three-quarters of an inch in diameter," and equivalent to the elevation of "25.68 pounds of ice-cold water" to the boiling-point, or 4,784.4 heat-units. The time was stated at "150 minutes." Taking the actual power of Rumford's Bavarian "one horse" as the most probable figure, 25,000 pounds raised one foot high per minute,' this gives the "mechanical equivalent

1 This idea was not by any means original with Rumford. Bacon seems to have had the same idea; and Locke says, explicitly enough: "Heat is a very brisk agitation of the insensible parts of the object. . . . so that what in our sensation is heat, in the object is nothing but motion."

2 The British heat-unit is the quantity of heat required to heat one pound of water 1° Fahr. from the temperature of maximum density.

* Rankine gives 25,920 foot-pounds per minute-or 432 per secondfor the average draught-horse in Great Britain, which is probably too high

of the foot-pound as 783.8 heat-units, differing but 1.5 per cent. from the now accepted value.

Had Rumford been able to eliminate all losses of heat by evaporation, radiation, and conduction, to which losses he refers, and to measure the power exerted with accuracy, the approximation would have been still closer. Rumford thus made the experimental discovery of the real nature of heat, proving it to be a form of energy, and, publishing the fact a half-century before the now standard determinations were made, gave us a very close approximation to the value of the heat-equivalent. Rumford also observed that the heat generated was "exactly proportional to the force with which the two surfaces are pressed together, and to the rapidity of the friction," which is a simple statement of equivalence between the quantity of work done, or energy expended, and the quantity of heat produced. This was the first great step toward the formation of a Science of Thermo-dynamics. Rumford's work was the corner-stone of the science.

Sir Humphry Davy, a little later (1799), published the details of an experiment which conclusively confirmed these deductions from Rumford's work. He rubbed two pieces of ice together, and found that they were melted by the friction so produced. He thereupon concluded: "It is evident that ice by friction is converted into water. .. Friction, consequently, does not diminish the capacity of bodies for heat."

Bacon and Newton, and Hooke and Boyle, seem to have anticipated-long before Rumford's time—all later philosophers, in admitting the probable correctness of that modern dynamical, or vibratory, theory of heat which considers it a mode of motion; but Davy, in 1812, for the first

for Bavaria. The engineer's "horse-power" -33,000 foot-pounds per minute-is far in excess of the average power of even a good draughthorse, which latter is sometimes taken as two-thirds the former.

time, stated plainly and precisely the real nature of heat, saying: "The immediate cause of the phenomenon of heat, then, is motion, and the laws of its communication are precisely the same as the laws of the communication of motion." The basis of this opinion was the same that had previously been noted by Rumford.

So much having been determined, it became at once evident that the determination of the exact value of the mechanical equivalent of heat was simply a matter of experiment; and during the succeeding generation this determination was made, with greater or less exactness, by several distinguished men. It was also equally evident that the laws governing the new science of thermo-dynamics could be mathematically expressed.

Fourier had, before the date last given, applied mathematical analysis in the solution of problems relating to the transfer of heat without transformation, and his "Théorie de la Chaleur" contained an exceedingly beautiful treatment of the subject. Sadi Carnot, twelve years later (1824), published his "Réflexions sur la Puissance Motrice du Feu," in which he made a first attempt to express the principles involved in the application of heat to the production of mechanical effect. Starting with the axiom that a body which, having passed through a series of conditions modifying its temperature, is returned to "its primitive physical state as to density, temperature, and molecular constitution," must contain the same quantity of heat which it had contained originally, he shows that the efficiency of heatengines is to be determined by carrying the working fluid through a complete cycle, beginning and ending with the same set of conditions. Carnot had not then accepted the vibratory theory of heat, and consequently was led into some errors; but, as will be seen hereafter, the idea just expressed is one of the most important details of a theory of the steam-engine.

Seguin, who has already been mentioned as one of the