[112] _See_ Porter on the Steam-Engine Indicator for the best set of Regnault"s tables generally accessible.

Regnault found that the total heat of steam is not constant, but that the latent heat varies, and that the sum of the latent and sensible heats, or the total heat, increases 0.305 of a degree for each degree of increase in the sensible heat, making 0.305 the specific heat of saturated steam. He found the specific heat of superheated steam to be 0.4805.

Regnault promptly detected the fact that steam was not subject to Boyle"s law, and showed that the difference is very marked. In expressing his results, he not only tabulated them but also laid them down graphically; he further determined exact constants for Biot"s algebraic expression,

log. _p_ = _a_ - _b_A^{_x_} - _c_B^{_x_};

making _x_ = 20 + _t_ Cent.; _a_ = 6.264035; log. _b_ = 0.1397743; log. _c_ = 0.6924351; log. A = [=1].9940493, and log. B = [=1].9983439; _p_ is the pressure in atmospheres. Regnault, in the expression for the total heat, H = A + _bt_, determined on the centigrade scale [theta] = 606.5 + 0.305 _t_ Cent. For the Fahrenheit scale, we have the following equivalent expressions:

H = 1,113.44 + 0.305 _t_ Fahr., if measured from 0 Fahr.

= 1,091.9 + 0.305 (_t_ - 32) Fahr.,; } if measured from = 1,081.94 + 0.305 _t_ Fahr., } the freezing-point.

For latent heat, we have:

L = 606.5 - 0.695 _t_ Cent.

= 1,091.7- 0.695 (_t_ - 32) Fahr.

= 1,113.94- 0.695 _t_ Fahr.

Since Regnault"s time, nothing of importance has been done in this direction. There still remains much work to be done in the extension of the research to higher pressures, and under conditions which obtain in the operation of the steam-engine. The volumes and densities of steam require further study, and the behavior of steam in the engine is still but little known, otherwise than theoretically. Even the true value of Joule"s equivalent is not undisputed.

Some of the most recent experimental work bearing directly upon the philosophy of the steam-engine is that of Hirn, whose determination of the value of the mechanical equivalent was less than two per cent.

below that of Joule. Hirn tested by experiment, in 1853, and repeatedly up to 1876, the a.n.a.lytical work of Rankine, which led to the conclusion that steam doing work by expansion must become gradually liquefied. Constructing a gla.s.s steam-engine cylinder, he was enabled to see plainly the clouds of mist which were produced by the expansion of steam behind the piston, where Regnault"s experiments prove that the steam should become drier and superheated, were no heat transformed into mechanical energy. As will be seen hereafter, this great discovery of Rankine is more important in its bearing upon the theory of the steam-engine than any made during the century. Hirn"s confirmation stands, in value, beside the original discovery. In 1858 Hirn confirmed the work of Mayer and Joule by determining the work done and the carbonic acid produced, as well as the increased temperature due to their presence, where men were set at work in a treadmill; he found the elevation of temperature to be much greater in proportion to gas produced when the men were resting than when they were at work. He thus proved conclusively the conversion of heat-energy into mechanical work. It was from these experiments that Helmholtz deduced the "modulus of efficiency" of the human machine at one-fifth, and concluded that the heart works with eight times the efficiency of a locomotive-engine, thus confirming a statement of Rumford, who a.s.serted the higher efficiency of the animal.

Hirn"s most important experiments in this department were made upon steam-engines of considerable size, including simple and compound engines, and using steam sometimes saturated and sometimes superheated to temperatures as high, on some occasions, as 340 Cent. He determined the work done, the quant.i.ty of heat entering, and the amount rejected from, the steam-cylinder, and thus obtained a coa.r.s.e approximation to the value of the heat-equivalent. His figure varied from 296 to 337 kilogrammetres. But, in all cases, the loss of heat due to work done was marked, and, while these researches could not, in the nature of the case, give accurate quant.i.tative results, they are of great value as qualitatively confirming Mayer and Joule, and proving the transformation of energy.

Thus, as we have seen, experimental investigation and a.n.a.lytical research have together created a new science, and the philosophy of the steam-engine has at last been given a complete and well-defined form, enabling the intelligent engineer to comprehend the operation of the machine, to perceive the conditions of efficiency, and to look forward in a well-settled direction for further advances in its improvement and in the increase of its efficiency.

A very concise _resume_ of the princ.i.p.al facts and laws bearing upon the philosophy of the steam-engine will form a fitting conclusion to this historical sketch.

The term "energy" was first used by Dr. Young as the equivalent of the work of a moving body, in his hardly yet obsolete "Lectures on Natural Philosophy."

Energy is the capacity of a moving body to overcome resistance offered to its motion; it is measured either by the product of the mean resistance into the s.p.a.ce through which it is overcome, or by the half-product of the ma.s.s of the body into the square of its velocity.

Kinetic energy is the actual energy of a moving body; potential energy is the measure of the work which a body is capable of doing under certain conditions which, without expending energy, may be made to affect it, as by the breaking of a cord by which a weight is suspended, or by firing a ma.s.s of explosive material. The British measure of energy is the foot-pound; the metric measure is the kilogrammetre.

Energy, whether kinetic or potential, may be observable and due to ma.s.s-motion; or it may be invisible and due to molecular movements.

The energy of a heavenly body or of a cannon-shot, and that of heat or of electrical action, are ill.u.s.trations of the two cla.s.ses. In Nature we find utilizable potential energy in fuel, in food, in any available head of water, and in available chemical affinities. We find kinetic energy in the motion of the winds and the flow of running water, in the heat-motion of the sun"s rays, in heat-currents on the earth, and in many intermittent movements of bodies acted on by applied forces, natural or artificial. The potential energy of fuel and of food has already been seen to have been derived, at an earlier period, from the kinetic energy of the sun"s rays, the fuel or the food being thus made a storehouse or reservoir of energy. It is also seen that the animal system is simply a "mechanism of transmission" for energy, and does not create but simply diverts it to any desired direction of application.

All the available forms of energy can be readily traced back to a common origin in the potential energy of a universe of nebulous substance (chaos), consisting of infinitely diffused matter of immeasurably slight density, whose "energy of position" had been, since the creation, gradually going through a process of transformation into the several forms of kinetic and potential energy above specified, through intermediate methods of action which are usually still in operation, such as the potential energy of chemical affinity, and the kinetic forms of energy seen in solar radiation, the rotation of the earth, and the heat of its interior.

The _measure_ of any given quant.i.ty of energy, whatever may be its form, is the product of the resistance which it is capable of overcoming into the s.p.a.ce through which it can move against that resistance, i. e., by the product RS. Or it is measured by the equivalent expressions (MV^{2})/2, or WV^{2}/2_g_, in which W is the weight, M is the "ma.s.s" of matter in motion, V the velocity, and _g_ the dynamic measure of the force of gravity, 32-1/6 feet, or 9.8 metres, per second.

There are three great laws of energetics:

1. The sum total of the energy of the universe is invariable.

2. The several forms of energy are interconvertible, and possess an exact quant.i.tative equivalence.

3. The tendency of all forms of kinetic energy is continually toward reduction to forms of molecular motion, and to their final dissipation uniformly throughout s.p.a.ce.

The history of the first two of these laws has already been traced.

The latter was first enunciated by Prof. Sir William Thomson in 1853.

Undissipated energy is called "Entrophy."

The science of thermo-dynamics is, as has been stated, a branch of the science of energetics, and is the only branch of that science in the domain of the physicist which has been very much studied. This branch of science, which is restricted to the consideration of the relations of heat-energy to mechanical energy, is based upon the great fact determined by Rumford and Joule, and considers the behavior of those fluids which are used in heat-engines as the media through which energy is transferred from the one form to the other. As now accepted, it a.s.sumes the correctness of the hypothesis of the dynamic theory of fluids, which supposes their expansive force to be due to the motion of their molecules.

This idea is as old as Lucretius, and was distinctly expressed by Bernouilli, Le Sage and Prevost, and Herapath. Joule recalled attention to this idea, in 1848, as explaining the pressure of gases by the impact of their molecules upon the sides of the containing vessels. Helmholtz, ten years later, beautifully developed the mathematics of media composed of moving, frictionless particles, and Clausius has carried on the work still further.

The general conception of a gas, as held to-day, including the vortex-atom theory of Thomson and Rankine, supposes all bodies to consist of small particles called molecules, each of which is a chemical aggregation of its ultimate parts or atoms. These molecules are in a state of continual agitation, which is known as heat-motion.

The higher the temperature, the more violent this agitation; the total quant.i.ty of motion is measured as _vis viva_ by the half-product of the ma.s.s into the square of the velocity of molecular movement, or in heat-units by the same product divided by Joule"s equivalent. In solids, the range of motion is circ.u.mscribed, and change of form cannot take place. In fluids, the motion of the molecules has become sufficiently violent to enable them to break out of this range, and their motion is then no longer definitely restricted.

The laws of thermo-dynamics are, according to Rankine:

1. Heat-energy and mechanical energy are mutually convertible, one British thermal unit being the equivalent in heat-energy of 772 foot-pounds of mechanical energy, and one metric _calorie_ equal to 423.55 kilogrammetres of work.

2. The energy due to the heat of each of the several equal parts into which a uniformly hot substance may be divided is the same; and the total heat-energy of the ma.s.s is equal to the sum of the energies of its parts.[113]

[113] This uniformity is not seen where a substance is changing its physical state while developing its heat-energy, as occurs with steam doing work while expanding.

It follows that the work performed by the transformation of the energy of heat, during any indefinitely small variation of the state of a substance as respects temperature, is measured by the product of the absolute temperature into the variation of a "function," which function is the rate of variation of the work so done with temperature. This function is the quant.i.ty called by Rankine the "heat-potential" of the substance for the given kind of work. A similar function, which comprehends the total heat-variation, including both heat transformed and heat needed to effect accompanying physical changes, is called the "thermo-dynamic function." Rankine"s expression for the general equation of thermo-dynamics includes the latter, and is given by him as follows:

J_dh_ = _d_H = _kd_[tau] + [tau]_d_F = [tau]_d_[phi],

in which J is Joule"s equivalent, _dh_ the variation of total heat in the substance, _kd_[tau] the product of the "dynamic specific heat"

into the variation of temperature, or the total heat demanded to produce other changes than a transformation of energy, and [tau]_d_F is the work done by the transformation of heat-energy, or the product of the absolute temperature, [tau], into the differential of the heat-potential. [phi] is the thermo-dynamic function, and [tau]_d_[phi] measures the whole heat needed to produce, simultaneously, a certain amount of work or of mechanical energy, and, at the same time, to change the temperature of the working substance.

Studying the behavior of gases and vapors, it is found that the work done when they are used, like steam, in heat-engines, consists of three parts:

(_a._) The change effected in the total actual heat-motion of the fluid.

(_b._) That heat which is expended in the production of internal work.

(_c._) That heat which is expended in doing the external work of expansion.

In any case in which the total heat expended exceeds that due the production of work on external bodies, the excess so supplied is so much added to the intrinsic energy of the substance absorbing it.

The application of these laws to the working of steam in the engine is a comparatively recent step in the philosophy of the steam-engine, and we are indebted to Rankine for the first, and as yet only, extended and in any respect complete treatise embodying these now accepted principles.

It was fifteen years after the publication of the first logical theory of the steam-engine, by Pambour,[114] before Rankine, in 1859, issued the most valuable of all his works, "The Steam-Engine and other Prime Movers." The work is far too abstruse for the general reader, and is even difficult reading for many accomplished engineers. It is excellent beyond praise, however, as a treatise on the thermo-dynamics of heat-engines. It will be for his successors the work of years to extend the application of the laws which he has worked out, and to place the results of his labors before students in a readily comprehended form.

[114] "Theorie de la Machine a Vapeur," par le Chevalier F. M. G. de Pambour, Paris, 1844.

William J. Macquorn Rankine, the Scotch engineer and philosopher, will always be remembered as the author of the modern philosophy of the steam-engine, and as the greatest among the founders of the science of thermo-dynamics. His death, while still occupying the chair of engineering at the University of Glasgow, December 24, 1872, at the early age of fifty-two, was one of the greatest losses to science and to the profession which have occurred during the century.

CHAPTER VIII.