shown that, at a certain point, which he calls the "critical point," the properties of the two states of the fluid fade into each other, and that, at that point, the two become continuous. With carbonic acid, this occurs at 75 atmospheres, about 1,125 pounds per square inch, a pressure which would counterbalance a column of mercury 60 yards, or nearly as many metres, high. The temperature at this point is about 90° Fahr., or 31° Cent. For ether, the temperature is 370° Fahr., and the pressure 38 atmospheres; for alcohol, they are 498° Fahr., and 120 atmospheres; and for bisulphide of carbon, 505° Fahr., and 67 atmospheres. For water, the pressure is too high to be determined; but the temperature is about 775° Fahr., or 413° Cent.

Donny and Dufour have shown that these normal properties of vapors and liquids are subject to modification by certain conditions, as previously (1818) noted by Gay-Lussac, and have pointed out the bearing of this fact upon the safety of steam-boilers. It was discovered that the boilingpoint of water could be elevated far above its ordinary temperature of ebullition by expedients which deprive the liquid of the air usually condensed within its mass, and which prevent contact with rough or metallic surfaces. By suspension in a mixture of oils which is of nearly the same density, Dufour raised drops of water under atmospheric pressure to a temperature of 356° Fahr.-180° Cent.the temperature of steam of about 150 pounds per square inch. Prof. James Thompson has, on theoretical grounds, indicated that a somewhat similar action may enable vapor, under some conditions, to be cooled below the normal temperature of condensation, without liquefaction.

Fairbairn and Tate repeated the attempt to determine the volume and temperature of water at pressures extending beyond those in use in the steam-engine, and incomplete determinations have also been made by others.

Regnault is the standard authority on these data. His experiments (1847) were made at the expense of the French

Government, and under the direction of the French Academy. They were wonderfully accurate, and extended through a very wide range of temperatures and pressures. The results remain standard after the lapse of a quarter of a century, and are regarded as models of precise physical work.'

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. pab Ac B';

making = 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 0 = 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.,

=

=

(82) the freezing-point.

1 See Porter on the Steam-Engine Indicator for the best set of Regnault's

tables generally accessible.

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 analytical work of Rankine, which led to the conclusion that steam doing work by expansion must become gradually liquefied. Constructing a glass 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 asserted 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 quantity of heat entering, and the amount rejected from, the steam-cylinder, and thus obtained a coarse 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 quantitative 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 analytical 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 résumé of the principal 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 space through which it is overcome, or by the half-product of the mass 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 mass of explosive material. The British measure of energy is the footpound; the metric measure is the kilogrammetre.

Energy, whether kinetic or potential, may be observable and due to mass-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 illustrations of the two classes. 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 quantity of energy, whatever