may be its form, is the product of the resistance which it is capable of overcoming into the space through which it can move against that resistance, i. e., by the product RS. Or it is measured by the equivalent expressions MV', or WV 2

in which W is the weight, M is the " mass of mat2 g ter in motion, V the velocity, and g the dynamic measure of the force of gravity, 324 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 quantitative 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 space.

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 assumes 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 Prévost, 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 quantity of motion is measured as vis viva by the half-product of the mass 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 circumscribed, 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:

1. Heat-energy and mechanical energy are mutually convertible, one British thermal unit being the equivalent in heat-energy of 778 foot-pounds of mechanical energy, and one metric calorie equal to 426.8 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 mass is equal to the sum of the energies of its parts.'

It follows that the work performed by the transformation of the energy of heat, during any indefinitely small

1 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.

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 quantity called by Rankine the "heatpotential" 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 hnn as follows:

Jdh = d H = k dτ + тd F =

ταφ,

in which J is Joule's equivalent, dh the variation of total heat in the substance, kdr 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 7 d F is the work done by the transformation of heat-energy, or the product of the absolute temperature, 7, into the differential of the heat-potential.

is the thermo-dynamic function, and do 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 heatengines, 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 ex

cess 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,' 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 thermodynamics 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.

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.

1 "Théorie de la Machine à Vapeur," par le Chevalier F. M. G. de Pambour, Paris, 1844.

2 For a more complete and formal account of this development of a new science, see a paper by the author, published in "Trans. Brit. Assoc. for Advancement of Science," 1884; also "Manual of the Steam-Engine," part i, chap. iii.

CHAPTER VIII.

THE PHILOSOPHY OF THE STEAM-ENGINE.

ITS APPLICATION; ITS TEACHINGS RESPECTING THE CONSTRUCTION OF THE ENGINE AND ITS IMPROVEMENT.

"OFTENTIMES an Uncertaintie hindered our going on so merrily, but by persevering the Difficultie was mastered, and the new Triumph gave stronger Heart unto us."-RALEIGH.

"If everything which we cannot comprehend is to be called an impossibility, how many are daily presented to our eyes! and in contemning as false that which we consider to be impossible, may we not be depreciating a giant's effort to give an importance to our own weakness?"-MON

TAIGNE.

"They who aim vigorously at perfection will come nearer to it than those whose laziness or despondency makes them give up its pursuit from the feeling of its being unattainable."-CHESTERFIELD.

As has been already stated, the steam-engine is a machine which is especially designed to transform energy, originally dormant or potential, into active and usefully available kinetic energy.

When, millions of years ago, in that early period which the geologists call the carboniferous, the kinetic energy of the sun's rays, and of the glowing interior of the earth, was expended in the decomposition of the vast volumes of carbonic acid with which air was then charged, and in the production of a life-sustaining atmosphere and of the immense forests which then covered the earth with their al