Chapter III: Part 3

[2] This is often called bulbus arteriosus, but it will be seen that
the term is used rather differently in comparative anatomy.

HEART-BURIAL, the burial of the heart apart from the body. This is a very ancient practice, the special reverence shown towards the heart being doubtless due to its early association with the soul of man, his affections, courage and conscience. In medieval Europe heart-burial was fairly common. Some of the more notable cases are those of Richard I., whose heart, preserved in a casket, was placed in Rouen cathedral; Henry III., buried in Normandy; Eleanor, queen of Edward I., at Lincoln; Edward I., at Jerusalem; Louis IX., Philip III., Louis XIII. and Louis XIV., in Paris. Since the 17th century the hearts of deceased members of the house of Habsburg have been buried apart from the body in the Loretto chapel in the Augustiner Kirche, Vienna. The most romantic story of heart-burial is that of Robert Bruce. He wished his heart to rest at Jerusalem in the church of the Holy Sepulchre, and on his deathbed entrusted the fulfilment of his wish to Douglas. The latter broke his journey to join the Spaniards in their war with the Moorish king of Granada, and was killed in battle, the heart of Bruce enclosed in a silver casket hanging round his neck. Subsequently the heart was buried at Melrose Abbey. The heart of James, marquess of Montrose, executed by the Scottish Covenanters in 1650, was recovered from his body, which had been buried by the roadside outside Edinburgh, and, enclosed in a steel box, was sent to the duke of Montrose, then in exile. It was lost on its journey, and years afterwards was discovered in a curiosity shop in Flanders. Taken by a member of the Montrose family to India, it was stolen as an amulet by a native chief, was once more regained, and finally lost in France during the Revolution. Of notable 17th-century cases there is that of James II., whose heart was buried in the church of the convent of the Visitation at Chaillot near Paris, and that of Sir William Temple, at Moor Park, Farnham. The last ceremonial burial of a heart in England was that of Paul Whitehead, secretary to the Monks of Medmenham club, in 1775, the interment taking place in the Le Despenser mausoleum at High Wycombe, Bucks. Of later cases the most notable are those of Daniel O'Connell, whose heart is at Rome, Shelley at Bournemouth, Louis XVII. at Venice, Kosciusko at the Polish museum at Rapperschwyll, Lake Zurich, and the marquess of Bute, taken by his widow to Jerusalem for burial in 1900. Sometimes other parts of the body, removed in the process of embalming, are given separate and solemn burial. Thus the viscera of the popes from Sixtus V. (1590) onward have been preserved in the parish church of the Quirinal. The custom of heart-burial was forbidden by Pope Boniface VIII. (1294-1303), but Benedict XI. withdrew the prohibition.

See Pettigrew, _Chronicles of the Tombs_ (1857).

HEARTH (a word which appears in various forms in several Teutonic languages, cf. Dutch _haard_, German _Herd_, in the sense of "floor"), the part of a room where a fire is made, usually constructed of stone, bricks, tiles or earth, beaten hard and having a chimney above; the fire being lighted either on the hearth itself, or in a receptacle placed there for the purpose. Like the Latin _focus_, especially in the phrase for "hearth and home" answering to _pro aris et focis_, the word is used as equivalent to the home or household. The word is also applied to the fire and cooking apparatus on board ship; the floor of a smith's forge; the floor of a reverberatory furnace on which the ore is exposed to the flame; the lower part of a blast furnace through which the metal goes down into the crucible; in soldering, a portable brazier or chafing dish, and an iron box sunk in the middle of a flat iron plate or table. An "open-hearth furnace" is a regenerative furnace of the reverberatory type used in making steel, hence "open-hearth steel" (see IRON AND STEEL).

Hearth-money, hearth tax or chimney-money, was a tax imposed in England on all houses except cottages at a rate of two shillings for every hearth. It was first levied in 1662, but owing to its unpopularity, chiefly caused by the domiciliary visits of the collectors, it was repealed in 1689, although it was producing L170,000 a year. The principle of the tax was not new in the history of taxation, for in Anglo-Saxon times the king derived a part of his revenue from a _fumage_ or tax of smoke farthings levied on all hearths except those of the poor. It appears also in the hearth-penny or tax of a penny on every hearth, which as early as the 10th century was paid annually to the pope (see PETER'S PENCE).

HEARTS, a game of cards of recent origin, though founded upon the same principle as many old games, such as _Slobberhannes_, _Four Jacks_ and _Enfle_, namely, that of losing instead of winning as many tricks as possible. Hearts is played with a full pack, ace counting highest and deuce lowest. In the four-handed game, which is usually played, the entire pack is dealt out as at whist (but without turning up the last card, since there are no trumps), and the player at the dealer's left begins by leading any card he chooses, the trick being taken by the highest card of the suit led. Each player must follow suit if he can; if he has no cards of the suit led he is privileged to throw away any card he likes, thus having an opportunity of getting rid of his hearts, which is the object of the game. When all thirteen tricks have been played each player counts the hearts he has taken in and pays into the pool a certain number of counters for them, according to an arrangement made before beginning play. In the four-handed, or sweepstake, game the method of settling called "Howell's," from the name of the inventor, has been generally adopted, according to which each player begins with an equal number of chips, say 100, and, after the hand has been played, pays into the pool as many chips for each heart he had taken as there are players besides himself. Then each player takes out of the pool one chip for every heart he did not win. The pool is thus exhausted with every deal. Hearts may be played by two, three, four or even more players, each playing for himself.

_Spot Hearts._--In this variation the hearts count according to the
number of spots on the cards, excepting that the ace counts 14, the
king 13, queen 12 and knave 11, the combined score of the thirteen
hearts being thus 104.

_Auction Hearts._--In this the eldest hand examines his hand and bids
a certain number of counters for the privilege of naming the suit to
be got rid of, but without naming the suit. The other players in
succession have the privilege of outbidding him, and whoever bids most
declares the suit and pays the amount of his bid into the pool, the
winner taking it.

_Joker Hearts._--Here the deuce of hearts is discarded, and an extra
card, called the joker, takes its place, ranking in value between ten
and knave. It cannot be thrown away, excepting when hearts are led and
an ace or court card is played, though if an opponent discards the ace
or a court card of hearts, then the holder of the joker may discard
it. The joker is usually considered worth five chips, which are either
paid into the pool or to the player who succeeds in discarding the
joker.

_Heartsette._--In this variation the deuce of spades is deleted and
the three cards left after dealing twelve cards to each player are
called the _widow_ (or _kitty_), and are left face downward on the
table. The winner of the first trick must take the widow without
showing it to his opponents.

_Slobberhannes._--The object of this older form of Hearts is to avoid
taking either the first or last trick or a trick containing the queen
of clubs. A euchre pack (thirty two-cards, lacking all below the 7) is
used, and each player is given 10 counters, one being forfeited to the
pool if a player takes the first or last trick, or that containing the
club queen. If he takes all three he forfeits four points.

_Four Jacks (Polignac or Quatre-Valets)_ is usually played with a
piquet pack, the cards ranking in France as at ecarte, but in Great
Britain and America as at piquet. There is no trump suit. Counters are
used, and the object of the game is to avoid taking any trick
containing a knave, especially the knave of spades, called _Polignac_.
The player taking such a trick forfeits one counter to the pool.

_Enfle_ (or _Schwellen_) is usually played by four persons with a
piquet pack and for a pool. The cards rank as at Hearts, and there is
no trump suit. A player must follow suit if he can, but if he cannot
he may not discard, but must take up all tricks already won and add
them to his hand. Play is continued until one player gets rid of all
his cards and thus wins.

HEAT (O. E. _haetu_, which like "hot," Old Eng. _hat_, is from the Teutonic type _haita, hit_, to be hot; cf. Ger. _hitze, heiss_; Dutch, _hitte, heet_, &c.), a general term applied to that branch of physical science which deals with the effects produced by heat on material bodies, with the laws of transference of heat, and with the transformations of heat into other kinds of energy. The object of the present article is to give a brief sketch of the historical development of the science of heat, and to indicate the relation of the different branches of the subject, which are discussed in greater detail with reference to the latest progress in separate articles.

1. _Meanings of the Term Heat._--The term heat is employed in ordinary language in a number of different senses. This makes it a convenient term to employ for the general title of the science, but the different meanings must be carefully distinguished in scientific reasoning. For the present purpose, omitting metaphorical significations, we may distinguish four principal uses of the term: (a) Sensation of heat; (b) Temperature, or degree of hotness; (c) Quantity of thermal energy; (d) Radiant heat, or energy of radiation.

(a) From the sense of heat, aided in the case of very hot bodies by
the sense of sight, we obtain our first rough notions of heat as a
physical entity, which alters the state of a body and its condition in
respect of warmth, and is capable of passing from one body to another.
By touching a body we can tell whether it is warmer or colder than the
hand, and, by touching two similar bodies in succession, we can form a
rough estimate, by the acuteness of the sensation experienced, of
their difference in hotness or coldness over a limited range. If a hot
iron is placed on a cold iron plate, we may observe that the plate is
heated and the iron cooled until both attain appreciably the same
degree of warmth; and we infer from similar cases that something which
we call "heat" tends to pass from hot to cold bodies, and to attain
finally a state of equable diffusion when all the bodies concerned are
equally warm or cold. Ideas such as these derived entirely from the
sense of heat, are, so to speak, embedded in the language of every
nation from the earliest times.

(b) From the sense of heat, again, we naturally derive the idea of a
continuous scale or order, expressed by such terms as summer heat,
blood heat, fever heat, red heat, white heat, in which all bodies may
be placed with regard to their degrees of hotness, and we speak of the
_temperature_ of a body as denoting its place in the scale, in
contradistinction to the quantity of heat it may contain.

(c) The quantity of heat contained in a body obviously depends on the
size of the body considered. Thus a large kettleful of boiling water
will evidently contain more heat than a teacupful, though both may be
at the same temperature. The temperature does not depend on the size
of the body, but on the degree of concentration of the heat in it,
i.e. on the quantity of heat per unit mass, other things being equal.
We may regard it as axiomatic that a given body (say a pound of water)
in a given state (say boiling under a given pressure) must always
contain the same quantity of heat, and conversely that, if it contains
a given quantity of heat, and if it is under conditions in other
respects, it must be at a definite temperature, which will always be
the same for the same given conditions.

(d) It is a matter of common observation that rays of the sun or of a
fire falling on a body warm it, and it was in the first instance
natural to suppose that heat itself somehow travelled across the
intervening space from the sun or fire to the body warmed, in much the
same way as heat may be carried by a current of hot air or water. But
we now know that energy of radiation is not the same thing as heat,
though it is converted into heat when the rays strike an absorbing
substance. The term "radiant heat," however, is generally retained,
because radiation is commonly measured in terms of the heat it
produces, and because the transference of energy by radiation and
absorption is the most important agency in the diffusion of heat.

2. _Evolution of the Thermometer._--The first step in the development of the science of heat was necessarily the invention of a thermometer, an instrument for indicating temperature and measuring its changes. The first requisite in the case of such an instrument is that it should always give, at least approximately the same indication at the same temperature. The air-thermoscope of Galileo, illustrated in fig. 1, which consisted of a glass bulb containing air, connected to a glass tube of small bore dipping into a coloured liquid, though very sensitive to variations of temperature, was not satisfactory as a measuring instrument, because it was also affected by variations of atmospheric pressure. The invention of the type of thermometer familiar at the present day, containing a liquid hermetically sealed in a glass bulb with a fine tube attached, is also generally attributed to Galileo at a slightly later date, about 1612. Alcohol was the liquid first employed, and the degrees, intended to represent thousandths of the volume of the bulb, were marked with small beads of enamel fused on the stem, as shown in fig. 2. In order to render the readings of such instruments comparable with each other, it was necessary to select a fixed point or standard temperature as the zero or starting-point of the graduations. Instead of making each degree a given fraction of the volume of the bulb, which would be difficult in practice, and would give different values for the degree with different liquids, it was soon found to be preferable to take _two fixed points_, and to divide the interval between them into the same number of degrees. It was natural in the first instance to take the temperature of the human body as one of the fixed points. In 1701 Sir Isaac Newton proposed a scale in which the freezing-point of water was taken as zero, and the temperature of the human body as 12 deg. About the same date (1714) Gabriel Daniel Fahrenheit proposed to take as zero the lowest temperature obtainable with a freezing mixture of ice and salt, and to divide the interval between this temperature and that of the human body into 12 deg. To obtain finer graduations the number was subsequently increased to 96 deg. The freezing-point of water was at that time supposed to be somewhat variable, because as a matter of fact it is possible to cool water several degrees below its freezing-point in the absence of ice. Fahrenheit showed, however, that as soon as ice began to form the temperature always rose to the same point, and that a mixture of ice or snow with pure water always gave the same temperature. At a later period he also showed that the temperature of boiling water varied with the barometric pressure, but that it was always the same at the same pressure, and might therefore be used as the second fixed point (as Edmund Halley and others had suggested) provided that a definite pressure, such as the average atmospheric pressure, were specified. The freezing and boiling-points on one of his thermometers, graduated as already explained, with the temperature of the body as 96 deg., came out in the neighbourhood of 32 deg. and 212 deg. respectively, giving an interval of 180 deg. between these points. Shortly after Fahrenheit's death (1736) the freezing and boiling-points of water were generally recognized as the most convenient fixed points to adopt, but different systems of subdivision were employed. Fahrenheit's scale, with its small degrees and its zero below the freezing-point, possesses undoubted advantages for meteorological work, and is still retained in most English-speaking countries. But for general scientific purposes, the centigrade system, in which the freezing-point is marked 0 deg. and the boiling-point 100 deg., is now almost universally employed, on account of its greater simplicity from an arithmetical point of view. For work of precision the fixed points have been more exactly defined (see THERMOMETRY), but no change has been made in the fundamental principle of graduation.

3. _Comparison of Scales based on Expansion._--Thermometers constructed in the manner already described will give strictly comparable readings, provided that the tubes be of uniform bore, and that the same liquid and glass be employed in their construction. But they possess one obvious defect from a theoretical point of view, namely, that the subdivision of the temperature scale depends on the expansion of the particular liquid selected as the standard. A liquid such as water, which, when continuously heated at a uniform rate from its freezing-point, first contracts and then expands, at a rapidly increasing rate, would obviously be unsuitable. But there is no a priori reason why other liquids should not behave to some extent in a similar way. As a matter of fact, it was soon observed that thermometers carefully constructed with different liquids, such as alcohol, oil and mercury, did not agree precisely in their indications at points of the scale intermediate between the fixed points, and diverged even more widely outside these limits. Another possible method, proposed in 1694 by Carlo Renaldeni (1615-1698), professor of mathematics and philosophy at Pisa, would be to determine the intermediate points of the scale by observing the temperatures of mixtures of ice-cold and boiling water in varying proportions. On this method, the temperature of 50 deg. C. would be defined as that obtained by mixing equal weights of water at 0 deg. C. and 100 deg. C.; 20 deg. C., that obtained by mixing 80 parts of water at 0 deg. C. with 20 parts of water at 100 deg. C. and so on. Each degree rise of temperature in a mass of water would then represent the addition of the same quantity of heat. The scale thus obtained would, as a matter of fact, agree very closely with that of a mercury thermometer, but the method would be very difficult to put in practice, and would still have the disadvantage of depending on the properties of a particular liquid, namely, water, which is known to behave in an anomalous manner in other respects. At a later date, the researches of Gay-Lussac (1802) and Regnault (1847) showed that the laws of the expansion of gases are much simpler than those of liquids. Whereas the expansion of alcohol between 0 deg. C. and 100 deg. C. is nearly seven times as great as that of mercury, all gases (excluding easily condensible vapours) expand equally, or so nearly equally that the differences between them cannot be detected without the most refined observations. This equality of expansion affords a strong a priori argument for selecting the scale given by the expansion of a gas as the standard scale of temperature, but there are still stronger theoretical grounds for this choice, which will be indicated in discussing the absolute scale (S 21). Among liquids mercury is found to agree most nearly with the gas scale, and is generally employed in thermometers for scientific purposes on account of its high boiling-point and for other reasons. The differences of the mercurial scale from the gas scale having been carefully determined, the mercury thermometer can be used as a secondary standard to replace the gas thermometer within certain limits, as the gas thermometer would be very troublesome to employ directly in ordinary investigations. For certain purposes, and especially at temperatures beyond the range of mercury thermometers, electrical thermometers, also standardized by reference to the gas thermometer, have been very generally employed in recent years, while for still higher temperatures beyond the range of the gas thermometer, thermometers based on the recently established laws of radiation are the only instruments available. For a further discussion of the theory and practice of the measurement of temperature, the reader is referred to the article THERMOMETRY.

_4. Change of State._--Among the most important effects of heat is that of changing the state of a substance from solid to liquid, or from liquid to vapour. With very few exceptions, all substances, whether simple or compound, are known to be capable of existing in each of the three states under suitable conditions of temperature and pressure. The transition of any substance, from the state of liquid to that of solid or vapour under the ordinary atmospheric pressure, takes place at fixed temperatures, the freezing and boiling-points, which are very sharply defined for pure crystalline substances, and serve in fact as fixed points of the thermometric scale. A change of state cannot, however, be effected in any case without the addition or subtraction of a certain definite quantity of heat. If a piece of ice below the freezing-point is gradually heated at a uniform rate, its temperature may be observed to rise regularly till the freezing-point is reached. At this point it begins to melt, and its temperature ceases to rise. The melting takes a considerable time, during the whole of which heat is being continuously supplied without producing any rise of temperature, although if the same quantity of heat were supplied to an equal mass of water, the temperature of the water would be raised nearly 80 deg. C. Heat thus absorbed in producing a change of state without rise of temperature is called "Latent Heat," a term introduced by Joseph Black, who was one of the first to study the subject of change of state from the point of view of heat absorbed, and who in many cases actually adopted the comparatively rough method described above of estimating quantities of heat by observing the time required to produce a given change when the substance was receiving heat at a steady rate from its surroundings. For every change of state a definite quantity of heat is required, without which the change cannot take place. Heat must be added to melt a solid, or to vaporize a solid or a liquid, and conversely, heat must be subtracted to reverse the change, i.e. to condense a vapour or freeze a liquid. The quantity required for any given change depends on the nature of the substance and the change considered, and varies to some extent with the conditions (as to pressure, &c.) under which the change is made, but is always the same for the same change under the same conditions. A rough measurement of the latent heat of steam was made as early as 1764 by James Watt, who found that steam at 212 deg. F., when passed from a kettle into a jar of cold water, was capable of raising nearly six times its weight of water to the boiling point. He gives the volume of the steam as about 1800 times that of an equal weight of water.

The phenomena which accompany change of state, and the physical laws
by which such changes are governed, are discussed in a series of
special articles dealing with particular cases. The articles on FUSION
and ALLOYS deal with the change from the solid to the liquid state,
and the analogous case of solution is discussed in the article on
SOLUTION. The articles on CONDENSATION OF GASES, LIQUID GASES and
VAPORIZATION deal with the theory of the change of state from liquid
to vapour, and with the important applications of liquid gases to
other researches. The methods of measuring the latent heat of fusion
or vaporization are described in the article CALORIMETRY, and need not
be further discussed here except as an introduction to the history of
the evolution of knowledge with regard to the nature of heat.

5. _Calorimetry by Latent Heat._--In principle, the simplest and most direct method of measuring quantities of heat consists in observing the effects produced in melting a solid or vaporizing a liquid. It was, in fact, by the fusion of ice that quantities of heat were first measured. If a hot body is placed in a cavity in a block of ice at 0 deg. C., and is covered by a closely fitting slab of ice, the quantity of ice melted will be directly proportional to the quantity of heat lost by the body in cooling to 0 deg. C. None of the heat can possibly escape through the ice, and conversely no heat can possibly get in from outside. The body must cool exactly to 0 deg. C., and every fraction of the heat it loses must melt an equivalent quantity of ice. Apart from heat lost in transferring the heated body to the ice block, the method is theoretically perfect. The only difficulty consists in the practical measurement of the quantity of ice melted. Black estimated this quantity by mopping out the cavity with a sponge before and after the operation. But there is a variable film of water adhering to the walls of the cavity, which gives trouble in accurate work. In 1780 Laplace and Lavoisier used a double-walled metallic vessel containing broken ice, which was in many respects more convenient than the block, but aggravated the difficulty of the film of water adhering to the ice. In spite of this practical difficulty, the quantity of heat required to melt unit weight of ice was for a long time taken as the unit of heat. This unit possesses the great advantage that it is independent of the scale of temperature adopted. At a much later date R. Bunsen (_Phil. Mag._, 1871), adopting a suggestion of Sir John Herschel's, devised an ice-calorimeter suitable for measuring small quantities of heat, in which the difficulty of the water film was overcome by measuring the change in volume due to the melting of the ice. The volume of unit mass of ice is approximately 1.0920 times that of unit mass of water, so that the diminution of volume is 0.092 a cubic centimetre for each gramme of ice melted. The method requires careful attention to details of manipulation, which are more fully discussed in the article on CALORIMETRY.

For measuring large quantities of heat, such as those produced by the combustion of fuel in a boiler, the most convenient method is the evaporation of water, which is commonly employed by engineers for the purpose. The natural unit in this case is the quantity of heat required to evaporate unit mass of water at the boiling point under atmospheric pressure. In boilers working at a higher pressure, or supplied with water at a lower temperature, appropriate corrections are applied to deduce the quantity evaporated in terms of this unit.

For laboratory work on a small scale the converse method of condensation has been successfully applied by John Joly, in whose steam-calorimeter the quantity of heat required to raise the temperature of a body from the atmospheric temperature to that of steam condensing at atmospheric pressure is observed by weighing the mass of steam condensed on it. (See CALORIMETRY.)

6. _Thermometric Calorimetry._--For the majority of purposes the most convenient and the most readily applicable method of measuring quantities of heat, is to observe the rise of temperature produced in a known mass of water contained in a suitable vessel or calorimeter. This method was employed from a very early date by Count Rumford and other investigators, and was brought to a high pitch of perfection by Regnault in his extensive calorimetric researches (_Memoires de l'Institut de Paris_, 1847); but it is only within comparatively recent years that it has really been placed on a satisfactory basis by the accurate definition of the units involved. The theoretical objections to the method, as compared with latent heat calorimetry, are that some heat is necessarily lost by the calorimeter when its temperature is raised above that of the surroundings, and that some heat is used in heating the vessel containing the water. These are small corrections, which can be estimated with considerable accuracy in practice. A more serious difficulty, which has impaired the value of much careful work by this method, is that the quantity of heat required to raise the temperature of a given mass of water 1 deg. C. depends on the temperature at which the water is taken, and also on the scale of the thermometer employed. It is for this reason, in many cases, impossible to say, at the present time, what was the precise value, within 1/2 or even 1% of the heat unit, in terms of which many of the older results, such as those of Regnault, were expressed. For many purposes this would not be a serious matter, but for work of scientific precision such a limitation of accuracy would constitute a very serious bar to progress. The unit generally adopted for scientific purposes is the quantity of heat required to raise 1 gram (or kilogram) of water 1 deg. C., and is called the calorie (or kilo-calorie). English engineers usually state results in terms of the British Thermal Unit (B.Th.U.), which is the quantity of heat required to raise 1 lb. of water 1 deg. F.

7. _Watt's Indicator Diagram; Work of Expansion._--The rapid development of the steam-engine (q.v.) in England during the latter part of the 18th century had a marked effect on the progress of the science of heat. In the first steam-engines the working cylinder served both as boiler and condenser, a very wasteful method, as most of the heat was transferred directly from the fire to the condensing water without useful effect. The first improvement (about 1700) was to use a separate boiler, but the greater part of the steam supplied was still wasted in reheating the cylinder, which had been cooled by the injection of cold water to condense the steam after the previous stroke. In 1769 James Watt showed how to avoid this waste by using a separate condenser and keeping the cylinder as hot as possible. In his earlier engines the steam at full boiler pressure was allowed to raise the piston through nearly the whole of its stroke. Connexion with the boiler was then cut off, and the steam at full pressure was discharged into the condenser. Here again there was unnecessary waste, as the steam was still capable of doing useful work. He subsequently introduced "expansive working," which effected still further economy. The connexion with the boiler was cut off when a fraction only, say 1/4, of the stroke had been completed, the remainder of the stroke being effected by the expansion of the steam already in the cylinder with continually diminishing pressure. By the end of the stroke, when connexion was made to the condenser, the pressure was so reduced that there was comparatively little waste from this cause. Watt also devised an instrument called an _indicator_ (see STEAM ENGINE), in which a pencil, moved up and down vertically by the steam pressure, recorded the pressure in the cylinder at every point of the stroke on a sheet of paper moving horizontally in time with the stroke of the piston. The diagram thus obtained made it possible to study what was happening inside the cylinder, and to deduce the work done by the steam in each stroke. The method of the indicator diagram has since proved of great utility in physics in studying the properties of gases and vapours. The work done, or the useful effect obtained from an engine or any kind of machine, is measured by the product of the resistance overcome and the distance through which it is overcome. The result is generally expressed in terms of the equivalent weight raised through a certain height against the force of gravity.[1] If, for instance, the pressure on a piston is 50 lb. per sq. in., and the area of the piston is 100 sq. in., the force on the piston is 5000 lb. weight. If the stroke of the piston is 1 ft., the work done per stroke is capable of raising a weight of 5000 lb. through a height of 1 ft., or 50 lb. through a height of 100 ft. and so on.

Fig. 3 represents an imaginary indicator diagram for a steam-engine,
taken from one of Watt's patents. Steam is admitted to the cylinder
when the piston is at the beginning of its stroke, at S. ST represents
the length of the stroke or the limit of horizontal movement of the
paper on which the diagram is drawn. The indicating pencil rises to
the point A, representing the absolute pressure of 60 lb. per sq. in.
As the piston moves outwards the pencil traces the horizontal line AB,
the pressure remaining constant till the point B is reached, at which
connexion to the boiler is cut off. The work done so far is
represented by the area of the rectangle ABSF, namely AS X SF,
multiplied by the area of the piston in sq. in. The result is in
foot-pounds if the fraction of the stroke SF is taken in feet. After
cut-off at B the steam expands under diminishing pressure, and the
pencil falls gradually from B to C, following the steam pressure until
the exhaust valve opens at the end of the stroke. The pressure then
falls rapidly to that of the condenser, which for an ideal case may be
taken as zero, following Watt. The work done during expansion is found
by dividing the remainder of the stroke FT into a number of equal
parts (say 8, Watt takes 20) and measuring the pressure at the points
1, 2, 3, 4, &c., corresponding to the middle of each. We thus obtain a
number of small rectangles, the sum of which is evidently very nearly
equal to the whole area BCTF under the expansion curve, or to the
remainder of the stroke FT multiplied by the average or mean value of
the pressure. The whole work done in the forward stroke is represented
by the area ABCTSA, or by the average value of the pressure P over the
whole stroke multiplied by the stroke L. This area must be multiplied
by the area of the piston A in sq. in. as before, to get the work done
per stroke in foot-pounds, which is PLA. If the engine repeats this
cycle N times per minute, the work done per minute is PLAN
foot-pounds, which is reduced to horse-power by dividing by 33,000. If
the steam is ejected by the piston at atmospheric pressure (15 lb. per
sq. in.) instead of being condensed at zero pressure, the area CDST
under the atmospheric line CD, representing work done against
back-pressure on the return stroke must be subtracted. If the engine
repeats the same cycle or series of operations continuously, the
indicator diagram will be a closed curve, and the nett work done per
cycle will be represented by the included area, whatever the form of
the curve.

8. _Thermal Efficiency._--The thermal efficiency of an engine is the ratio of the work done by the engine to the heat supplied to it. According to Watt's observations, confirmed later by Clement and Desormes, the total heat required to produce 1 lb. of saturated steam at any temperature from water at 0 deg. C. was approximately 650 times the quantity of heat required to raise 1 lb. of water 1 deg. C. Since 1 lb. of steam represented on this assumption a certain quantity of heat, the efficiency could be measured naturally in foot-pounds of work obtainable per lb. of steam, or conversely in pounds of steam consumed per horse-power-hour.

In his patent of 1782 Watt gives the following example of the improvement in thermal efficiency obtained by expansive working. Taking the diagram already given, if the quantity of steam represented by AB, or 300 cub. in. at 60 lb. pressure, were employed without expansion, the work realized, represented by the area ABSF, would be 6000/4 = 1500 foot-pounds. With expansion to 4 times its original volume, as shown in the diagram by the whole area ABCTSA, the mean pressure (as calculated by Watt, assuming Boyle's law) would be 0.58 of the original pressure, and the work done would be 6000 X 0.58 = 3480 foot-pounds for the same quantity of steam, or the thermal efficiency would be 2.32 times greater. The advantage actually obtained would not be so great as this, on account of losses by condensation, back-pressure, &c., which are neglected in Watt's calculation, but the margin would still be very considerable. Three hundred cub. in. of steam at 60 lb. pressure would represent about .0245 of 1 lb. of steam, or 28.7 B.Th.U., so that, neglecting all losses, the possible thermal efficiency attainable with steam at this pressure and four expansions (1/4 cut-off) would be 3480/28.7, or 121 foot-pounds per B.Th.U. At a later date, about 1820, it was usual to include the efficiency of the boiler with that of the engine, and to reckon the efficiency or "duty" in foot-pounds per bushel or cwt. of coal. The best Cornish pumping-engines of that date achieved about 70 million foot-pounds per cwt., or consumed about 3.2 lb. per horse-power-hour, which is roughly equivalent to 43 foot-pounds per B.Th.U. The efficiency gradually increased as higher pressures were used, with more complete expansion, but the conditions upon which the efficiency depended were not fully worked out till a much later date. Much additional knowledge with regard to the nature of heat, and the properties of gases and vapours, was required before the problem could be attacked theoretically.

9. _Of the Nature of Heat._--In the early days of the science it was natural to ascribe the manifestations of heat to the action of a subtle imponderable fluid called "caloric," with the power of penetrating, expanding and dissolving bodies, or dissipating them in vapour. The fluid was imponderable, because the most careful experiments failed to show that heat produced any increase in weight. The opposite property of levitation was often ascribed to heat, but it was shown by more cautious investigators that the apparent loss of weight due to heating was to be attributed to evaporation or to upward air currents. The fundamental idea of an imaginary fluid to represent heat was useful as helping the mind to a conception of something remaining invariable in quantity through many transformations, but in some respects the analogy was misleading, and tended greatly to retard the progress of science. The caloric theory was very simple in its application to the majority of calorimetric experiments, and gave a fair account of the elementary phenomena of change of state, but it encountered serious difficulties in explaining the production of heat by friction, or the changes of temperature accompanying the compression or expansion of a gas. The explanation which the calorists offered of the production of heat by friction or compression was that some of the latent caloric was squeezed or ground out of the bodies concerned and became "sensible." In the case of heat developed by friction, they supposed that the abraded portions of the material were capable of holding a smaller quantity of heat, or had less "capacity for heat," than the original material. From a logical point of view, this was a perfectly tenable hypothesis, and one difficult to refute. It was easy to account in this way for the heat produced in boring cannon and similar operations, where the amount of abraded material was large. To refute this explanation, Rumford (_Phil. Trans._, 1798) made his celebrated experiments with a blunt borer, in one of which he succeeded in boiling by friction 26.5 lb. of cold water in 2(1/2) hours, with the production of only 4145 grains of metallic powder. He then showed by experiment that the metallic powder required the same amount of heat to raise its temperature 1 deg., as an equal weight of the original metal, or that its "capacity for heat" (in this sense) was unaltered by reducing it to powder; and he argued that "in any case so small a quantity of powder could not possibly account for all the heat generated, that the supply of heat appeared to be inexhaustible, and that heat could not be a material substance, but must be something of the nature of motion." Unfortunately Rumford's argument was not quite conclusive. The supporters of the caloric theory appear, whether consciously or unconsciously, to have used the phrase "capacity for heat" in two entirely distinct senses without any clear definition of the difference. The phrase "capacity for heat" might very naturally denote the total quantity of heat contained in a body, which we have no means of measuring, but it was generally used to signify the quantity of heat required to raise the temperature of a body one degree, which is quite a different thing, and has no necessary relation to the total heat. In proving that the powder and the solid metal required the same quantity of heat to raise the temperature of equal masses of either one degree, Rumford did not prove that they contained equal quantities of heat, which was the real point at issue in this instance. The metal tin actually changes into powder below a certain temperature, and in so doing evolves a measurable quantity of heat. A mixture of the gases oxygen and hydrogen, in the proportions in which they combine to form water, evolves when burnt sufficient heat to raise more than thirty times its weight of water from the freezing to the boiling point; and the mixture of gases may, in this sense, be said to contain so much more heat than the water, although its capacity for heat in the ordinary sense is only about half that of the water produced. To complete the refutation of the calorists' explanation of the heat produced by friction, it would have been necessary for Rumford to show that the powder when reconverted into the same state as the solid metal did not absorb a quantity of heat equivalent to that evolved in the grinding; in other words that the heat produced by friction was not simply that due to the change of state of the metal from solid to powder.

Shortly afterwards, in 1799, Davy[2] described an experiment in which he melted ice by rubbing two blocks together. This experiment afforded a very direct refutation of the calorists' view, because it was a well-known fact that ice required to have a quantity of heat added to it to convert it into water, so that the water produced by the friction contained more heat than the ice. In stating as the conclusion to be drawn from this experiment that "friction consequently does not diminish the capacity of bodies for heat," Davy apparently uses the phrase capacity for heat in the sense of total heat contained in a body, because in a later section of the same essay he definitely gives the phrase this meaning, and uses the term "capability of temperature" to denote what we now term capacity for heat.

The delay in the overthrow of the caloric theory, and in the acceptance of the view that heat is a mode of motion, was no doubt partly due to some fundamental confusion of ideas in the use of the term "capacity for heat" and similar phrases. A still greater obstacle lay in the comparative vagueness of the motion or vibration theory. Davy speaks of heat as being "repulsive motion," and distinguishes it from light, which is "projective motion"; though heat is certainly not a substance--according to Davy in the essay under discussion--and may not even be treated as an imponderable fluid, light as certainly is a material substance, and is capable of forming chemical compounds with ordinary matter, such as oxygen gas, which is not a simple substance, but a compound, termed phosoxygen, of light and oxygen. Accepting the conclusions of Davy and Rumford that heat is not a material substance but a mode of motion, there still remains the question, what definite conception is to be attached to a quantity of heat? What do we mean by a quantity of vibratory motion, how is the quantity of motion to be estimated, and why should it remain invariable in many transformations? The idea that heat was a "mode of motion" was applicable as a qualitative explanation of many of the effects of heat, but it lacked the quantitative precision of a scientific statement, and could not be applied to the calculation and prediction of definite results. The state of science at the time of Rumford's and Davy's experiments did not admit of a more exact generalization. The way was paved in the first instance by a more complete study of the laws of gases, to which Laplace, Dalton, Gay-Lussac, Dulong and many others contributed both on the experimental and theoretical side. Although the development proceeded simultaneously along many parallel lines, it is interesting and instructive to take the investigation of the properties of gases, and to endeavour to trace the steps by which the true theory was finally attained.

10. _Thermal Properties of Gases._--The most characteristic property of a gaseous or elastic fluid, namely, the elasticity, or resistance to compression, was first investigated scientifically by Robert Boyle (1662), who showed that the pressure p of a given mass of gas varied inversely as the volume v, provided that the temperature remained constant. This is generally expressed by the formula pv = C, where C is a constant for any given temperature, and v is taken to represent the specific volume, or the volume of unit mass, of the gas at the given pressure and temperature. Boyle was well aware of the effect of heat in expanding a gas, but he was unable to investigate this properly as no thermometric scale had been defined at that date. According to Boyle's law, when a mass of gas is compressed by a small amount at constant temperature, the percentage increase of pressure is equal to the percentage diminution of volume (if the compression is v/100, the increase of pressure is very nearly p/100). Adopting this law, Newton showed, by a most ingenious piece of reasoning (_Principia_, ii., sect. 8), that the velocity of sound in air should be equal to the velocity acquired by a body falling under gravity through a distance equal to half the height of the atmosphere, considered as being of uniform density equal to that at the surface of the earth. This gave the result 918 ft. per sec. (280 metres per sec.) for the velocity at the freezing point. Newton was aware that the actual velocity of sound was somewhat greater than this, but supposed that the difference might be due in some way to the size of the air particles, of which no account could be taken in the calculation. The first accurate measurement of the velocity of sound by the French Academie des Sciences in 1738 gave the value 332 metres per sec. as the velocity at 0 deg. C. The true explanation of the discrepancy was not discovered till nearly 100 years later.

The law of expansion of gases with change of temperature was investigated by Dalton and Gay-Lussac (1802), who found that the volume of a gas under constant pressure increased by 1/267th part of its volume at 0 deg. C. for each 1 deg. C. rise in temperature. This value was generally assumed in all calculations for nearly 50 years. More exact researches, especially those of Regnault, at a later date, showed that the law was very nearly correct for all permanent gases, but that the value of the coefficient should be 1/273rd. According to this law the volume of a gas at any temperature t deg. C. should be proportional to 273 + t, i.e. to the temperature reckoned from a zero 273 deg. below that of the Centigrade scale, which was called the absolute zero of the gas thermometer. If T = 273 + t, denotes the temperature measured from this zero, the law of expansion of a gas may be combined with Boyle's law in the simple formula

pv = RT (1)

which is generally taken as the expression of the gaseous laws. If equal volumes of different gases are taken at the same temperature and pressure, it follows that the constant R is the same for all gases. If equal masses are taken, the value of the constant R for different gases varies inversely as the molecular weight or as the density relative to hydrogen.

Dalton also investigated the laws of vapours, and of mixtures of gases and vapours. He found that condensible vapours approximately followed Boyle's law when compressed, until the condensation pressure was reached, at which the vapour liquefied without further increase of pressure. He found that when a liquid was introduced into a closed space, and allowed to evaporate until the space was saturated with the vapour and evaporation ceased, the increase of pressure in the space was equal to the condensation pressure of the vapour, and did not depend on the volume of the space or the presence of any other gas or vapour provided that there was no solution or chemical action. He showed that the condensation or saturation-pressure of a vapour depended only on the temperature, and increased by nearly the same fraction of itself per degree rise of temperature, and that the pressures of different vapours were nearly the same at equal distances from their boiling points. The increase of pressure per degree C. at the boiling point was about 1/28th of 760 mm. or 27.2 mm., but increased in geometrical progression with rise of temperature. These results of Dalton's were confirmed, and in part corrected, as regards increase of vapour-pressure, by Gay-Lussac, Dulong, Regnault and other investigators, but were found to be as close an approximation to the truth as could be obtained with such simple expressions. More accurate empirical expressions for the increase of vapour-pressure of a liquid with temperature were soon obtained by Thomas Young, J. P. L. A. Roche and others, but the explanation of the relation was not arrived at until a much later date (see VAPORIZATION).