They found that the cooling effect of convection, unlike that of
radiation, was independent of the nature of the surface of the
thermometer, whether silvered or blackened, that it varied as some power
c of the pressure p, and that it was independent of the absolute
temperature of the enclosure, but varied as the excess temperature (t -
t0) raised to the power 1.233. This highly artificial result undoubtedly
contains some elements of truth, but could only be applied to
experiments similar to those from which it was derived. F. Herve de la
Provostaye and P. Q. Desains (_Ann. Chim. Phys._, 1846, 16, p. 337), in
repeating these experiments under various conditions, found that the
coefficients A and B were to some extent dependent on the temperature,
and that the manner in which the cooling effect varied with the pressure
depended on the form and size of the enclosure. It is evident that this
should be the case, since the cooling effect of the gas depends partly
on convective currents. which are necessarily greatly modified by the
form of the enclosure in a manner which it would appear hopeless to
attempt to represent by any general formula.
28. _Surface Emissivity._--The same remark applies to many attempts
which have since been made to determine the general value of the
constant termed by Fourier and early writers the "exterior
conductibility," but now called the surface emissivity. This coefficient
represents the rate of loss of heat from a body per unit area of surface
per degree excess of temperature, and includes the effects of radiation,
convection and conduction. As already pointed out, the combined effect
will be nearly proportional to the excess of temperature in any given
case provided that the excess is small, but it is not necessarily
proportional to the extent of surface exposed except in the case of pure
radiation. The rate of loss by convection and conduction varies greatly
with the form of the surface, and, unless the enclosure is very large
compared with the cooling body, the effect depends also on the size and
form of the enclosure. Heat is necessarily communicated from the cooling
body to the layer of gas in contact with it by conduction. If the linear
dimensions of the body are small, as in the case of a fine wire, or if
it is separated from the enclosure by a thin layer of gas, the rate of
loss depends chiefly on conduction. For very fine metallic wires heated
by an electric current, W. E. Ayrton and H. Kilgour (_Phil. Trans._,
1892) showed that the rate of loss is nearly independent of the surface,
instead of being directly proportional to it. This should be the case,
as Porter has shown (_Phil. Mag._, March 1895), since the effect depends
mainly on conduction. The effects of conduction and radiation may be
approximately estimated if the conductivity of the gas and the nature
and forms of the surfaces of the body and enclosure are known, but the
effect of convection in any case can be determined only by experiment.
It has been found that the rate of cooling by a current of air is
approximately proportional to the velocity of the current, other things
being equal. It is obvious that this should be the case, but the result
cannot generally be applied to convection currents. Values which are
commonly given for the surface emissivity must therefore be accepted
with great reserve. They can be regarded only as approximate, and as
applicable only to cases precisely similar to those for which they were
experimentally obtained. There cannot be said to be any general law of
convection. The loss of heat is not necessarily proportional to the area
of the surface, and no general value of the coefficient can be given to
suit all cases. The laws of conduction and radiation admit of being more
precisely formulated, and their effects predicted, except in so far as
they are complicated by convection.
29. _Conduction of Heat._--The laws of transference of heat in the
interior of a solid body formed one of the earliest subjects of
mathematical and experimental treatment in the theory of heat. The law
assumed by Fourier was of the simplest possible type, but the
mathematical application, except in the simplest cases, was so difficult
as to require the development of a new mathematical method. Fourier
succeeded in showing how, by his method of analysis, the solution of any
given problem with regard to the flow of heat by conduction in any
material could be obtained in terms of a physical constant, the thermal
conductivity of the material, and that the results obtained by
experiment agreed in a qualitative manner with those predicted by his
theory. But the experimental determination of the actual values of these
constants presented formidable difficulties which were not surmounted
till a later date. The experimental methods and difficulties are
discussed in a special article on CONDUCTION OF HEAT. It will suffice
here to give a brief historical sketch, including a few of the more
important results by way of illustration.
30. _Comparison of Conducting Powers._--That the power of transmitting
heat by conduction varied widely in different materials was probably
known in a general way from prehistoric times. Empirical knowledge of
this kind is shown in the construction of many articles for heating,
cooking, &c., such as the copper soldering bolt, or the Norwegian
cooking-stove. One of the earliest experiments for making an actual
comparison of conducting powers was that suggested by Franklin, but
carried out by Jan Ingenhousz (_Journ. de phys._, 1789, 34, pp. 68 and
380). Exactly similar bars of different materials, glass, wood, metal,
&c., thinly coated with wax, were fixed in the side of a trough of
boiling water so as to project for equal distances through the side of
the trough into the external air. The wax coating was observed to melt
as the heat travelled along the bars, the distance from the trough to
which the wax was melted along each affording an approximate indication
of the distribution of temperature. When the temperature of each bar had
become stationary the heat which it gained by conduction from the trough
must be equal to the heat lost to the surrounding air, and must
therefore be approximately proportional to the distance to which the wax
had melted along the bar. But the temperature fall per unit length, or
the temperature-gradient, in each bar at the point where it emerged from
the trough would be inversely proportional to the same distance. For
equal temperature-gradients the quantities of heat conducted (or the
relative conducting powers of the bars) would therefore be proportional
to the squares of the distances to which the wax finally melted on each
bar. This was shown by Fourier and Despretz (_Ann. chim. phys._, 1822,
19, p. 97).
31. _Diffusion of Temperature._--It was shown in connexion with this
experiment by Sir H. Davy, and the experiment was later popularized by
John Tyndall, that the rate at which wax melted along the bar, or the
rate of propagation of a given temperature, during the first moments of
heating, as distinguished from the melting-distance finally attained,
depended on the specific heat as well as the conductivity. Short prisms
of iron and bismuth coated with wax were placed on a hot metal plate.
The wax was observed to melt first on the bismuth, although its
conductivity is less than that of iron. The reason is that its specific
heat is less than that of iron in the proportion of 3 to 11. The
densities of iron and bismuth being 7.8 and 9.8, the thermal capacities
of equal prisms will be in the ratio .86 for iron to .29 for bismuth. If
the prisms receive heat at equal rates, the bismuth will reach the
temperature of melting wax nearly three times as quickly as the iron. It
is often stated on the strength of this experiment that the rate of
propagation of a temperature wave, which depends on the ratio of the
conductivity to the specific heat per unit volume, is greater in bismuth
than in iron (e.g. Preston, _Heat_, p. 628). This is quite incorrect,
because the conductivity of iron is about six times that of bismuth, and
the rate of propagation of a temperature wave is therefore twice as
great in iron as in bismuth. The experiment in reality is misleading
because the rates of reception of heat by the prisms are limited by the
very imperfect contact with the hot metal plate, and are not
proportional to the respective conductivities. If the iron and bismuth
bars are properly faced and soldered to the top of a copper box (in
order to ensure good metallic contact, and exclude a non-conducting film
of air), and the box is then heated by steam, the rates of reception of
heat will be nearly proportional to the conductivities, and the wax will
melt nearly twice as fast along the iron as along the bismuth. A bar of
lead similarly treated will show a faster rate of propagation than iron,
because, although its conductivity is only half that of iron, its
specific heat per unit volume is 2.5 times smaller.
32. _Bad Conductors. Liquids and Gases._--Count Rumford (1792) compared
the conducting powers of substances used in clothing, such as wool and
cotton, fur and down, by observing the time which a thermometer took to
cool when embedded in a globe filled successively with the different
materials. The times of cooling observed for a given range varied from
1300 to 900 seconds for different materials. The low conducting power of
such materials is principally due to the presence of air in the
interstices, which is prevented from forming convection currents by the
presence of the fibrous material. Finely powdered silica is a very bad
conductor, but in the compact form of rock crystal it is as good a
conductor as some of the metals. According to the kinetic theory of
gases, the conductivity of a gas depends on molecular diffusion. Maxwell
estimated the conductivity of air at ordinary temperatures at about
20,000 times less than that of copper. This has been verified
experimentally by Kundt and Warburg, Stefan and Winkelmann, by taking
special precautions to eliminate the effects of convection currents and
radiation. It was for some time doubted whether a gas possessed any true
conductivity for heat. The experiment of T. Andrews, repeated by Grove,
and Magnus, showing that a wire heated by an electric current was raised
to a higher temperature in air than in hydrogen, was explained by
Tyndall as being due to the greater mobility of hydrogen which gave rise
to stronger convection currents. In reality the effect is due chiefly to
the greater velocity of motion of the ultimate molecules of hydrogen,
and is most marked if molar (as opposed to molecular) convection is
eliminated. Molecular convection or diffusion, which cannot be
distinguished experimentally from conduction, as it follows the same
law, is also the main cause of conduction of heat in liquids. Both in
liquids and gases the effects of convection currents are so much greater
than those of diffusion or conduction that the latter are very difficult
to measure, and, except in special cases, comparatively unimportant as
affecting the transference of heat. Owing to the difficulty of
eliminating the effects of radiation and convection, the results
obtained for the conductivities of liquids are somewhat discordant, and
there is in most cases great uncertainty whether the conductivity
increases or diminishes with rise of temperature. It would appear,
however, that liquids, such as water and glycerin, differ remarkably
little in conductivity in spite of enormous differences of viscosity.
The viscosity of a liquid diminishes very rapidly with rise of
temperature, without any marked change in the conductivity, whereas the
viscosity of a gas increases with rise of temperature, and is always
nearly proportional to the conductivity.
33. _Difficulty of Quantitative Estimation of Heat Transmitted._--The
conducting powers of different metals were compared by C. M. Despretz,
and later by G. H. Wiedemann and R. Franz, employing an extension of the
method of Jan Ingenhousz, in which the temperatures at different points
along a bar heated at one end were measured by thermometers or
thermocouples let into small holes in the bars, instead of being
measured at one point only by means of melting wax. These experiments
undoubtedly gave fairly accurate relative values, but did not permit the
calculation of the absolute amounts of heat transmitted. This was first
obtained by J. D. Forbes (_Brit. Assoc. Rep._, 1852; _Trans. Roy. Soc.
Ed._, 1862, 23, p. 133) by deducing the amount of heat lost to the
surrounding air from a separate experiment in which the rate of cooling
of the bar was observed (see CONDUCTION OF HEAT). Clement (_Ann. chim.
phys._, 1841) had previously attempted to determine the conductivities
of metals by observing the amount of heat transmitted by a plate with
one side exposed to steam at 100 deg. C., and the other side cooled by
water at 28 deg. C. Employing a copper plate 3 mm. thick, and assuming
that the two surfaces of the plate were at the same temperatures as the
water and the steam to which they were exposed, or that the
temperature-gradient in the metal was 72 deg. in 3 mm., he had thus
obtained a value which we now know to be nearly 200 times too small. The
actual temperature difference in the metal itself was really about 0.36
deg. C. The remainder of the 72 deg. drop was in the badly conducting
films of water and steam close to the metal surface. Similarly in a
boiler plate in contact with flame at 1500 deg. C. on one side and water
at, say, 150 deg. C. on the other, the actual difference of temperature
in the metal, even if it is an inch thick, is only a few degrees. The
metal, unless badly furred with incrustation, is but little hotter than
the water. It is immaterial so far as the transmission of heat is
concerned, whether the plates are iron or copper. The greater part of
the resistance to the passage of heat resides in a comparatively
quiescent film of gas close to the surface, through which film the heat
has to pass mainly by conduction. If a Bunsen flame, preferably coloured
with sodium, is observed impinging on a cold metal plate, it will be
seen to be separated from the plate by a dark space of a millimetre or
less, throughout which the temperature of the gas is lowered by its own
conductivity below the temperature of incandescence. There is no abrupt
change of temperature in passing from the gas to the metal, but a
continuous temperature-gradient from the temperature of the metal to
that of the flame. It is true that this gradient may be upwards of 1000
deg. C. per mm., but there is no discontinuity.
34. _Resistance of a Gas Film to the Passage of Heat._--It is possible
to make a rough estimate of the resistance of such a film to the passage
of heat through it. Taking the average conductivity of the gas in the
film as 10,000 times less than that of copper (about double the
conductivity of air at ordinary temperatures) a millimetre film would be
equivalent to a thickness of 10 metres of copper, or about 1.2 metres of
iron. Taking the temperature-gradient as 1000 deg. C. per mm. such a
film would transmit 1 gramme-calorie per sq. cm. per sec., or 36,000
kilo-calories per sq. metre per hour. With an area of 100 sq. cms. the
heat transmitted at this rate would raise a litre of water from 20 deg.
C. to 100 deg. C. in 800 secs. By experiment with a strong Bunsen flame
it takes from 8 to 10 minutes to do this, which would indicate that on
the above assumptions the equivalent thickness of quiescent film should
be rather less than 1 mm. in this case. The thickness of the film
diminishes with the velocity of the burning gases impinging on the
surface. This accounts for the rapidity of heating by a blowpipe flame,
which is not due to any great increase in temperature of the flame as
compared with a Bunsen. Similarly the efficiency of a boiler is but
slightly reduced if half the tubes are stopped up, because the increase
of draught through the remainder compensates partly for the diminished
heating surface. Some resistance to the passage of heat into a boiler is
also due to the water film on the inside. But this is of less account,
because the conductivity of water is much greater than that of air, and
because the film is continually broken up by the formation of steam,
which abstracts heat very rapidly.
35. _Heating by Condensation of Steam._--It is often stated that the
rate at which steam will condense on a metal surface at a temperature
below that corresponding to the saturation pressure of the steam is
practically infinite (e.g. Osborne Reynolds, _Proc. Roy. Soc. Ed._,
1873, p. 275), and conversely that the rate at which water will abstract
heat from a metal surface by the formation of steam (if the metal is
above the temperature of saturation of the steam) is limited only by the
rate at which the metal can supply heat by conduction to its surface
layer. The rate at which heat can be supplied by condensation of steam
appears to be much greater than that at which heat can be supplied by a
flame under ordinary conditions, but there is no reason to suppose that
it is infinite, or that any discontinuity exists. Experiments by H. L.
Callendar and J. T. Nicolson by three independent methods (_Proc. Inst.
Civ. Eng._, 1898, 131, p. 147; _Brit. Assoc. Rep._ p. 418) appear to
show that the rate of abstraction of heat by evaporation, or that of
communication of heat by condensation, depends chiefly on the difference
of temperature between the metal surface and the saturated steam, and is
nearly proportional to the temperature difference (not to the pressure
difference, as suggested by Reynolds) for such ranges of pressure as are
common in practice. The rate of heat transmission they observed was
equivalent to about 8 calories per sq. cm. per sec., for a difference of
20 deg. C. between the temperature of the metal surface and the
saturation temperature of the steam. This would correspond to a
condensation of 530 kilogrammes of steam at 100 deg. C. per sq. metre
per hour, or 109 lb. per sq. ft. per hour for the same difference of
temperature, values which are many times greater than those actually
obtained in ordinary surface condensers. The reason for this is that
there is generally some air mixed with the steam in a surface condenser,
which greatly retards the condensation. It is also difficult to keep the
temperature of the metal as much as 20 deg. C. below the temperature of
the steam unless a very free and copious circulation of cold water is
available. For the same difference of temperature, steam can supply heat
by condensation about a thousand times faster than hot air. This rate is
not often approached in practice, but the facility of generation and
transmission of steam, combined with its high latent heat and the
accuracy of control and regulation of temperature afforded, render it
one of the most convenient agents for the distribution of large
quantities of heat in all kinds of manufacturing processes.
36. _Spheroidal State._--An interesting contrast to the extreme rapidity
with which heat is abstracted by the evaporation of a liquid in contact
with a metal plate, is the so-called spheroidal state. A small drop of
liquid thrown on a red-hot metal plate assumes a spheroidal form, and
continues swimming about for some time, while it slowly evaporates at a
temperature somewhat below its boiling-point. The explanation is simply
that the liquid itself cannot come in actual contact with the metal
plate (especially if the latter is above the critical temperature), but
is separated from it by a badly conducting film of vapour, through
which, as we have seen, the heat is comparatively slowly transmitted
even if the difference of temperature is several hundred degrees. If the
metal plate is allowed to cool gradually, the drop remains suspended on
its cushion of vapour, until, in the case of water, a temperature of
about 200 deg. C. is reached, at which the liquid comes in contact with
the plate and boils explosively, reducing the temperature of the plate,
if thin, almost instantaneously to 100 deg. C. The temperature of the
metal is readily observed by a thermo-electric method, employing a
platinum dish with a platinum-rhodium wire soldered with gold to its
under side. The absence of contact between the liquid and the dish in
the spheroidal state may also be shown by connecting one terminal of a
galvanometer to the drop and the other through a battery to the dish,
and observing that no current passes until the drop boils.
37. _Early Theories of Radiation._--It was at one time supposed that
there were three distinct kinds of radiation--thermal, luminous and
actinic, combined in the radiation from a luminous source such as the
sun or a flame. The first gave rise to heat, the second to light and the
third to chemical action. The three kinds were partially separated by a
prism, the actinic rays being generally more refracted, and the thermal
rays less refracted than the luminous. This conception arose very
naturally from the observation that the feebly luminous blue and violet
rays produced the greatest photographic effects, which also showed the
existence of dark rays beyond the violet, whereas the brilliant yellow
and red were practically without action on the photographic plate. A
thermometer placed in the blue or violet showed no appreciable rise of
temperature, and even in the yellow the effect was hardly discernible.
The effect increased rapidly as the light faded towards the extreme red,
and reached a maximum beyond the extreme limits of the spectrum
(Herschel), showing that the greater part of the thermal radiation was
altogether non-luminous. It is now a commonplace that chemical action,
colour sensation and heat are merely different effects of one and the
same kind of radiation, the particular effect produced in each case
depending on the frequency and intensity of the vibration, and on the
nature of the substance on which it falls. When radiation is completely
absorbed by a black substance, it is converted into heat, the quantity
of heat produced being equivalent to the total energy of the radiation
absorbed, irrespective of the colour or frequency of the different rays.
The actinic or chemical effects, on the other hand, depend essentially
on some relation between the period of the vibration and the properties
of the substance acted on. The rays producing such effects are generally
those which are most strongly absorbed. The spectrum of chlorophyll, the
green colouring matter of plants, shows two very strong absorption bands
in the red. The red rays of corresponding period are found to be the
most active in promoting the growth of the plant. The chemically active
rays are not necessarily the shortest. Even photographic plates may be
made to respond to the red rays by staining them with pinachrome or some
other suitable dye.
The action of light rays on the retina is closely analogous to the
action on a photographic plate. The retina, like the plate, is sensitive
only to rays within certain restricted limits of frequency. The limits
of sensitiveness of each colour sensation are not exactly defined, but
vary slightly from one individual to another, especially in cases of
partial colour-blindness, and are modified by conditions of fatigue. We
are not here concerned with these important physiological and chemical
effects of radiation, but rather with the question of the conversion of
energy of radiation into heat, and with the laws of emission and
absorption of radiation in relation to temperature. We may here also
assume the identity of visible and invisible radiations from a heated
body in all their physical properties. It has been abundantly proved
that the invisible rays, like the visible, (1) are propagated in
straight lines in homogeneous media; (2) are reflected and diffused from
the surface of bodies according to the same law; (3) travel with the
same velocity in free space, but with slightly different velocities in
denser media, being subject to the same law of refraction; (4) exhibit
all the phenomena of diffraction and interference which are
characteristic of wave-motion in general; (5) are capable of
polarization and double refraction; (6) exhibit similar effects of
selective absorption. These properties are more easily demonstrated in
the case of visible rays on account of the great sensitiveness of the
eye. But with the aid of the thermopile or other sensitive radiometer,
they may be shown to belong equally to all the radiations from a heated
body, even such as are thirty to fifty times slower in frequency than
the longest visible rays. The same physical properties have also been
shown to belong to electromagnetic waves excited by an electric
discharge, whatever the frequency, thus including all kinds of aetherial
radiation in the same category as light.
38. _Theory of Exchanges._--The apparent concentration of cold by a
concave mirror, observed by G. B. Porta and rediscovered by M. A.
Pictet, led to the enunciation of the theory of exchanges by Pierre
Prevost in 1791. Prevost's leading idea was that all bodies, whether
cold or hot, are constantly radiating heat. Heat equilibrium, he says,
consists in an equality of exchange. When equilibrium is interfered
with, it is re-established by inequalities of exchange. If into a
locality at uniform temperature a refracting or reflecting body is
introduced, it has no effect in the way of changing the temperature at
any point of that locality. A reflecting body, heated or cooled in the
interior of such an enclosure, will acquire the surrounding temperature
more slowly than would a non-reflector, and will less affect another
body placed at a little distance, but will not affect the final equality
of temperature. Apparent radiation of cold, as from a block of ice to a
thermometer placed near it, is due to the fact that the thermometer
being at a higher temperature sends more heat to the ice than it
received back from it. Although Prevost does not make the statement in
so many words, it is clear that he regards the radiation from a body as
depending only on its own nature and temperature, and as independent of
the nature and presence of any adjacent body. Heat equilibrium in an
enclosure of constant temperature such as is here postulated by Prevost,
has often been regarded as a consequence of Carnot's principle. Since
difference of temperature is required for transforming heat into work,
no work could be obtained from heat in such a system, and no spontaneous
changes of temperature can take place, as any such changes might be
utilized for the production of work. This line of reasoning does not
appear quite satisfactory, because it is tacitly assumed, in the
reasoning by which Carnot's principle was established, as a result of
universal experience, that a number of bodies within the same impervious
enclosure, which contains no source of heat, will ultimately acquire the
same temperature, and that difference of temperature is required to
produce flow of heat. Thus although we may regard the equilibrium in
such an enclosure as being due to equal exchanges of heat in all
directions, the equal and opposite streams of radiation annul and
neutralize each other in such a way that no actual transfer of energy in
any direction takes place. The state of the medium is everywhere the
same in such an enclosure, but its energy of agitation per unit volume
is a function of the temperature, and is such that it would not be in
equilibrium with any body at a different temperature.
39. _"Full" and Selective Radiation. Correspondence of Emission and
Absorption._--The most obvious difficulties in the way of this theory
arise from the fact that nearly all radiation is more or less selective
in character, as regards the quality and frequency of the rays emitted
and absorbed. It was shown by J. Leslie, M. Melloni and other
experimentalists that many substances such as glass and water, which are
very transparent to visible rays, are extremely opaque to much of the
invisible radiation of lower frequency; and that polished metals, which
are perfect reflectors, are very feeble radiators as compared with dull
or black bodies at the same temperature. If two bodies emit rays of
different periods in different proportions, it is not at first sight
easy to see how their radiations can balance each other at the same
temperature. The key to all such difficulties lies in the fundamental
conception, so strongly insisted on by Balfour Stewart, of the absolute
uniformity (qualitative as well as quantitative) of the full or complete
radiation stream inside an impervious enclosure of uniform temperature.
It follows from this conception that the proportion of the full
radiation stream absorbed by any body in such an enclosure must be
exactly compensated in quality as well as quantity by the proportion
emitted, or that the emissive and absorptive powers of any body at a
given temperature must be precisely equal. A good reflector, like a
polished metal, must also be a feeble radiator and absorber. Of the
incident radiation it absorbs a small fraction and reflects the
remainder, which together with the radiation emitted (being precisely
equal to that absorbed) makes up the full radiation stream. A partly
transparent material, like glass, absorbs part of the full radiation and
transmits part. But it emits rays precisely equal in quality and
intensity to those which it absorbs, which together with the transmitted
portion make up the full stream. The ideal black body or perfect
radiator is a body which absorbs all the radiation incident on it. The
rays emitted from such a body at any temperature must be equal to the
full radiation stream in an isothermal enclosure at the same
temperature. Lampblack, which may absorb between 98 to 99% of the
incident radiation, is generally taken as the type of a black body. But
a closer approximation to full radiation may be obtained by employing a
hollow vessel the internal walls of which are blackened and maintained
at a uniform temperature by a steam jacket or other suitable means. If a
relatively small hole is made in the side of such a vessel, the
radiation proceeding through the aperture will be the full radiation
corresponding to the temperature. Such a vessel is also a perfect
absorber. Of radiation entering through the aperture an infinitesimal
fraction only could possibly emerge by successive reflection even if the
sides were of polished metal internally. A thin platinum tube heated by
an electric current appears feebly luminous as compared with a blackened
tube at the same temperature. But if a small hole is made in the side of
the polished tube, the light proceeding through the hole appears
brighter than the blackened tube, as though the inside of the tube were
much hotter than the outside, which is not the case to any appreciable
extent if the tube is thin. The radiation proceeding through the hole is
nearly that of a perfectly black body if the hole is small. If there
were no hole the internal stream of radiation would be exactly that of a
black body at the same temperature however perfect the reflecting power,
or however low the emissive power of the walls, because the defect in
emissive power would be exactly compensated by the internal reflection.
Balfour Stewart gave a number of striking illustrations of the
qualitative identity of emission and absorption of a substance. Pieces
of coloured glass placed in a fire appear to lose their colour when at
the same temperature as the coals behind them, because they compensate
exactly for their selective absorption by radiating chiefly those
colours which they absorb. Rocksalt is remarkably transparent to thermal
radiation of nearly all kinds, but it is extremely opaque to radiation
from a heated plate of rocksalt, because it emits when heated precisely
those rays which it absorbs. A plate of tourmaline cut parallel to the
axis absorbs almost completely light polarized in a plane parallel to
the axis, but transmits freely light polarized in a perpendicular plane.
When heated its radiation is polarized in the same plane as the
radiation which it absorbs. In the case of incandescent vapours, the
exact correspondence of emission and absorption as regards wave-length
of frequency of the light emitted and absorbed forms the foundation of
the science of spectrum analysis. Fraunhofer had noticed the coincidence
of a pair of bright yellow lines seen in the spectrum of a candle flame
with the dark D lines in the solar spectrum, a coincidence which was
afterwards more exactly verified by W. A. Miller. Foucault found that
the flame of the electric arc showed the same lines bright in its
spectrum, and proved that they appeared as dark lines in the otherwise
continuous spectrum when the light from the carbon poles was transmitted
through the arc. Stokes gave a dynamical explanation of the phenomenon
and illustrated it by the analogous case of resonance in sound.
Kirchhoff completed the explanation (_Phil. Mag._, 1860) of the dark
lines in the solar spectrum by showing that the reversal of the spectral
lines depended on the fact that the body of the sun giving the
continuous spectrum was at a higher temperature than the absorbing layer
of gases surrounding it. Whatever be the nature of the selective
radiation from a body, the radiation of light of any particular
wave-length cannot be greater than a certain fraction E of the radiation
R of the same wave-length from a black body at the same temperature. The
fraction E measures the emissive power of the body for that particular
wave-length, and cannot be greater than unity. The same fraction, by the
principle of equality of emissive and absorptive powers, will measure
the proportion absorbed of incident radiation R'. If the black body
emitting the radiation R' is at the same temperature as the absorbing
layer, R = R', the emission balances the absorption, and the line will
appear neither bright nor dark. If the source and the absorbing layer
are at different temperatures, the radiation absorbed will be ER', and
that transmitted will be R' - ER'. To this must be added the radiation
emitted by the absorbing layer, namely ER, giving R' - E(R' - R). The
lines will appear darker than the background R' if R' is greater than R,
but bright if the reverse is the case. The D lines are dark in the sun
because the photosphere is much hotter than the reversing layer. They
appear bright in the candle-flame because the outside mantle of the
flame, in which the sodium burns and combustion is complete, is hotter
than the inner reducing flame containing the incandescent particles of
carbon which give rise to the continuous spectrum. This qualitative
identity of emission and absorption as regards wave-length can be most
exactly and easily verified for luminous rays, and we are justified in
assuming that the relation holds with the same exactitude for
non-luminous rays, although in many cases the experimental proof is less
complete and exact.
40. _Diathermancy._--A great array of data with regard to the
transmissive power or diathermancy of transparent substances for the
heat radiated from various sources at different temperatures were
collected by Melloni, Tyndall, Magnus and other experimentalists. The
measurements were chiefly of a qualitative character, and were made by
interposing between the source and a thermopile a layer or plate of the
substance to be examined. This method lacked quantitative precision, but
led to a number of striking and interesting results, which are admirably
set forth in Tyndall's _Heat_. It also gave rise to many curious
discrepancies, some of which were recognized as being due to selective
absorption, while others are probably to be explained by imperfections
in the methods of experiment adopted. The general result of such
researches was to show that substances, like water, alum and glass,
which are practically opaque to radiation from a source at low
temperature, such as a vessel filled with boiling water, transmit an
increasing percentage of the radiation when the temperature of the
source is increased. This is what would be expected, as these substances
are very transparent to visible rays. That the proportion transmitted is
not merely a question of the temperature of the source, but also of the
quality of the radiation, was shown by a number of experiments. For
instance, K. H. Knoblauch (_Pogg. Ann._, 1847) found that a plate of
glass interposed between a spirit lamp and a thermopile intercepts a
larger proportion of the radiation from the flame itself than of the
radiation from a platinum spiral heated in the flame, although the
spiral is undoubtedly at a lower temperature than the flame. The
explanation is that the spiral is a fairly good radiator of the visible
rays to which the glass is transparent, but a bad radiator of the
invisible rays absorbed by the glass which constitute the greater
portion of the heat-radiation from the feebly luminous flame.
[Illustration: FIG. 6.--Tyndall's Apparatus for observing absorption of
heat by gas and vapours.]
Assuming that the radiation from the source under investigation is
qualitatively determinate, like that of a black body at a given
temperature, the proportion transmitted by plates of various substances
may easily be measured and tabulated for given plates and sources. But
owing to the highly selective character of the radiation and absorption,
it is impossible to give any general relation between the thickness of
the absorbing plate or layer and the proportion of the total energy
absorbed. For these reasons the relative diathermancies of different
materials do not admit of any simple numerical statement as physical
constants, though many of the qualitative results obtained are very
striking. Among the most interesting experiments were those of Tyndall,
on the absorptive powers of gases and vapours, which led to a good deal
of controversy at the time, owing to the difficulty of the experiments,
and the contradictory results obtained by other observers. The
arrangement employed by Tyndall for these measurements is shown in Fig.
6. A brass tube AB, polished inside, and closed with plates of highly
diathermanous rocksalt at either end, was fitted with stopcocks C and D
for exhausting and admitting air or other gases or vapours. The source
of heat S was usually a plate of copper heated by a Bunsen burner, or a
Leslie cube containing boiling water as shown at E. To obtain greater
sensitiveness for differential measurements, the radiation through the
tube AB incident on one face of the pile P was balanced against the
radiation from a Leslie cube on the other face of the pile by means of
an adjustable screen H. The radiation on the two faces of the pile being
thus balanced with the tube exhausted, Tyndall found that the admission
of dry air into the tube produced practically no absorption of the
radiation, whereas compound gases such as carbonic acid, ethylene or
ammonia absorbed 20 to 90%, and a trace of aqueous vapour in the air
increased its absorption 50 to 100 times. H. G. Magnus, on the other
hand, employing a thermopile and a source of heat, both of which were
enclosed in the same exhausted receiver, in order to avoid interposing
any rocksalt or other plates between the source and the pile, found an
absorption of 11% on admitting dry air, but could not detect any
difference whether the air were dry or moist. Tyndall suggested that the
apparent absorption observed by Magnus may have been due to the cooling
of his radiating surface by convection, which is a very probable source
of error in this method of experiment. Magnus considered that the
remarkable effect of aqueous vapour observed by Tyndall might have been
caused by condensation on the polished internal walls of his
experimental tube, or on the rocksalt plates at either end.[7] The
question of the relative diathermancy of air and aqueous vapour for
radiation from the sun to the earth and from the earth into space is one
of great interest and importance in meteorology. Assuming with Magnus
that at least 10% of the heat from a source at 100 deg. C. is absorbed in
passing through a single foot of air, a very moderate thickness of
atmosphere should suffice to absorb practically all the heat radiated
from the earth into space. This could not be reconciled with well-known
facts in regard to terrestrial radiation, and it was generally
recognized that the result found by Magnus must be erroneous. Tyndall's
experiment on the great diathermancy of dry air agreed much better with
meteorological phenomena, but he appears to have exaggerated the effect
of aqueous vapour. He concluded from his experiments that the water
vapour present in the air absorbs at least 10% of the heat radiated from
the earth within 10 ft. of its surface, and that the absorptive power of
the vapour is about 17,000 times that of air at the same pressure. If
the absorption of aqueous vapour were really of this order of magnitude,
it would exert a far greater effect in modifying climate than is
actually observed to be the case. Radiation is observed to take place
freely through the atmosphere at times when the proportion of aqueous
vapour is such as would practically stop all radiation if Tyndall's
results were correct. The very careful experiments of E. Lecher and J.
Pernter (_Phil. Mag._, Jan. 1881) confirmed Tyndall's observations on
the absorptive powers of gases and vapours satisfactorily in nearly all
cases with the single exception of aqueous vapour. They found that there
was no appreciable absorption of heat from a source at 100 deg. C. in
passing through 1 ft. of air (whether dry or moist), but that CO and CO2
at atmospheric pressure absorbed about 8%, and ethylene (olefiant gas)
about 50% in the same distance; the vapours of alcohol and ether showed
absorptive powers of the same order as that of ethylene. They confirmed
Tyndall's important result that the absorption does not diminish in
proportion to the pressure, being much greater in proportion for smaller
pressures in consequence of the selective character of the effect. They
also supported his conclusion that absorptive power increases with the
complexity of the molecule. But they could not detect any absorption by
water vapour at a pressure of 7 mm., though alcohol at the same pressure
absorbed 3% and acetic acid 10%. Later researches, especially those of
S. P. Langley with the spectro-bolometer on the infra-red spectrum of
sunlight, demonstrated the existence of marked absorption bands, some of
which are due to water vapour. From the character of these bands and the
manner in which they vary with the state of the air and the thickness
traversed, it may be inferred that absorption by water vapour plays an
important part in meteorology, but that it is too small to be readily
detected by laboratory experiments in a 4 ft. tube, without the aid of
spectrum analysis.
41. _Relation between Radiation and Temperature._--Assuming, in
accordance with the reasoning of Balfour Stewart and Kirchhoff, that the
radiation stream inside an impervious enclosure at a uniform temperature
is independent of the nature of the walls of the enclosure, and is the
same for all substances at the same temperature, it follows that the
full stream of radiation in such an enclosure, or the radiation emitted
by an ideal black body or full radiator, is a function of the
temperature only. The form of this function may be determined
experimentally by observing the radiation between two black bodies at
different temperatures, which will be proportional to the difference of
the full radiation streams corresponding to their several temperatures.
The law now generally accepted was first proposed by Stefan as an
empirical relation. Tyndall had found that the radiation from a white
hot platinum wire at 1200 deg. C. was 11.7 times its radiation when dull
red at 525 deg. C. Stefan (_Wien. Akad. Ber._, 1879, 79, p. 421) noticed
that the ratio 11.7 is nearly that of the fourth power of the absolute
temperatures as estimated by Tyndall. On making the somewhat different
assumption that the radiation between two bodies varied as the
difference of the fourth powers of their absolute temperatures, he found
that it satisfied approximately the experiments of Dulong and Petit and
other observers. According to this law the radiation between a black
body at a temperature [theta] and a black enclosure or a black
radiometer at a temperature [theta]0 should be proportional to
([theta]^4 - [theta]0^4). The law was very simple and convenient in
form, but it rested so far on very insecure foundations. The
temperatures given by Tyndall were merely estimated from the colour of
the light emitted, and might have been some hundred degrees in error. We
now know that the radiation from polished platinum is of a highly
selective character, and varies more nearly as the fifth power of the
absolute temperature. The agreement of the fourth power law with
Tyndall's experiment appears therefore to be due to a purely accidental
error in estimating the temperatures of the wire. Stefan also found a
very fair agreement with Draper's observations of the intensity of
radiation from a platinum wire, in which the temperature of the wire was
deduced from the expansion. Here again the apparent agreement was
largely due to errors in estimating the temperature, arising from the
fact that the coefficient of expansion of platinum increases
considerably with rise of temperature. So far as the experimental
results available at that time were concerned, Stefan's law could be
regarded only as an empirical expression of doubtful significance. But
it received a much greater importance from theoretical investigations
which were even then in progress. James Clerk Maxwell (_Electricity and
Magnetism_, 1873) had shown that a directed beam of electromagnetic
radiation or light incident normally on an absorbing surface should
produce a mechanical pressure equal to the energy of the radiation per
unit volume. A. G. Bartoli (1875) took up this idea and made it the
basis of a thermodynamic treatment of radiation. P. N. Lebedew in 1900,
and E. F. Nichols and G. F. Hull in 1901, proved the existence of this
pressure by direct experiments. L. Boltzmann (1884) employing radiation
as the working substance in a Carnot cycle, showed that the energy of
full radiation at any temperature per unit volume should be proportional
to the fourth power of the absolute temperature. This law was first
verified in a satisfactory manner by Heinrich Schneebeli (_Wied. Ann._,
1884, 22, p. 30). He observed the radiation from the bulb of an air
thermometer heated to known temperatures through a small aperture in the
walls of the furnace. With this arrangement the radiation was very
nearly that of a black body. Measurements by J. T. Bottomley, August
Schleiermacher, L. C. H. F. Paschen and others of the radiation from
electrically heated platinum, failed to give concordant results on
account of differences in the quality of the radiation, the importance
of which was not fully realized at first. Later researches by Paschen
with improved methods verified the law, and greatly extended our
knowledge of radiation in other directions. One of the most complete
series of experiments on the relation between full radiation and
temperature is that of O. R. Lummer and Ernst Pringsheim (_Ann. Phys._,
1897, 63, p. 395). They employed an aperture in the side of an enclosure
at uniform temperature as the source of radiation, and compared the
intensities at different temperatures by means of a bolometer. The
fourth power law was well satisfied throughout the whole range of their
experiments from -190 deg. C. to 2300 deg. C. According to this law, the
rate of loss of heat by radiation R from a body of emissive power E and
surface S at a temperature [theta] in an enclosure at [theta]0 is given
by the formula
R = [sigma]ES([theta]^4 - [theta]0^4),
where [sigma] is the radiation constant. The absolute value of [sigma]
was determined by F. Kurlbaum using an electric compensation method
(_Wied. Ann._, 1898, 65, p. 746), in which the radiation received by a
bolometer from a black body at a known temperature was measured by
finding the electric current required to produce the same rise of
temperature in the bolometer. K. Angstrom employed a similar method for
solar radiation. Kurlbaum gives the value [sigma] = 5.32 X 10^(-5) ergs
per sq. cm. per sec. C. Christiansen (_Wied. Ann._, 1883, 19, p. 267)
had previously found a value about 5% smaller, by observing the rate of
cooling of a copper plate of known thermal capacity, which is probably a
less accurate method.
42. _Theoretical Proof of the Fourth Power Law._--The proof given by
Boltzmann may be somewhat simplified if we observe that full radiation
in an enclosure at constant temperature behaves exactly like a
saturated vapour, and must therefore obey Carnot's or Clapeyron's
equation given in section 17. The energy of radiation per unit volume,
and the radiation-pressure at any temperature, are functions of the
temperature only, like the pressure of a saturated vapour. If the
volume of the enclosure is increased by any finite amount, the
temperature remaining the same, radiation is given off from the walls
so as to fill the space to the same pressure as before. The heat
absorbed when the volume is increased corresponds with the latent heat
of vaporization. In the case of radiation, as in the case of a vapour,
the latent heat consists partly of internal energy of formation and
partly of external work of expansion at constant pressure. Since in
the case of full or undirected radiation the pressure is one-third of
the energy per unit volume, the external work for any expansion is
one-third of the internal energy added. The latent heat absorbed is,
therefore, four times the external work of expansion. Since the
external work is the product of the pressure P and the increase of
volume V, the latent heat per unit increase of volume is four times
the pressure. But by Carnot's equation the latent heat of a saturated
vapour per unit increase of volume is equal to the rate of increase of
saturation-pressure per degree divided by Carnot's function or
multiplied by the absolute temperature. Expressed in symbols we have,
[theta](dP/d[theta]) = L/V = 4P,
where (dP/d[theta]) represents the rate of increase of pressure. This
equation shows that the percentage rate of increase of pressure is
four times the percentage rate of increase of temperature, or that if
the temperature is increased by 1%, the pressure is increased by 4%.
This is equivalent to the statement that the pressure varies as the
fourth power of the temperature, a result which is mathematically
deduced by integrating the equation.
43. _Wien's Displacement Law._--Assuming that the fourth power law gives
the quantity of full radiation at any temperature, it remains to
determine how the quality of the radiation varies with the temperature,
since as we have seen both quantity and quality are determinate. This
question may be regarded as consisting of two parts. (1) How is the
wave-length or frequency of any given kind of radiation changed when its
temperature is altered? (2) What is the form of the curve expressing the
distribution of energy between the various wave-lengths in the spectrum
of full radiation, or what is the distribution of heat in the spectrum?
The researches of Tyndall, Draper, Langley and other investigators had
shown that while the energy of radiation of each frequency increased
with rise of temperature, the maximum of intensity was shifted or
displaced along the spectrum in the direction of shorter wave-lengths or
higher frequencies. W. Wien (_Ann. Phys._, 1898, 58, p. 662), applying
Doppler's principle to the adiabatic compression of radiation in a
perfectly reflecting enclosure, deduced that the wave-length of each
constituent of the radiation should be shortened in proportion to the
rise of temperature produced by the compression, in such a manner that
the product [lambda][theta] of wave-length and the absolute temperature
should remain constant. According to this relation, which is known as
Wien's Displacement Law, the frequency corresponding to the maximum
ordinate of the energy curve of the normal spectrum of full radiation
should vary directly (or the wave-length inversely) as the absolute
temperature, a result previously obtained by H. F. Weber (1888).
Paschen, and Lummer and Pringsheim verified this relation by observing
with a bolometer the intensity at different points in the spectrum
produced by a fluorite prism. The intensities were corrected and reduced
to a wave-length scale with the aid of Paschen's results on the
dispersion formula of fluorite (_Wied. Ann._, 1894, 53, p. 301). The
curves in fig. 7 illustrate results obtained by Lummer and Pringsheim
(_Ber. deut. phys. Ges._, 1899, 1, p. 34) at three different
temperatures, namely 1377 deg., 1087 deg. and 836 deg. absolute, plotted
on a wave-length base with a scale of microns ([mu]) or millionths of a
metre. The wave-lengths Oa, Ob, Oc, corresponding to the maximum
ordinates of each curve, vary inversely as the absolute temperatures
given. The constant value of the product [lambda][theta] at the maximum
point is found to be 2920. Thus for a temperature of 1000 deg. Abs. the
maximum is at wave-length 2.92 [mu]; at 2000 deg. the maximum is at 1.46
[mu].
44. _Form of the Curve representing the Distribution of Energy in the
Spectrum._--Assuming Wien's displacement law, it follows that the form
of the curve representing the distribution of energy in the spectrum of
full radiation should be the same for different temperatures with the
maximum displaced in proportion to the absolute temperature, and with
the total area increased in proportion to the fourth power of the
absolute temperature. Observations taken with a bolometer along the
length of a normal or wave-length spectrum, would give the form of the
curve plotted on a wave-length base. The height of the ordinate at each
point would represent the energy included between given limits of
wave-length, depending on the width of the bolometer strip and the slit.
Supposing that the bolometer strip had a width corresponding to .01
[mu], and were placed at 1.0 [mu] in the spectrum of radiation at 2000
deg. Abs., it would receive the energy corresponding to wave-lengths
between 1.00 and 1.01 [mu]. At a temperature of 1000 deg. Abs. the
corresponding part of the energy, by Wien's displacement law, would lie
between the limits 2.00 and 2.02 [mu], and the total energy between
these limits would be 16 times smaller. But the bolometer strip placed
at 2.0 [mu] would now receive only half of the energy, or the energy in
a band .01 [mu] wide, and the deflection would be 32 times less.
Corresponding ordinates of the curves at different temperatures will
therefore vary as the fifth power of the temperature, when the curves
are plotted on a wave-length base. The maximum ordinates in the curves
already given are found to vary as the fifth powers of the corresponding
temperatures. The equation representing the distribution of energy on a
wave-length base must be of the form
E = C[lambda]^(-5) F([lambda][theta]) =
C[theta]^5 ([lambda][theta])^(-5) F([lambda][theta])
where F([lambda][theta]) represents some function of the product of the
wave-length and temperature, which remains constant for corresponding
wave-lengths when [theta] is changed. If the curves were plotted on a
frequency base, owing to the change of scale, the maximum ordinates
would vary as the cube of the temperature instead of the fifth power,
but the form of the function F would remain unaltered. Reasoning on the
analogy of the distribution of velocities among the particles of a gas
on the kinetic theory, which is a very similar problem, Wien was led to
assume that the function F should be of the form e^(-c/[lambda][theta]),
where e is the base of Napierian logarithms, and c is a constant having
the value 14,600 if the wave-length is measured in microns [mu]. This
expression was found by Paschen to give a very good approximation to the
form of the curve obtained experimentally for those portions of the
visible and infra-red spectrum where observations could be most
accurately made. The formula was tested in two ways: (1) by plotting the
curves of distribution of energy in the spectrum for constant
temperatures as illustrated in fig. 7; (2) by plotting the energy
corresponding to a given wave-length as a function of the temperature.
Both methods gave very good agreement with Wien's formula for values of
the product [lambda][theta] not much exceeding 3000. A method of
isolating rays of great wave-length by successive reflection was devised
by H. Rubens and E. F. Nichols (_Wied. Ann._, 1897, 60, p. 418). They
found that quartz and fluorite possessed the property of selective
reflection for rays of wave-length 8.8 [mu] and 24 [mu] to 32 [mu]
respectively, so that after four to six reflections these rays could be
isolated from a source at any temperature in a state of considerable
purity. The residual impurity at any stage could be estimated by
interposing a thin plate of quartz or fluorite which completely
reflected or absorbed the residual rays, but allowed the impurity to
pass. H. Beckmann, under the direction of Rubens, investigated the
variation with temperature of the residual rays reflected from fluorite
employing sources from -80 deg. to 600 deg. C., and found the results
could not be represented by Wien's formula unless the constant c were
taken as 26,000 in place of 14,600. In their first series of
observations extending to 6 [mu] O. R. Lummer and E. Pringsheim (_Deut.
phys. Ges._, 1899, 1, p. 34) found systematic deviations indicating an
increase in the value of the constant c for long waves and high
temperatures. In a theoretical discussion of the subject, Lord Rayleigh
(_Phil. Mag._, 1900, 49, p. 539) pointed out that Wien's law would lead
to a limiting value C[lambda]^(-5), of the radiation corresponding to
any particular wave-length when the temperature increased to infinity,
whereas according to his view the radiation of great wave-length should
ultimately increase in direct proportion to the temperature. Lummer and
Pringsheim (_Deut. phys. Ges._, 1900, 2, p. 163) extended the range of
their observations to 18 [mu] by employing a prism of sylvine in place
of fluorite. They found deviations from Wien's formula increasing to
nearly 50% at 18 [mu], where, however, the observations were very
difficult on account of the smallness of the energy to be measured.
Rubens and F. Kurlbaum (_Ann. Phys._, 1901, 4, p. 649) extended the
residual reflection method to a temperature range from -190 deg. to 1500
deg. C., and employed the rays reflected from quartz 8.8 [mu], and
rocksalt 51 [mu], in addition to those from fluorite. It appeared from
these researches that the rays of great wave-length from a source at a
high temperature tended to vary in the limit directly as the absolute
temperature of the source, as suggested by Lord Rayleigh, and could not
be represented by Wien's formula with any value of the constant c. The
simplest type of formula satisfying the required conditions is that
proposed by Max Planck (_Ann. Phys._, 1901, 4, p. 553) namely,
E = C[lambda]^(-5) (e^c/[lambda][theta] - 1)^(-1),
[Illustration: FIG. 7.--Distribution of energy in the spectrum of a
black body.]
[Illustration: FIG. 8.--Distribution of energy in the spectrum of full
radiation at 2000 deg. Abs. according to formulae of Planck & Wien.]
which agrees with Wien's formula when [theta] is small, where Wien's
formula is known to be satisfactory, but approaches the limiting form E
= C[lambda]^(-4)[theta]/c, when [theta] is large, thus satisfying the
condition proposed by Lord Rayleigh. The theoretical interpretation of
this formula remains to some extent a matter of future investigation,
but it appears to satisfy experiment within the limits of observational
error. In order to compare Planck's formula graphically with Wien's, the
distribution curves corresponding to both formulae are plotted in fig. 8
for a temperature of 2000 deg. abs., taking the value of the constant c
= 14,600 with a scale of wave-length in microns [mu]. The curves in fig.
9 illustrate the difference between the two formulae for the variation
of the intensity of radiation corresponding to a fixed wave-length 30
[mu]. Assuming Wien's displacement law, the curves may be applied to
find the energy for any other wave-length or temperature, by simply
altering the wave-length scale in inverse ratio to the temperature, or
vice versa. Thus to find the distribution curve for 1000 deg. abs., it
is only necessary to multiply all the numbers in the wave-length scale
of fig. 8 by 2; or to find the variation curve for wave-length 60 [mu],
the numbers on the temperature scale of fig. 9 should be divided by 2.
The ordinate scales must be increased in proportion to the fifth power
of the temperature, or inversely as the fifth power of the wave-length
respectively in figs. 8 and 9 if comparative results are required for
different temperatures or wave-lengths. The results hitherto obtained
for cases other than full radiation are not sufficiently simple and
definite to admit of profitable discussion in the present article.
[Illustration: FIG. 9.--Variation of energy of radiation corresponding
to wave-length 30 [mu], with temperature of source.]
BIBLIOGRAPHY.--It would not be possible, within the limits of an
article like the present, to give tables of the specific thermal
properties of different substances so far as they have been
ascertained by experiment. To be of any use, such tables require to be
extremely detailed, with very full references and explanations with
regard to the value of the experimental evidence, and the limits
within which the results may be relied on. The quantity of material
available is so enormous and its value so varied, that the most
elaborate tables still require reference to the original authorities.
Much information will be found collected in Landolt and Bornstein's
_Physical and Chemical Tables_ (Berlin, 1905). Shorter tables, such as
Everett's _Units and Physical Constants_, are useful as illustrations
of a system, but are not sufficiently complete for use in scientific
investigations. Some of the larger works of reference, such as A. A.
Winkelmann's _Handbuch der Physik_, contain fairly complete tables of
specific properties, but these tables occupy so much space, and are so
misleading if incomplete, that they are generally omitted in
theoretical textbooks.
Among older textbooks on heat, Tyndall's _Heat_ may be recommended for
its vivid popular interest, and Balfour Stewart's _Heat_ for early
theories of radiation. Maxwell's _Theory of Heat_ and Tait's _Heat_
give a broad and philosophical survey of the subject. Among modern
textbooks, Preston's _Theory of Heat_ and Poynting and Thomson's
_Heat_ are the best known, and have been brought well up to date.
Sections on heat are included in all the general textbooks of Physics,
such as those of Deschanel (translated by Everett), Ganot (translated
by Atkinson), Daniell, Watson, &c. Of the original investigations on
the subject, the most important have already been cited. Others will
be found in the collected papers of Joule, Kelvin and Maxwell.
Treatises on special branches of the subject, such as Fourier's
_Conduction of Heat_, are referred to in the separate articles in this
encyclopaedia dealing with recent progress, of which the following is
a list: CALORIMETRY, CONDENSATION OF GASES, CONDUCTION OF HEAT,
DIFFUSION, ENERGETICS, FUSION, LIQUID GASES, RADIATION, RADIOMETER,
SOLUTION, THERMODYNAMICS, THERMOELECTRICITY, THERMOMETRY,
VAPORIZATION. For the practical aspects of heating see HEATING.
(H. L. C.)