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 rescarches 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. 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 FIG. 6.-Tyndall's Apparatus for observing absorption of heat by gas and vapours. 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° 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° 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 protube AB, polished inside, and closed with plates of highly portion to the pressure, being much greater in proportion for diathermanous rocksalt at either end, was fitted with stopcocks the effect. They also supported his conclusion that absorptive smaller pressures in consequence of the selective character of 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 power increases with the complexity of the molecule. But they could not detect any absorption by water vapour at a pressure by a Bunsen burner, or a Leslie cube containing boiling water as shown at E. To obtain greater sensitiveness for differential of 7 mm., though alcohol at the same pressure absorbed 3% and acetic acid 10%. Later researches, especially those of measurements, the radiation through the tube AB incident on S. P. Langley with the spectro-bolometer on the infra-red 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 adjust-spectrum of sunlight, demonstrated the existence of marked able screen H. The radiation on the two faces of the pile being From the character of these bands and the manner in which absorption bands, some of which are due to water vapour. thus balanced with the tube exhausted, Tyndall found that the admission of dry air into the tube produced practically no absorp- they vary with the state of the air and the thickness traversed, tion of the radiation, whereas compound gases such as carbonic it may be inferred that absorption by water vapour plays an acid, ethylene or ammonia absorbed 20 to 90%, and a trace important part in meteorology, but that it is too small to be of aqueous vapour in the air increased its absorption 50 to 100 temperature of the plate. Assuming that the vapour pressure of times. H. G. Magnus, on the other hand, employing a thermopile the saturated salt solution is only half that of pure water, it would and a source of heat, both of which were enclosed in the same plates in saturated air at 15° C. It is only fair to say that the laws require an elevation of temperature of 10° C. to dry the rocksalt exhausted receiver, in order to avoid interposing any rocksalt of the vapour pressures of solutions were unknown in Tyndall's or other plates between the source and the pile, found an absorp- time, and that it was usual to assume that the plates would not tion of 11% on admitting dry air, but could not detect any become wetted until the dew-point was reached. The writer has difference whether the air were dry or moist. Tyndall suggested tubes in the possession of the Royal College of Science, fitted with repeated Tyndall's experiments with a facsimile of one of Tyndall's that the apparent absorption observed by Magnus may have plates of rocksalt cut from the same block as Tyndall's, and therefore been due to the cooling of his radiating surface by convection, of the same hygroscopic quality. Employing a reflecting galvanowhich is a very probable source of error in this method of experi- meter in conjunction with a differential bolometer, which is quicker ment. Magnus considered that the remarkable effect of aqueous difference between dry and moist air, provided that the latter is not in its action than Tyndall's pile, there appears to be hardly any vapour observed by Tyndall might have been caused by conmore than half saturated. Using saturated air with a Leslie cube densation on the polished internal walls of his experimental as source of heat, both rocksalt plates invariably become wet in a tube, or on the rocksalt plates at either end. The question of minute or two and the absorption rises to 10 or 20% according to the thickness of the film of deposited moisture. Employing the open In reference to this objection, Tyndall remarks (Phil. Mag., tube method as described by Tyndall, without the rocksalt plates, 1862, p. 422; Heat, p. 385); "In the first place the plate of salt the absorption is certainly less than 1% in 3 ft. of air saturated at ncarest the source of heat is never moistened, unless the experiments 20° C., unless condensation is induced on the walls of the tube. It are of the roughest character. Its proximity to the source enables is possible that the walls of Tyndall's tube may have become covered the heat to chase away every trace of humidity from its surface." with a very hygroscopic film from the powder of the calcium chloride He therefore took precautions to dry only the circumferential por- which he was in the habit of introducing near one end. Such a film tions of the plate nearest the pile, assuming that the flux of heat would be exceedingly difficult to remove, and would account for the through the central portions would suffice to keep them dry. This excessive precautions which he found necessary in drying the air reasoning is not at all satisfactory, because rocksalt is very hygro- in order to obtain the same transmitting power as a vacuum. scopic and becomes wet, even in unsaturated air, if the vapour probable that Tyndall's experiments on aqueous vapour were effected pressure is greater than that of a saturated solution of salt at the by experimental errors of this character. It is readily detected by laboratory experiments in a 4 ft. tube, with- | the relation between full radiation and temperature is that of out 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° C. was 11.7 times its radiation when dull red at 525° 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 and a black enclosure or a black radiometer at a temperature 。 should be proportional to (04-001). 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 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° C. to 2300° 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 in an enclosure at 0, is given by the formula RES(0-0), where is the radiation constant. The absolute value of a 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. Ångstrom employed a similar method for solar radiation. Kurlbaum gives the value = 5.32 X 10 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 like a saturated vapour, and must therefore obey Carnot's or Clapeyradiation in an enclosure at constant temperature behaves exactly ron'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 formation and partly of external work of expansion at constant of a vapour, the latent heat consists partly of internal energy of pressure. Since in the case of full or undirected radiation the pres sure 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, e(dP/de)=L/V=4P, This where (dP/de) represents the rate of increase of pressure. 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 mathematic. ally 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 wavelengths 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 wavelengths 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 X of | fig. 7; (2) by plotting the energy corresponding to a given wavewave-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°, 1087° and 836° absolute, plotted on a wavelength base with a scale of microns (μ) 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 No at the maximum point is found to be 2920 Thus for a temperature of 1000° Abs. the maximum is at wave-length 2.92 μ; at 2000° the maximum is at 1.46 μ. 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 orμ, and were placed at 1.0μ in the spectrum of radiation at 2000° Abs., it would receive the energy corresponding to wave-lengths between 1.00 and 1.01 μ. At a temperature of 1000° Abs. the corresponding part of the energy, by Wien's displacement law, would lie between the limits 2.00 and 2-02 μ, and the total energy between these limits would be 16 times smaller. But the bolometer strip placed at 2.0μ would now receive only half of the energy, or the energy in a band or μ 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 wavelength base must be of the form where F(X) represents some function of the product of the wave-length and temperature, which remains constant for corresponding wave-lengths when 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, 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 μ. 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 20 length as a function of the temperature. Both methods gave FIG. 7.-Distribution of energy in the SCALE OF VERVELENGTH IN MICRONS A 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, which agrees with Wien's formula when @ is small, where Wien's formula is known to be satisfactory, but approaches the limiting ENERGY OF PARATION APLANCK ABSOLUTE TEMPERATURS FIG. 9. Variation of energy of radiation corresponding to wavelength 30, with temperature of source. notes on Burmann's and Martyn's editions of Virgil, on Euripides, Catullus, Tibullus, and the greater part of Hesiod. In some of these he adopts the whimsical name Dexiades Ericius. His Revisal of Shakespear's Text (1765) was an answer to the "insolent dogmatism" of Bishop Warburton. The Essay towards a Demonstrative Proof of the Divine Existence, Unity and Allributes (1740) was intended to combat the opinions of Voltaire, Rousseau and Hume. Two of his sons (among a family of thirteen) were Benjamin, headmaster of Harrow (1771-1785), and George, headmaster of Eton (1796). His collection of rare classical works formed the nucleus of his son Benjamin's famous library (Bibliotheca Heathiana). An account of the Heath family will be found in Sir W. R. Drake's Heathiana (1882). form E-CX/c, when is large, thus satisfying the condition | D.C.L. from Oxford (31st of March 1752). He also left MS. 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° abs., taking the value of the constant c=14,600 with a scale of wave-length in microns μ. 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 μ. 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° 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 μ, 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. 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 Ileat 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 Ileat 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, THERMO- HEATH, BENJAMIN (1704–1766), English classical scholar and bibliophile, was born at Exeter on the 20th of April 1704. He was the son of a wealthy merchant, and was thus able to devote himself mainly to travel and book-collecting. He became town clerk of his native city in 1752, and held the office till his death on the 13th of September 1766. In 1763 he had published a pamphlet advocating the repeal of the cider tax in Devonshire, and his endeavours led to success three years later. As a classical scholar he made his reputation by his critical and metrical notes on the Greek tragedians, which procured him an honorary HEATH, NICHOLAS (c. 1501-1578), archbishop of York and lord chancellor, was born in London about 1501 and graduated B.A. at Oxford in 1519. He then migrated to Christ's College, Cambridge, where he graduated B.A. in 1520, M.A. in 1522, and was elected fellow in 1524. After holding minor preferments he was appointed archdeacon of Stafford in 1534 and graduated D.D. in 1535. He then accompanied Edward Fox (q.v.), bishop of Hereford, on his mission to promote a theological and political understanding with the Lutheran princes of Germany. His selection for this duty implies a readiness on Heath's part to proceed some distance along the path of reform; but his dealings with the Lutherans did not confirm this tendency, and Heath's subsequent career was closely associated with the cause of reaction. In 1539, the year of the Six Articles, he was made bishop of Rochester, and in 1543 he succeeded Latimer at Worcester. His Catholicism, however, was of a less rigid type than Gardiner's and Bonner's; he felt something of the force of the national antipathy to foreign influence, whether ecclesiastical or secular, and was always impressed by the necessity of national unity, so far as was possible, in matters of faith. Apparently he made no difficulty about carrying out the earlier reforms of Edward VI., and he accepted the first book of common prayer after it had been modified by the House of Lords in a Catholic direction. His definite breach with the Reformation occurred on the grounds, on which four centuries later Leo XIII. denied the Catholicity of the reformed English Church, namely, on the question of the Ordinal drawn up in February 1550. Heath refused to accept it, was imprisoned, and in 1551 deprived of his bishopric. On Mary's accession he was released and restored, and made president of the council of the Marches and Wales. In 1555 he was promoted to the archbishopric of York, which he did much to enrich after the Protestant spoliation; he built After Gardiner's death he was York House in the Strand. appointed lord chancellor, probably on Pole's recommendation; for Heath, like Pole himself, disliked the Spanish party in England. Unlike Pole, however, he seems to have been averse from the excessive persecution of Mary's reign, and no Protestants were burnt in his diocese. He exercised, however, little influence on Mary's secular or ecclesiastical policy. Elizabeth. Like Sir Thomas More he held that it was entirely On Mary's death Heath as chancellor at once proclaimed within the competence of the national state, represented by parliament, to determine questions of the succession to the throne; and although Elizabeth did not renew his commission as lord chancellor, he continued to sit in the privy council for two months until the government had determined to complete the breach with the Roman Catholic Church; and as late as April 1559 he assisted the government by helping to arrange the Westminster Conference, and reproving his more truculent co-religionists. He refused to crown Elizabeth because she would not have the coronation service accompanied with the elevation of the Host; and ecclesiastical ceremonies and doctrine could not, in Heath's view, be altered or abrogated by any mere national authority. Hence he steadily resisted Elizabeth's acts of supremacy and uniformity, although he had acquiesced in the acts of 1534 and 1549. Like others of Henry's bishops, he had been convinced by the events of Edward VI.'s reign that Sir |