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green leaves of plants. But the same solar radiation, when | (8 8), since part of it might be degraded into low-temperature broken up into diffused sky light, which has no definite direction, heat, or there might be other compensation of chemical type has fallen into equilibrium with a much lower temperature, for any abnormally high availability. that might exist in the through loss of its reversibility. It has been remarked that the fluorescent radiation. It has been found that fluorescent temperatures of the planets can be roughly compared by means radiation, showing a continuous or banded spectrum, can be of this principle, if their coefficients of absorption of the solar excited in many gases and vapours; milky phosphorescence radiation are assumed; that of Neptune comes out below of considerable duration, and thus doubtless associated with - 200° C., if we suppose that it is not kept higher by a supply chemical change, is produced in vacuum tubes, containing of internal heat.

oxygen or other complexly constituted gases, by the electric i To obtain dynamical precision in this discussion an exact discharge. definition of the narrow beam such as is usually called a ray is 11. Entropy of a Ray.-If each definitely constituted beam essential. It can be specified as a narrow filament of radiation, of radiation has its own temperature and everything is reversuch as may be isolated within an infinitely thin, impermeable, sible as above, a question arises as to the location of the process bounding tube without thereby producing any disturbance of of averaging which enters into the idea of temperature. The the motion. If either the tube or the surrounding radiaticn answer can depend only on the fact, that although the beam is were not present to keep the beam in shape, it would spread definite as to wave-length and intensity, yet it is far from being sideways, as in optical diffraction. But the function of the a simple wave-train, in that it is constituted of trains of limited tube is one of pure constraint; thus the change of energy lengths and various phases and polarizations, coming from the content of a given length of the tube is represented by energy independent radiating molecules. When such a beam has flowing into it at the end where the radiation enters, and leaving once emerged, it travels without change, and can be reflected it at the other end, but with no leakage at the sides. The total back intact to its source, and is in so far reversible; but when radiation may be considered as made up of such filaments. it has arrived there, the molecules of the source will have

9. Temperature of the Sun. - The mean temperature of the changed their positions, and it cannot be wholly reabsorbed radiating layers of the Sun may be estimated from Stefan's law, in the same manner as it was emitted. There must thus be by computing the intensity of the radiation at his surface some feature in the ultimate averaged constitution of the beam, from that terrestrially observed, on the basis of the law of emitted from a body in the definite stcady state of internal inverse squares; the result is about 6500° C. The application motion determined by its temperature, which adapts it for of Wien's law, which makes the wave-length of maximum spontaneous uncompensated reabsorption into a body at its energy vary inversely as the temperature, for the case of a own (or a lower) temperature, but not at a higher one. perfectly radiating source, gives a result 5500°C. These numbers The question of the determination of the form of the function will naturally differ because (i) the Sun is not a perfect radiator, in § 6 would thus appear to be closely connected with the the constitution of his radiation in fact not following the law other problems, hitherto imperfectly fathomed, relating to of that of a black body, (ii) the various radiating layers have the statistics of kinetic molecular theory. A very interesting different temperatures, (iii) the radiation may be in part due attack on the problem from this point of view has recently to chemical and electrical causes, and in so far would not been made in various forms by Planck. It of course suffices be determined by the temperature alone. The fair agreement to examine some simple type of radiating system, and the of these two estimates indicates, however, that the radiation results will be of general validity. He considers an enclosure is largely regulated by the temperature, that the layers from filled with radiation involving an entirely arbitrary succession which the main part of it comes are at temperatures not very of phases and polarizations along each ray, and also containing different, and that not very much of the complete radiation a system of fixed linear electric oscillators of the Hertzian established in these layers and emitted from them is absorbed type, which are taken to represent the transforming action of by the overlying layers.

radiating and absorbing matter. The radiation contained in · 10. Fluorescence.—When radiation of certain wave-lengths the enclosure will be passed through these oscillators over and falls on a fluorescent body, it is largely absorbed, but in such over again, now absorbed, now radiated, and cach constituent manner as directly to excite other radiation of different type will thus settle down in a unilateral or irreversible manner which is emitted in addition to the true temperature-radiation towards some definite intensity and composition. But it of the body. The distinction involved is that the latter radia does not appear that a system of vibrators of this kind, each tion is spontaneously convertible with the heat of the absorbing with its own period, can perform one of the main functions of body at its own temperature, without any external stimulus a material absorber, namely, the transformation of the relative

, in fact, on the basis of this convertibility intensities of the various types of radiation in the enclosure that the thermodynamic relations of the temperature-radiation to those corresponding to a common temperature. There have been established. According to the experimental law of would be equilibrium established only between the mean Stokes, the wave-lengths of the fluorescent radiation are longer internal vibratory energy in the vibrators of each period and than those of the radiation which excites it. If the latter the density of radiation of that period; there is needed also were directly transformed, in undiminished amount, into the some means of interchanging energy between vibrators of fluorescent kind, this is what would be expected. For such difierent periods, which probably involves doing away with & spontaneous change must involve loss of availability; and, their fixity, or else employing more complex vibrators and beyond the wavc-length of maximum energy in the spectrum, assuming a law of distribution of their internal energy. In the the temperature of a given density of radiation is greater the absence of any method of introducing this temperature equilishorter its wave-length, as it is a function of that density and brium directly, Planck originally sought, in the case of each the wave-length alone such that greater radiation always independent constituent, for a function of its intensity of corresponds to higher temperature. But it would appear that energy and its wave-length, restricted as to form by a certain the opposite should be the case for radiation of long wave- assumed molecular relation, which has the property of continulengths, lying on the other side of the maximum, in which the ally increasing after the manner of entropy, during the progress tendency would thus be for spontaneous change into shorter of that constituent of the radiation in such a system towards waves; this may perhaps be related to the fact that the lines its steady state. If the actual entropy S per unit volume of longer wave-lengths in spectra often come out brighter at could be thus determined, the relation of Clausius SS=8E/T lower temperatures, for they are then thrown on the other side would supply the connexion between the temperature and the of the maximum and cannot be thus degraded. The principle density of radiant energy E. This procedure led him, in an does not, however, have free play in the present case, even indirect and tentative manner, to a relation dS/DE?=-a/E, so when the incident radiation is diffused and so has not the that S:--a E logB E, where a, Bare functions of a; an expression abnormally high temperature associated with a directed beam / which conducts through Clausius's relation to E=(eß)-617. The previous argument then gives E(X, T)) = cid-be-c/1982, 1.4455 in c.g.s. measure, but not so well when the range is farther a type of formula which was originally suggested by Wien on extended: it appeared that a larger value of c was needed to the basis of the analogy that it assigns the same distribution represent the radiation for high values of TX, that is, for high for the radiant energy, among the various frequencies of vibra- temperature or for very long wave-lengths. Thiesen proposed tion, as for the energy of the molecules in a gas among their the somewhat more general form ci(TN)*c-4/1^, and suggested various velocities of translation. But the experimental in- that the value k=} agrees better with the experimental numbers adequacy of this formula afterwards suggested a new pro- than Wien's value k=o. Lord Rayleigh was led (Phil. Mag., cedure, as infra.

June 1900) towards this form with k equal to unity from entirely Processes may be theoretically assigned for the direct continuous different theoretical considerations, on the assumption of the transíormation of radiant into mechanical energy. Thus we can Maxwell-Boltzmann distribution of the energy of a system, imagine a radiating body at the centre of a wheel, carrying oblique

consisting of an isolated block of aether, among its free periods vanes along its circumference, which reflect the radiation on to a ring of parallel fixed vanes, which finally reverse its path and return

of vibration, infinite in number; in some cases this form appeared it to the centre. The pressure of the radiation will drive the wheel, to give as good results as Wien's own. and in case its motion is not resisted, a very great velocity may be

Acting on a suggestion advanced by Lord Rayleigh, Rubens theoretically obtained. The thermodynamic compensation in such

and Kurlbaum soon afterwards widely extended the test of the cases lies in the reduction of the effective temperature of the portion of the radiation not thus used up. We might even do away with

formulae by means of the so-called Reststrahlen. A substance the radiating body at the centre of the wheel, and consider a beam such as an aniline dye, which exhibits selective absorption of of definite radiation reflected backwards and forwards across a any group of rays, also powerfully reflects those rays; and diameter. It is easy to see that its path will remain diametral; | Rubens has been able thus to isolate in considerable purity the the work done by it in driving the wheel will be concomitant with increase of the wave-length, and therefore with expansion of the

rays belonging to absorption bands very far down in the invisible length occupied by the beam. The thermodynamic features are ultra-red, having wave-length of order 10-4 cm., which are thus analogous to those of the more familiar case of an envelope intensely absorbed by substances such as sylvine, by means of filled with gas, which can change its thermal energy into mechanical

five or six successive reflexions of the beam of radiation. By energy by expansion of the envelope against mechanical resistances. In the case of the expanding gas pu=3E., where E, is the total trans

experiments ranging between temperatures -200° C. and latory energy of the molecules, while in adiabatic expansion = ku-Y. + 1500° C. of the source of radiation, it has been found that the Thus the work gained in unlimited expansion, Spdo, is jE/(y-I). intensity of this definite radiation tends to vary simply as T, The final temperature being absolute zero, this should by Carnot's

with close approximation, thus increasing indefinitely with principle be equal to the total initial energy of the gas that is in connexion with temperature, constitutive energy of the molecules

the temperature, whereas Wien's formula would make it tend being excluded; when yol is less than there is thus internal to a definite limit. The only existing formula (except the thermal energy in the molecules in addition to the translatory one suggested by Lord Raylсigh) that proved to be in accord energy. In the case of the beam of radiation, of length I, between with this result was a new one advanced shortly before and n and nton reflexions, where an is an integer, its tolal energy E is

supported on theoretical grounds by Planck, namely, E.,= by $ 2 reduced according to the law E --400on. Also = 2001: 18 to the law E- (+3) Also Tetoi CX-581/( T-1), which for small values of T agrees with Wien's

original form, known to be there satisfactory, while for larger thus E=mctu T 9. When v is small compared with c, this gives

values it tends towards C/c..-T; the new formula is, in fact, the E=x2-7; and P is then 2E!), so that spdl=e, the temperature

simplest and most likely form that satisfies these two conditions. of the beam being ultimately reduced to absolute zero by the The point of Lord Rayleigh's argument was that, at any rate at unlimited expansion. This is in accord with Carnot's principle, in that the whole energy of the beam travelling in a vacuum is mechani. | low frequencies, the law of distribution would suggest an equable cally available when reduction to absolute zero of temperature is partition of the energy between temperature heat and radiant in our power.

vibrations, and that therefore the energy of the latter should 12. Experimental Knowledge. Under the stimulus of Wien's ultimately vary as T: and this prediction, which has thus been investigation and of improvements in the construction of linear verified, may be grafted on to any formula that is in other thermopiles and bolometers for the refined measurement of the

respects appropriate. distribution of energy along a spectrum, the general character Recognizing that his previous hypothesis, restricting the nature of the curve connecting energy and wave-length in the complete of the entropy in addition to its property of continually inradiation at a given temperature has been experimentally creasing, had thus to be abandoned, Planck had in fact made ascertained over a wide range. At each temperature there is a a fresh start on the basis of a train of ideas which was introduced wave-length dom of maximum radiation, which is displaced by Boltzmann in 1877, in order to obtain a precise physical towards the ultra-violet as the temperature rises, and Wien's conception of entropy. According to the latter, for an indefinitely law of homology (8 6) shows that T should be constant. This numerous system of molecules, with known properties and in deduction, and the law of homology itself, as also the law of given circumstances, there is a definite probability of the Stefan and Boltzmann that the total radiation varies as T', occurrence of each statistical distribution of velocities, or say have been closely verified by the experiments of Rubens and each “complexion" of the system, that is formally possible Kurlbaum, Lummer and Pringsheim, Paschen and others. when all velocities consistent with given total energy are conThey established a steady field of radiation inside a material sidered to be.equally likely as regards each molecule; the distri. enclosure by raising the walls to a definite temperature, and bution of greatest possible probability is the state of thermal measured the radiant intensity emitted from it through an equilibrium of the system, and the probability of any other opening or slit in the walls, hy means of a bolometer or thermo- state is a function of the entropy of that state. This conception pile, this being the radiation of the so-called perfectly black body. can be developed only in very simple cases; the application to The principle here involved formed one of the foundations of an ideal monatomic gas-system led Boltzmann to take the Balfour Stewart's early treatment of the theory, and had already entropy proportional to the logarithm of the probability. This been employed by him and Stokes (1860) in experiments on the logarithmic law is in fact demanded in advance by the principle polarized emission from tourmaline: cf. Stokes, Math. and that the entropy of a system should be the sum of the entropies Phys. Papers, iv. 136. It has been remarked by Planck and of its parts. By means of a priori considerations of this nature, by Thiesen that the coefficient of T' in Stefan's law, and the referring to the distribution of internal vibratory energy among value of „T, are two absolute physical constants independent a system of linear electric vibrators of given period, and its of any particular kind of matter, which in conjunction with the equilibrium of exchanges with the surrounding radiant energy, constant of gravitation would determine an entirely absolute Planck has been guided to an expression for the law of dependsystem of physical units. The form of the function (TN)ence of the entropy of that system on the temperature, which adopted by Wien and in Planck's earlier discussions, namely, corresponds to the form of the law of radiation above stated. Geo/t, was found to agree fairly with experiment over the The result gains support from the fact that the expressions for range from 100° C. to 1300° C., when c=1024X10-5, and c= | the coefficients to which he is led give determinations of the absolute physical constants of molecular theory, such as the radiation) should be equal. This proposition is a genera! constant of Avogadro, which are in close accord with other dynamical consequence on the basis of the laws of reciprocity recent determinations. But on the other hand these deter- developed in this connexion (after W. Rowan Hamilton) mainly minations are already involved in the earlier formula of Rayleigh, by Helmholtz, Kirchhoff, and Rayleigh--of the form of the which expresses the distribution for long waves, based merely equations of propagation of vibrations in the medium. But in on the Maxwell-Boltzmann principle of the equable partition a material medium under the influence of a strong magnetic of the. energy among the high free periods belonging to the field these equations are altered by the addition of extraneous enclosure which contains it. It is maintained by Jeans that the terms involving differential coefficients of the third order, and reason why this principle is of avail only for very long wave the dynamical consistency of the cardinal principle of the lengths is that a steady state is never reached for the shorter ones, theory of exchanges is no longer thus directly verified. A a doctrine which as he admits would entirely remove the founda- system of this kind has, in fact, been imagined by Wien in which tions of the application of thermodynamic principles to this the principle is imperfectly fulfilled. A beam coming from a subject. By an argument based on the theory of dimensions, body A, and polarized by passage through a nicol, may have Lorentz has been led to the conclusion that consistency between its plane of vibration rotated through half a right angle by temperatures, as measured molecularly, and as measured by the crossing a magnetically active plate, and may then pass through laws of radiation, requires that the ultimate indivisible electric another nicol, properly orientated for transmission, so as finally charges or electrons must be the same in all kinds of matter. to fall on another body B. On the other hand, the radiation

The abstract statistical theory of entropy, which is here from B which gets through this adjacent nicol will have its invoked, admits of generalization in a way which is a modifica- plane of vibration rotated through another half right angle by tion of that of Planck, itself essentially different from the earlier the magnetically active plate, and so will not get through the idea of Boltzmann. The molecules of matter, whose interactions first nicol to the body A. Such possibilities of unequal excontrol physical phenomena, including radiation, are too change of radiation between A and B are the result of the want numerous to be attended to separately in our knowledge. They, of reversibility of the radiation in the extraneous magnetic and the phenomena in which they interact, must thus be sorted field, which might have been expected to lead to proportionate out into differential groups or classes. Elements of energy of inequalities of concentration; in this example, however, though specified types might at first sight constitute such classes: but the defect of reversibility is itself slight, its results appear at the identity of a portion of energy cannot be traced during its first sight to prevent any equilibrium at all. But a closer transformations, while an element of physical disturbance can examination removes this discrepancy. In order to make the be definitely followed, though its energy changes by interaction system self-contained, reflectors must be added to it, so as to with other elements as it proceeds. The whole disturbance send back into the sources the polarized constituents that are may thus be divided into classes, or groups of similar elements, turned aside out of the direct line by the nicols. Then, as each with permanent existence: and these may be considered Brillouin has pointed out, and as in fact Rayleigh had explained as distributed in series of cells, all equivalent in extent, which some years before, the radiation from B does ultimately get constitute and map out the material system or other domain of across to A after passage backward and forward to the reflectors the phenomena. The test of this equivalence of extent is and between the nicols: this, it is true, increases the length of superposition, in the sense that the same element of disturbance its path, and therefore diminishes the concentration of a single always occupies during its wanderings the same number of cells. narrow beam, but any large change of path would make the This framework being granted, the probability of any assigned beam too wide for the nicols, and thus require other corrections statistical distribution of the elements of disturbance now which may be supposed to compensate. The explanation of admits of calculation; and it represents, as above, the logarithm the slight difference that is to be anticipated on theoretical of the entropy of that distribution, multiplied however by a grounds might conceivably be that in such a case the magnetic cocfficient which must depend on the minuteness of scale of the influence, being operative on the phases, alters the statistical statistics. But in the calculation, all the physical laws which constitution of the radiation of given wave-length from the impose restrictions on the migrations of the elements of dis- special type that is in equilibrium with a definite temperature, turbance must be taken into account; it is only after this is so that after passage through the magnetic medium it is not in done that the rest of the circumstances can be treated as a condition to be entirely absorbed at that temperature; there fortuitous. All these physical laws are, however, required and would then be some other element, in addition to temperature. used up in determining the complex of equivalent cells into involved in equilibrium in a magnetic field. If this is not so, which the system which forms the seat of the energy is mapped there must be some thermodynamic compensation involving out. On this basis thermodynamics can be constructed in reaction, extremely small, however, on the magnetizing system. a priori abstract fashion, and with deeper and more complete 14. Origin of Specira.- In addition to the thermal radiations implications than the formal Carnot principle of negation of of material substances, those, namely, which establish temperpetual motions can by itself attain to. But the ratio of the perature-equilibrium of the enclosure in which they are confined, magnitude of the standard element of disturbance to the extent there are the fluorescent and other radiations excited by exof the standard cell remains inherent in the results, appearing traneous causes, radiant or electric or chemical. Such radia. as an absolute physical constant whose value is determined tions are an indication, by the presence of higher wave-lengths somehow by the other fundamental physical constants of than belong in any sensible degree to the temperature, that the nature. A prescribed ratio of this kind is, however, a different steady state has not arrived; they thus fade away, either thing from the hypothesis that energy is constituted atomically, immediately on the cessation of the exciting cause, or after an which underlics, as Lorentz pointed out, Planck's form of the interval. The radiations, consisting of definite narrow bright theory. It has indeed already been remarked that the mere bands in the spectrum, that are characteristic of the gaseous fact of the existence of a wave-length lm of maximum radiation, state in which each molecule can vibrate freely by itself, are whether obeying Wien's law im T=constant or not, implies usually excited by electric or chemical agency; thus there is by itself some prescribed absolute physical quantity of this no ground for assuming that they always constitute true temkind, whose existence thus cannot be evaded, though we may be perature radiation. The absorption of these radiations by at a loss to specify its nature.

strata of the same gases at low temperatures seems to prove 13. Modification by a Magnetic Field.-The theory of ex- that the unaltered molecules themselves possess these free changes of radiation, which makes the equilibrium of radiating periods, which do not, therefore, belong specially to dissociated bodies depend on temperaturt alone, requires that, when an ions. Although very difficult to excite directly, these free element of surface of one body is radiating to an element of vibrations are then excited and absorb the energy of the inci. surface of another body at the same temperature, the amounts dent waves, under the influence of resonance, which naturally of energy interchanged (when reflexion is counted in along with I becomes extremely powerful when the tuning is exact; thus indicates, moreover, that the true absorption bands in a gas progress has been made in recent years. The beginning of of sufficiently low density must be extremely narrow. There definite knowledge was the discovery of Balmor in 1885, that is direct evidence that many of the more permanent gases do the frequencies of vibration (n) of the hydrogen lines could not sensibly emit light on being subjected to high temperature be represented, very closely and within the limits of error of alone, when chemical action is excluded, while others give observation, by the formula 1 of 1-4m 3, when for m is subin these circumstances feeble continuous spectra; in fact, stituted the series of natural numbers 3, 4, 5, ... 15. Soon looking at the matter from the other side, the more permanent afterwards series of related lines were picked out gases are very transparent to most kinds of radiation, and spectra of other elements by Liveing and Dewar. Rydberg therefore must be very bad radiators as regards those kinds. conducted a systematic investigation on the basis of a modificaThe dark radiation of flames has been identified with that tion of Balmer's law for hydrogen, namely, n=n.-N/(m tu'. belonging to the specific radiation of their gaseous products He found that in the group of alkaline metals three series of of combustion. There is thus ground for the view that the lines exist, the so-called principal and two subordinate series, impacts of the colliding molecules in a gas, or rather their whose frequencies fit approximately into this formula, and mutual actions as they swing sharply round each other in that similar statements apply to other natural groups of eletheir orbits during an encounter, may not be sufficiently violentments; that the constant N is sensibly the same for all series to excite sensibly the free vibrations of the definite periods and all substances, while n, and u have different values for belonging to the molecules. But they may produce radiation each; and that other approximate numerical relations exist. in other ways. While the velocity of an electron or other In each series the lines of high frequency crowd together toelectric charge is being altered, it necessarily sends out a stream wards a definite limit on the more refrangible side; near this of radiation. Now the orbital motions of the electrons in an limit they would, if visible, constitute a band. The principal actual molecule must be so adjusted, as appears to be theo- or strongest series of lines shows reversal very readily. The retically possible, that it does not emit radiation when in a lines of the first subordinate series are usually nebular, while steady state and moving with constant velocity. But in the those of the second subordinate or weakest series are sharp; violent changes of velocity that occur during an encounter but with a tendency to broaden towards the less refrangible this equipoise will be disturbed, and a stream of radiation, side. In most series there are, however, not more than six without definite periods, but such as might constitute its share lines visible: helium and hydrogen are exceptions, no fewer of the equilibrium thermal radiation of the substance, may be than thirty lines of the principal series of the latter having expected while the encounter lasts. At very high temperatures been identified, the higher ones in stellar spectra only. But the energy of this thermal radiation in an enclosure entirely very remarkable progress has recently been made by R. W. overpowers the kinetic energy of the molecules present, for the Wood, by exciting fuorescent spectra in a metallic vapour, former varies as T', while the latter measures T itself when and also by applying a magnetic field to restore the lines sensitive the number of molecules remains the same. The radiation to the Zeeman effect after the spectrum has been cut off by which can be excited in gases, confined as it is to extremely crossed nicols. The large aggregates of lines thus definitely narrow bands in the spectrum, may indeed be expected to revealed are also resolved by him into systems in other ways; possess such intensity as to be thermally in equilibrium with when the stimulating light is confined to one period, say a extremely high temperatures. That the same gases absorb single bright line of another substance, the spectrum excited such radiations when comparatively cold and dark does not, consists of a limited number of lines equidistant in frequency, of course, affect the case, because emissive and absorptive the interval common to all being presumably the frequency of powers are proportional only for incident radiations of the some intrinsic orbital motion of the molecule. In this way the intensity and type corresponding to the temperature of the series belonging to some of the alkali metals have been obtained body. Thus if our adiabatic enclosure of $ 3 is prolonged into nearly complete. a tube of unlimited length which is filled with the gas, then. Simultaneously with Rydberg, the problem of series was when the temperature has become uniform that gas must send attacked by Kayser and Runge, who, in reducing their extensive back out of the tube as much radiation as has passed down the standard observations, used the formula n=A+Bm-' + 7 tube and been absorbed by it; but if the tube is maintained higher terms in this descending series being presumed to be at a lower temperature, -it may return much less. The fact negligible. This cannot be reconciled with Rydberg's form, that it is now possible by great optical dispersion to make the which gives on expansion terms involving m-3; but for the line-spectra of prominences in the middle of the Sun's disk higher values of m the discrepancies rapidly diminish, and do stand out bright against the backgroạnd of the continuous not prevent the picking out of the lines, the frequency-differences solar spectrum, shows that the intensities of the radiations of between successive lines then varying roughly as the inverse these prominences correspond to a much higher temperature squares of the series of natural numbers. For low values of than that of the general radiating layer underneath them; m neither mode of expression is applicable, as was to be ertheir luminosity would thus seem to be due to some cause pected; and it remains a problem for the future to ascertain (electric or chemical) other than mere temperature. On the is possible the rational formula to which they are approxima. other hand, the general reversing gaseous layer which originates tions. More complex formulas have been suggested by Ritz the dark Fraunhofer lines is at a lower temperature than the and others, partly on theoretical grounds. radiating layer; it is only when the light from the lower layers Considered dynamically, the question is that of the deteris eclipsed that its own direct bright-line spectrum flashes out. mination of the formula for the disturbed motions of the system It is not necessary to attribute this selective flash-spectrum to which constitutes the molecule. Although we are still far from temperature radiation; it can very well be ascribed to fluor- any definite line of attack, there are various indications that escence stimulated by the intense illumination from beneath the quest is a practicable one. The lines of each series, sorted When the radiation in a spectrum is constituted of wide out by aid of the formulae above given, have properties in bands it may on these principles be expected to be in equi- common: they are usually multiple lines, either all doublets librium with a lower temperature than when it is constituted in the case of monad elements, or generally triplets in the case of narrow lines, if the total intensity is the same in the cases of those of higher chemical valency; in very few cases are the compared; this is in keeping with the easier excitation of series constituted of single lines. It is found also that the band spectra (cf. the banded absorption spectra), and with the components of all the double or triple lines of a subordinate fact that various gases and vapours do appear to emit band series are equidistant as regards frequency. In the case of a spectra more or less related to the temperature.

related group of elements, for example the alkaline metals, 15. Constitution of Spectra.- In the problem of the unravelling it appears that corresponding series are displaced continually of the constitutions of the very complex systems of spectral towards the less refrangible end as the atomic weight rises; it lines belonging to the various kinds of matter, considerable l is found also that the interval in frequency between the double

lines of a series diminishes with the atomic weight, and is pro- such as, for example, a row of masses fixed along a tense cord, portional to its square. These relations suggest that the atomic and each subject to a restoring elastic force of its own in addition weight might here act in part after the manner of a load attached to the tension of the cord. A single spectral line might thus to a fundamental vibrating system, which might conceivably be transformed into a band of this type, as the effect of disbe formed on the same plan for all the metals of the group; turbance arising from slight elastic connexions established in such a load would depress all the periods, and at the same time the molecule between a system of similar vibrators. But it would split them up in the manner above described, if it the series in line-spectra are of entirely different constitution; introduced dissymmetry into the vibrator. The discovery of thus for the series expressed by the formula pe=po?-Bm-? Zeeman that a magnetic field triples each spectral line, and the corresponding period-equation might be expressed in some produces definite polarizations of the three components, in such form as sin k(pa - poa) 4 =constant, which belongs to no many cases further subdividing each component into lines type of vibrator hitherto analysed. placed usually all at equal intervals of frequency, is explained, AUTHORITIES.-The experimental memoirs on the constitution and was in part predicted, by Lorentz on the basis of the electron

of radiation are mostly in the Annalen der Physik; references

are given by P. Drude, Lehrbuch der Optik, Leipzig, 1900; cf. also theory, which finds the origin of radiation in a system of unitary

reports in the collection issued by the International Congress of electric charges describing orbits or executing vibrations in the

Physics, Paris, 1900. See also Lord Rayleigh's Scientific papers, molecule. Although these facts form substantial sign-posts, in various connexions; and Larmor, in Bril. Assoc. Reports, 1900it has not yet been found possible to assign any likely structure 1902, also the Bakerian Lecture, Roy. Soc. Proc., 1909, for a general

discussion of molecular statistical theory in this connexion. to a vibrating system which would lead to a frequency formula

Planck's Theorie der Wärmestrahlung, 1906, gives a discussion from for its free periods of the types given above. Indeed, the view

his point of view; there is a summary by Wien in Ency. Math. is open that the group of lines constituting a series form a Wiss. v. (3) pp. 282-357; also a lecture of H. A. Lorentz to the harmonic analysis of a single fundamental vibration not itself Math. Congress at Rome, 1908, and papers by J. H. Jeans, Phil. harmonic. If that be so, the intensities and other properties

Mag., 1909, on the partition of energy. In spectrum analysis

Kayser's extensive treatise is the standard authority. Winckelof the lines of a series ought all to vary together; it has in

mann's Handbuch der Physik, vol. ii. (by Kayser, Drude, &c.), may fact been found by Preston, and more fully verified by Runge also be consulted.

U. L.*) and others, that the lines are multiplied into the same number RADICAL (Lat. radix, a root), in English politics, a term of constituents in a magnetic field, with intervals in frequency applied to politicians who desire to make thorough, or radical, that are the same for all of them. When the series consists of changes in the constitution and in the social order generally. double or triple lines the separate components of the same | Although it had been used in a somewhat similar way during compound line are not affected similarly, which shows that

the reign of Charles II., the term Radical, in its political sense, they are difierently constituted. The view has also found

originated about the end of the 18th century, probably owing support that the different behaviours of the various groups of its existence to Charles James Fox, who, in 1797, declared lines in a spectrum show that they belong to independent that “ radical reform" was necessary. The ideas of the first vibrators. The form of the vibration sent out from a molecule Radicals were borrowed largely from the authors of the French into the aether depends on the form of the aggregate hodograph | Revolution. The word was more generally employed during of the electronic orbits, which is in keeping with Rayleigh's the disturbed period between the close of the Napoleonic wars remark that the serics-laws suggest the kinematic relations of

and the passing of the great Reform Bill of 1832, and was revolving bodies rather than the vibrations of steady dynamical applied to agitators like Henry Hunt and William Cobbett. systems.

After the Reform Bill had become law, the advocates of violent According to Rydberg, there is ground for the view that a change were drawn into the Chartist movement, and the natural group of chemical elements have all the same type of Radicals became less revolutionary both in speech and object. series spectrum, and that the various constants associated with | Thus in 1842 an observer writes:-" The term Radical, once this spectrum change rapidly in the same directions in passing employed as a name of low reproach, has found its way into from the elements of one group to the corresponding ones of high places, and is gone forth as the title of a class who glory the following groups, after the manner illustrated in graphical in their designation.” About this time many members of representations of Mendeléeff's law by means of a continuous Parliament were known as Radicals, among these men being wavy curve in which each group of elements lies along this George Grote and Joseph Hume. The Radicals never formed same ascending or descending branch; the chemical elements a distinct party in the House of Commons, and subsequently thus being built up in a series of types or groups, so that the they formed simply the advanced section of the Liber individuals in successive groups correspond one to one in a For a few years in the 19th century the wearing of a white hat regular progression, which may be put in evidence by connect was looked upon as the distinguishing mark of a Radical, a ing them by transverse curves. Illustrations have been hat of this colour having been worn by Hunt when addressing worked out mathematically by J. J. Thomson of the effect of meetings. adding successive outer rings of electrons to stable vibrating See W. Harris, History of the Radical Party in Parliament (1885): collocations.

S. Bamford, Passages in the Life of a Radical (new ed., 1893); C. B. The frequencies of the series of very close lines which con Roylance Kent, The English Radicals: an Historical Sketch (1899). stitute a single band in a banded spectrum are connected by a RADIOACTIVITY. The subject of radioactivity deals with law of quite different type, namely, in the simpler cases = phenomena exhibited by a special class of bodies of high atomic A-Bm”. It may be remarked that this is the kind of relation weight of which uranium, thorium, radium and actinium are the that would apply to a row of independent similar vibrators in best known examples. These substances possess the property which the neighbours exert slight mutual influence of elastic of spontaneously emitting radiations of a special character type. If & denote displacement and x distance along the row, which are able to penetrate through matter opaque to ordinary

light. The beginning of this subject dates from 1896, and the equation +=- would represent the general fea

was an indirect consequence of the discovery of the X rays tures of their vibration, the right-hand side arising from the

made a few months before by Röntgen. It was known that mutual elastic influences. If the ends of the line of vibrators, of

the production of X rays in a vacuum tube was accompanied length I, are fixed, or if the vibrators form a ring, the appropriate

by a strong phosphorescence of the glass, and it occurred to

several investigators that ordinary substances made phostype of solution is co sin jur sin pl, where al = mn and m is

phorescent by visible light might emit a penetrating radiation integral; further - petke gu?, hence pe = k2_81m2, which is of similar to X rays. Following out this idea, H. Becquerel (1),'

a distinguished French physicist, exposed amongst other the type above stated. Dynamical systems of this kind are substances a phosphorescent compound of uranium, uraniumillustrated by the Lagrangean linear system of connected bodies, These numbers refer to papers noted under References (below).

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