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Spectroscopy

SPECTROSCOPY (from Lat. spectrum, an appearance, and Gr. (TKOTretc, to see), that branch of physical science which has for its province the investigation of spectra, which may, for our present purpose, be regarded as the product of the resolution of composite luminous radiations into more homogeneous components. The instruments which effect such a resolution are called spectroscopes.

1. Introductory. The announcement of the first discoveries made through the application of spectroscopy, then called spectrum analysis, appealed to the imagination of the scientific world because it revealed a method of investigating the chemical nature of substances independently of their distances: a new science was thus created, inasmuch as chemical analysis could be applied to the Sun and other stellar bodies. But the beautiful simplicity of the first experiments, pointing apparently to the conclusion that each element had its characteristic and invariable spectrum whether in the free state or when combined with other bodies, was soon found to be affected by complications which all the subsequent years of study have not completely resolved. Compound bodies, we now know, have their own spectra, and only when dissociation occurs can the compound show the rays characteristic of the element: this perhaps was to be expected, but it came as a surprise and was not readily believed, that elements, as a rule, possess more than one spectrum according to the physical conditions under which they become luminous. Spectrum analysis thus passed quickly out of the stage in which its main purpose was " analysis " and became our most delicate and powerful method of investigating molecular properties; the old name being no longer appropriate, we now speak of the science of "Spectroscopy." 1 Within the limit of this article it is not possible to give a complete account of this most intricate branch of physics; the writer therefore confines himself to a summary of the problems which now engage scientific attention, referring the reader for details to H. Kayser's excellent and complete Handbuch der Spcctroscopie.

2. Instrumental. The spectroscope is an instrument which allows us to examine the vibrations sent out by a radiating source: it separates the component parts if they are homogeneous, i.e. of definite periodicity, and then also gives us the distribution of intensity along the homogeneous constituents. This resolution into simple periodic waves is arbitrary in the same sense as is the decomposition of forces along assumed 1 The present writer believes that he was the first to introduce the word " Spectroscopy " in a lecture delivered at the Royal Institution in 1882 (Proceedings, vol. ix.).

axes; but, in the same way also the results are correct if the resolution is treated as an analytical device and in the final result account is taken of all the overlapping components. Spectroscopes generally consist of three parts: (i) the collimator; (2) the analysing appliance, (3) the telescope. The slit of the collimator confines the light to a nearly linear source, the beam diverging from each point of the source being subsequently made parallel by means of a lens. The parallelism, which is required to avoid aberrations, otherwise introduced by the prism or grating, may often be omitted in instruments of small power. The lens may then be also dispensed with, and the whole collimator becomes unnecessary if the luminous source is narrow and at a great distance, as for instance in the case of the crescent of the Sun near the second and third contact of a total solar eclipse. The telescope serves to examine the image of the slit and to measure the angular separation of the different slit images; when photographic methods are employed the telescope is replaced by a camera.

The analysing appliance constitutes the main feature of a spectroscope. It may consist of one of the following:

a. A prism or a train of prisms. These are employed in instruments of small power, especially when luminosity is a consideration; but their advantage in this respect is to a great extent lost, when, in order to secure increased resolving power, the size of the prisms, or their number, is unduly increased.

b. A grating. Through H. A. Rowland's efforts the construction of gratings has been improved to such an extent that their use is becoming universal whenever great power or accuracy is required. By introducing the concave grating which (see DIFFRACTION OF LIGHT, 8) allows us to dispense with all lenses, Rowland produced a revolution in spectroscopic measurement. At present we have still to content ourselves with a much diminished intensity of light when working with gratings, but there is some hope that the efforts to concentrate the light into one spectrum will soon be successful.

c. An dchelon grating. Imagine a horizontal section of a beam of light, and this section divided into a number of equal parts. Let somehow or other retardations be introduced so that the optical length of the successive parts increases by the same quantity n\, n being some number and X the wave-length. If on emergence the different portions he brought together at the focus it is obvious that the optical action must be in every respect similar to that of a grating when the nth order of spectrum is considered. A. Michelson produced the successive retardations by inserting step-by-step plates of glass of equal thickness so that the different portions of the beam traversed thicknesses of glass equal to n\, 2n\, $n\, . . . NX. The optical effect as regards resolving power is the same as with a grating of N lines in the wth order, but, nearly all the light not absorbed by the glass may be concentrated in one or two orders. 1 d. Some other appliance in which interference with long difference of path is made use of, such as the interferometer of Fabry and Perot, or Lummer's plate (see INTERFERENCE OF LIGHT).

The echelon and interferometer serve only a limited purpose, but must be called into action when the detailed structure of lines is to be examined. For the study of Zeeman effects (see MAGNETO-OPTICS) the echelon seems specially adapted, while the great pliability of Fabry and Perot's methods, allowing a clear interpretation of results, is likely to secure them permanently an established place in measurements of precision.

The power of a spectroscope to perform its main function, which is to separate vibrations of different but closely adjacent frequencies, is called its " resolving power." The limitation of power is introduced as in all optical instruments, by the finiteness of the length of a wave of light which causes the image of an indefinitely narrow slit to spread out over a finite width in the focal plane of the observing telescope. The so-called " diffraction " image of a homogeneously illuminated slit shows a central band limited on either side by a line along which the 1 Michelson, Astrophys. Journ. (1898), 8, p. 36; A. Schuster, Theory of Optics, p. 115.

intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope. Lord Rayleigh, to whom we owe the first general discussion of the theory of the spectroscope, found by observation that if two spectroscopic lines of frequencies i and 2 are observed in an instrument, they are just seen as two separate lines when the centre of the central diffraction band of one coincides with the first minimum intensity of the other. In that case the image of the double line shows a diminution of intensity along the centre, just sufficient to give a clear impression that we are not dealing with a single line, and the intensity at the minimum is 0-81 of that at the point of maximum illumination. We may say therefore that if the difference between the frequencies HI and 2 of the two waves is such that in the combined image of the slit the intensity at the minimum between the two maxima falls to 0-81, the lines are just resolved and i/(i-2) may then be called the resolving power. There is something arbitrary in this definition, but as the practical importance of the question lies in the comparison between instruments of different types, the exact standard adopted is of minor importance, the chief consideration being simplicity of application. Lord Rayleigh's expression for the resolving power of different instruments is based on the assumption that the geometrical image of the slit is narrow compared with the width of the diffraction image. This condition is necessary if the full power of the instrument is to be called into action. Unfortunately considerations of luminosity compel the observer often to widen the slit much beyond the range within which the theoretical value of resolving power holds in practice. The extension of the investigation to wide slits was first made by the present writer in the article " Spectroscopy " in the gth edition of the Encyclopaedia Brilannica. Reconsideration of the subject led him afterwards to modify his views to some extent, and he has since more fully discussed the question. * Basing the investigation on the same criterion of resolution as in the case of narrow slits, we postulate for both narrow and wide slits that two lines are resolved when the intensity of the combined image falls to a value of 0-810 in the centre between the lines, the intensity at the maxima being unity. We must now however introduce a new criterion the " purity " and distinguish it from the resolving power: the purity is defined by Mi/(wi-w 2 ), where MI and n 2 are the frequencies of two lines such that they would just be resolved with the width of slit used. With an indefinitely narrow slit the purity is equal to the resolving power. As purity and resolving power are essentially positive quantities, HI in the above expression must be the greater of the two frequencies. With wide slits the difference HI-HZ depends on their width. If we write P = /> R where P denotes the purity and R the resolving power, we may call p the " purityfactor. " In the paper quoted the numerical values of p are given for different widths of slit, and a table shows to what extent the loss of purity due to a widening of the slit is accompanied by a gain in luminosity. The general results may be summarized as follows: if the width of the slit is equal to/X/4D (where X is the wave-length concerned, D the diameter of the collimator lens, and / its focal length) practically full resolving power is obtained and a further narrowing of the slit would lead to loss of light without corresponding gain. We call a slit of this width a " normal slit. " With a slit width equal to twice the normal one we lose 6% of resolution, but obtain twice the intensity of light. With a slit equal in width to eight times the normal one the purity is reduced to o-45R, so that we lose rather more than half the resolving power and increase the light 3-7 times. If we widen the slit still further rapid loss of purity results, with very little gain in light, the maximum luminosity obtainable with an indefinitely wide slit being four times that obtained with the normal one. It follows that for observations in which light is a consideration spectroscopes should be used which give about twice the resolving power of that actually required; we may then use a slit having a width of nearly eight times that of the normal one.

'Astrophys. Journ. (1905), 21, p. 197.

Theoretical resolving power can only be obtained when the whole collimator is filled with light and further (as pointed out by Lord Rayleigh in the course of discussion during a meeting of the " Optical Convention " in London, 1905) each portion of the collimator must be illuminated by each portion of the luminous source. These conditions may be generally satisfied by projecting the image of the source on the slit with a lens of sufficient aperture. When the slit is narrow light is lost through diffraction unless the angular aperture of this condensing lens, as viewed from the slit, is considerably greater than that of the collimator lens.

When spectroscopes are used for stellar purposes further considerations have to be taken account of in their construction; and these are discussed in a paper by H. F. Newall. 1 .

3. Speclroscopic Measurements and Standards of Wave-Length. All spectroscopic measurement should be reduced to wavelengths or wave-frequencies, by a process of interpolation between lines the wave-lengths of which are known with sufficient accuracy. The most convenient unit is that adopted by the International Union of Solar Research and is called an Angstrom (A) ; and is equal to icf 8 cms. A. Perot and C. Fabry, employing their interferometer methods, have compared the wave-length of the red cadmium line with the standard metre in Paris and found it to be equal to 6438-4696 A, the observations being taken in dry air at 1 8 C and at a pressure of 76 cms. (g= 980-665). This number agrees singularly well with that determined in 1893 by Michelson, who found for the same line 6438-4700. Perot's number is now definitely adopted to define the Angstrom, and need never be altered, for should at some future time further researches reveal a minute error, it will be only necessary to change slightly, the temperature or pressure of the air in which the wave-length is measured. A number of secondary standards separated by about 50 A, and tertiary standards at intervals of from 5 to 10 A have also been determined. By means of these, spectroscopists are enabled to measure by interpolation the wave-length of any line they may wish to determine. Interpolation is easy in the case of all observations taken with a grating. In the case of a prism some caution is necessary unless the standards used are very close together. The most convenient and accurate formula of interpolation seems to be that discovered by J. F. Hartmann. If D is the measured deviation of a ray, and Do, Xo, c and a are four constants, the equation X = Xo+ (D-D ) 1 " seems to represent the connexion between deviation and wavelength with considerable accuracy for prisms constructed with the ordinary media.

The constant a has the same value 1-2 for crown and flint glass, so that there are only three disposable constants left. In many cases it is sufficient to substitute unity for a and write which gives a convenient formula, which in this form was first used by A. Cornu. If within the range 5100-3700 A, the constants are determined once for all, the formula seems capable of giving by interpolation results accurate to 0-2 A, but as a rule the range to which the formula is applied will be much less with a corresponding gain in the accuracy of the results.

Every observer should not only record the resolving power of the instrument he uses, but also the purity-factor as defined above. The resolving power in the case of gratings is simply mn, where m is the order of spectrum used, and n the total number of lines ruled on the grating. In the case of prisms the resolving power is/ (dn/d\), where / is the effective thickness of the medium traversed by the ray. If fe and t\ are thicknesses traversed by the extreme rays, t = h li, and if, as is usually the case, the prism is filled right up to its refraction cap, t\ o, and / becomes equal to the greatest thickness of the medium which is made use of. When compound prisms are used in which, 1 Monthly Notices R.A.S. (1905), 65, p. 605.

for the purpose of obtaining smaller deviation, one part of the compound acts in opposition to the other, the resolving power of the opposing portion must be deducted in calculating the power of the whole. Opticians should supply sufficient information of the dispersive properties of their materials to allow dnld\ to be calculated easily for different parts of the spectrum.

The determination of the purity-factor requires the measurement of the width of the slit. This is best obtained by optical means. The collimator of a spectroscope should be detached, or moved so as to admit of the introduction of an auxiliary slit at a distance from the collimator lens equal to its focal length. If a source of light be placed behind the auxiliary slit a parallel beam of light will pass within the collimator and fall on the slit the width of which is to be measured. With fairly homogeneous light the diffraction pattern may be observed at a distance, varying with the width of the slit from about the length of the collimator to one quarter of that length. From the measured distances of the diffraction bands the width of the slit may be easily deduced.

4. Methods of Observation and Range of Wave-Lengths. Visual observation is limited to the range of frequencies to which our eyes are sensitive. Defining oscillation as is usual in spectroscopic measurement by wave-length, the visible spectrum is found to extend from about 7700 to 3900 A. In importance next to visual observation, and in the opinion of some, surpassing it, is the photographic method. We are enabled by means of it to extend materially the range of our observation, especially if the ordinary kinds of glass, which strongly absorb ultraviolet light, are avoided, and, when necessary, replaced by quartz. It is in this manner easy to reach a wave-length of 3000 A, and, with certain precautions, 1800 A. At that point, however, quartz and even atmospheric air become strongly absorbent and the expensive fluorspar becomes the only medium that can be used. Hydrogen still remains transparent. The beautiful researches of V. Schumann 2 have shown, however, that with the help of spectroscopes void of air and specially prepared photographic plates, spectra can be registered as far down as 1 200 A. Lyman more recently has been able to obtain photographs as far down as 1030 A with the help of a concave grating placed in vacuo. 3 Although the vibrations in the infra-red have a considerably greater intensity, they are more difficult to register than those in the ultra-violet. Photographic methods have been employed successfully by Sir W. Abney as far as 20,000 A, but long exposures are necessary. Bolometric methods may be used with facility and advantage in the investigation of the distribution of intensities in continuous or semi-continuous spectra but difficulties are met with in the case of line spectra. Good results in this respect have been obtained by B. W. Snow 4 and by E. P. Lewis, 6 lines as far as 11,500 having been measured by the latter. More recently F. Paschen 6 has further extended the method and added a number of infra-red lines to the spectra of helium, argon, oxygen and other elements. In the case of helium one line was found with a wave-length of 20,582 A. C. V. Boys' microradiometer has occasionally been made use of, and the extreme sensitiveness of the Crookes' radiometer has also given excellent results in the hands of H. Rubens and E. F. Nichols. In the opinion of the writer the latter instrument will ultimately replace the bolometer, its only disadvantage being that the radiations have to traverse the side of a vessel, and are therefore subject to absorption. In order to record line spectra it is by no means necessary that the receiving instrument (bolometer or radiometer) should be linear in shape, for the separation of adjacent lines may be obtained if the linear receiver be replaced by a narrow slit in a screen placed at the focus of the condensing lens. The sensitive vane or strip may then be placed behind the slit; its width will not affect the resolving power though there may be a diminution of sensitiveness. The longest waves 2 Wied. Annalen (1901), 5, p. 349.

3 Astrophys. Journ. (1906), 23, p. 181.

4 Wied. Annalen (1892), 47, p. 208. 6 Astrophys. Journ. (1895), 2, p. I.

6 Drude Annalen (1908), 27, p. 537 and (1909), 29.

observed up to the present are those recorded by H. Rubens and E. Aschkinass 1 (-0061 cms. or 610,000 A).

5. Methods of Rendering Gases Luminous. The extreme flexibility of the phenomena shown by radiating gases renders it a matter of great importance to examine them under all possible conditions of luminosity. Gases, like atmospheric air, hydrogen or carbon dioxide do not become luminous if they are placed in tubes, even when heated up far beyond white heat as in the electric furnace. This need not necessarily be interpreted as indicating the impossibility of rendering gases luminous by temperature only, for the transparency of the gas for luminous radiations may be such that the emission is too weak to be detected. When there is appreciable absorption as in the case of the vapours of chlorine, bromine, iodine, sulphur, selenium and arsenic, luminosity begins at a red heat. Thus G. Salet 2 observed that iodine gives a spectrum of bright bands when in contact with a platinum spiral made white hot by an electric current, and J. Evershed 3 has shown that in this and other cases the temperature at which emission becomes appreciable is about 700. It is only recently that owing to the introduction of carbon tubes heated electrically the excitement of the luminous vibrations of molecules by temperature alone has become an effective method for the study of their spectra even in the case of metals. Hitherto we were entirely and still are generally confined to electrical excitation or to chemical action as in the case of flames.

In the ordinary laboratory the Bunsen flame has become universal, and a number of substances, such as the salts of the alkalis and alkaline earths, show characteristic spectra when suitably placed in it. More information may be gained with the help of the oxyhydrogen flame, which with its higher temperature has not been used as frequently as it might have been, but W. N. Hartley has employed it with great success, and in cyanite (a silicate- of aluminium) has found a material which is infusible at the temperature of this flame, and is therefore Fuitable to hold the substance which it is desired to examine. An interesting and instructive manner of introducing salts into flames was discovered by A. Gouy, who forced the air before it entered the Bunsen burner, through a spray produce containing a salt in solution. By this method even such metals as iron and copper may be made to show some of their characteristic lines in the Bunsen burner. The spectra produced under these circumstances have been studied in detail by C. de Watteville. 4 Of more frequent use have been electric methods, owing to the greater intensity of the radiations which they yield. Especially when large gratings are employed do we find that the electric arc alone seems sufficient to give vibrations of the requisite power. The metals may be introduced into the arc in various ways, and in some cases where they can be obtained in sufficient quantity the metallic electrodes may be used in the place of carbon poles.

The usual method of obtaining spectra by the discharges from a Ruhmkorff coil or Wimshurst machine needs no description. The effects may be varied by altering the capacity and self-induction of the circuit which contains the spark gap. The insertion of self-induction has the advantage of avoiding the lines due to the gas through which the spark is taken, but it introduces other changes in the nature of the spark, so that the results obtained with and without self-induction are not directly comparable. Count Gramont 6 has been able to obtain spectroscopic evidence of the metalloids in a mineral by employing powerful condensers and heating the electrodes in an oxyhydrogen flame when these (as is often the case) are not sufficiently conducting.

When the substance to be examined spectroscopically is in solution the spark may be taken from the solution, which must then be used as kathode of air. The condenser is in this case 1 Wied. Annalen (1898), 65, p. 241. 1 Ann. Chim. Phys. (1873), 28.

3 Phil. Mag. (1895), 39, p. 460.

4 Phil. Trans. (1904), 204, A. p. 139. 6 Comptes rendus, vols. 121, 122, 124.

not necessary, in fact better results are obtained without it. Lecoq de Boisbaudran has applied this method with considerable success, and it is to be recommended whenever only small electric power is at the disposal of the observer. To diminish the resistance the current should pass through as small a layer of liquid as possible. It is convenient to place the liquid in a short tube, a platinum wire sealed in at the bottom to convey the current reaching to the level of the open end. If a thickwalled capillary tube is passed over the platinum tube and its length so adjusted that the liquid rises in it by capillary action just above the level of the tube, the spectrum may be examined directly, and the loss of light due to the passage through the partially wetted surface of the walls of the tube is avoided.

For the investigation of the spectra of gases at reduced pressures the so-called Pliicker tubes (more generally but incorrectly called Geissler tubes) are in common use. When the pressure becomes very low, inconvenience arises owing to the difficulty of establishing the discharge. In that case the method introduced by J. J. Thomson might with advantage be more frequently employed. Thomson 6 places spherical bulbs inside thick spiral conductors through which the oscillating discharge of a powerful battery is led. The rapid variation in the intensity of the magnetic field causes a brilliant electrodeless discharge which is seen in the form of a ring passing near the inner walls of the bulb when the pressure is properly adjusted. A variety of methods to render gases luminous should be at the command of the investigator, for nearly all show some distinctive peculiarity and any new modification generally results in fresh facts being brought to light. Thus E. Goldstein 7 was able to show that an increase in the current density is capable of destroying the well-known spectra of the alkali metals, replacing them by quite a new set of lines.

6. Theory of Radiation. The general recognition of spectrum analysis as a method of physical and chemical research occurred simultaneously with the theoretical foundation of the connexion between radiation and absorption. Though the experimental and theoretical developments were not necessarily dependent on each other, and by far the larger proportion of the subject which we now term " Spectroscopy " could stand irrespective of Gustav Kirchhoff's thermodynamical investigations, there is no doubt that the latter was, historically speaking, the immediate cause of the feeling of confidence with which the new branch of science was received, for nothing impresses the scientific world more strongly than just that little touch of mystery which attaches to a mathematical investigation which can only be understood by the few, and is taken on trust by the many, provided that the author is a man who commands general confidence. While Balfour Stewart's work on the theory of exchanges was too easily understood and therefore too easily ignored, the weak points in Kirchhoff's developments are only now beginning to be perceived. The investigations both of Balfour Stewart and of Kirchhoff are based on the idea of an enclosure at uniform temperature and the general results of the reasoning centre in the conclusion that the introduction of any body at the same temperature as the enclosure can make no difference to the streams of radiant energy which we imagine to traverse the enclosure. This result, which, accepting the possibility of having an absolutely opaque enclosure of uniform temperature, was clearly proved by Balfour Stewart for the total radiation, was further extended by Kirchhoff, who applied it (though not with mathematical rigidity as is sometimes supposed) to the separate wave-lengths. All Kirchhoff's further conclusions are based on the assumption that the radiation transmitted through a partially transparent body can be expressed in terms of two independent factors (i) an absorption of the incident radiation, and (2) the radiation of the absorbing medium, which takes place equally in 1 all directions. It is assumed further that the absorption is proportional to the incident radiation and (at any rate approximately) independent of the temperature, while the radiation is assumed to be a function of the temperature 6 Phil. Mag. 32, PP. 3 2 L 445- 7 Vertr. d. phys. Ces. (1904), 9, p. 321.

only and independent of the temperature of the enclosure. This division into absorption and radiation is to some extent artificial and will have to be revised when theohenomena of radiation are placed on a mechanical basis. For our present purpose it is only necessary to point out the difficulty involved in the assumption that the radiation of a body is independent of the temperature of the enclosure. The present writer drew attention to this difficulty as far back as iSSi, 1 when he pointed out that the different intensities of different spectral lines need not involve the consequence that in an enclosure of uniform temperature the energy is unequally partitioned between the corresponding degrees of freedom. When the molecule is losing energy the intensity of each kind of radiation depends principally on the rapidity with which it can be renewed by molecular impacts. The unequal intensities observed indicate a difference in the effectiveness of the channels through which energy is lost, and this need not be connected with the ultimate state of equilibrium when the body is kept at a uniform temperature. For our immediate purpose these considerations are of importance inasmuch as they bear on the question how far the spectra emitted by gases are thermal effects only. We generally observe spectra under conditions in which dissipation of energy takes place, and it is not obvious that we possess a definition of temperature which is strictly applicable to these cases. When, for instance, we observe the relation of the gas contained in a Pliicker tube through which an electric discharge is passing, there can be little doubt that the partition of energy is very different from what it would be in thermal equilibrium. In consequence the question as to the connexion of the spectrum with the temperature of the gas seems to the present writer to lose some of its force. We might define temperature in the case of a flame or vacuum tube by the temperature which a small totally reflecting body would tend to take up if placed at the spot, but this definition would fail in the case of a spark discharge. Adopting the definition we should have no difficulty in proving that in a vacuum tube gases may be luminous at very low temperatures, but we are doubtful whether such a conclusion is very helpful towards the elucidation of our problem. Radiation is a molecular process, and we can speak of the radiation of a molecule but not of its temperature. When we are trying to bring radiation into connexion with temperature, we must therefore take a sufficiently large group of molecules and compare their average energies with the average radiation. The question arises whether in a vacuum discharge, in which only a comparatively small proportion of the molecules are affected, we are to take the average radiation of the affected portion or include the whole lot of molecules, which at any moment are not concerned in the discharge at all. The two processes would lead to entirely different results. The problem, which, in the opinion of the present writer, is the one of interest and has more or less definitely been in the minds of those who have discussed the subject, is whether the type of wave sent out by a molecule only depends on the internal energy of that molecule, or on other considerations such as the mode of excitement. The average energy of a medium containing a mixture of dissimilar elements possesses in this respect only a very secondary interest.

We must now inquire a little more closely into the mechanical conception of radiation. According to present ideas, the wave originates in a disturbance of electrons within the molecules. The electrons responsible for the radiation are probably few and not directly involved in the structure of the atom, which according to the view at present in favour, is itself made up of electrons. As there is undoubtedly a connexion between thermal motion and radiation, the energy of these electrons within the atom must be supposed to increase with temperature. But we knpw also that in the complete radiation of a white body the radiative energy increases with the fourth power of the absolute temperature. Hence a part of what must be included in thermal energy is not simply proportional to temperature as is commonly assumed. The energy of radiation resides in the medium and not in the molecule. Even at the 1 Phil. Mag. (1881), 12, p. 261.

highest temperatures at our command it is small compared with the energy of translatory motion, but as the temperature increases, it must ultimately gain the upper hand, and if there is anywhere such a temperature as that of several million degrees, the greater part of the total energy of a body will be outside the atom and molecular motion ultimately becomes negligible compared with it. But these speculations, interesting and important as they are, lead us away from our main subject.

Considering the great variety of spectra, which one and the same body may possess, the idea lies near that free electrons may temporarily attach themselves to a molecule or detach , themselves from it, thereby altering the constitution of the vibrating system. This is most likely to occur in a discharge through a vacuum tube and it is just there that the greatest variety of spectra is observed.

It has been denied by some that pure thermal motion can ever give rise to line spectra, but that either chemical action or impact of electrons is necessary to excite the regular oscillations which give rise to line spectra. There is no doubt that the impact of electrons is likely to be effective in this respect, but it must be remembered that all bodies raised to a sufficient temperature are found to eject electrons, so that the presence of the free electrons is itself a consequence of temperature. The view that visible radiation must be excited by the impact of such an electron is therefore quite consistent with the view that there is no essential difference between the excitement due to chemical or electrical action and that resulting from a sufficient increase of temperature.

Chemical action has frequently been suggested as being a necessary factor in the luminosity of flame, not only in the sense that it causes a sufficient rise of temperature but as furnishing some special and peculiar though undefined stimulus. An important experiment by C. Gunther 2 seems however to show that the radiation of metallic salts in a flame has an intensity equal to that belonging to it in virtue of its temperature.

If a short length of platinum wire be inserted vertically into a lighted Bunsen burner the luminous line may be used as a slit and viewed directly through a prism. When now a small bead of a salt of sodium or lithium is placed in the flame the spectrum of the white hot platinum is traversed by the dark absorption of the D lines. This is consistent with Kirchhoff's law and shows that the sodium in a flame possesses the same relative radiation and absorption as sodium vapour heated thermally to the temperature of the flames. According to independent experiments by Paschen the radiation of the D line sent out by the sodium flame of sufficient density is nearly equal to that of a black body at the same temperature. 3 Other more recent experiments confirm the idea that the radiation of flames is mainly determined by their temperature.

The definition of temperature given above, though difficult in the case of a flame and perhaps still admissible in the case of an electric arc, becomes precarious when applied to the disruptive phenomena of a spark discharge. The only sense in which we might be justified in using the word temperature here is by taking account of the energy set free in each discharge and distributing it between the amount of matter to which the energy is supplied. With a guess at the specific heat we might then calculate the maximum temperature to which the substance might be raised, if there were no loss by radiation or otherwise. But the molecules affected by a spark discharge are not in any sense in equilibrium as regards their partition of energy and the word " temperature " cannot therefore be applied to them in the ordinary sense. We might probably with advantage find some definition of what may be called " radiation temperature " based on the relation bet ween radiation and absorption in Kirchhoff's sense, but further information based on experimental investigation is required.

7. Limits of Homogeneity and Structure of Lines. As a first approximation we may say that gases send out homogeneous 2 Wied. Ann. (1877), 2, p. 477.

3 Ibid. (1894), 51, p. 40.

radiations. A homogeneous oscillation is one which for all time is described by a circular function such as sm(nl-\-a), t being the time and n and a constants. The qualification that the circular function must apply to all time is important, and unless it is recognized as a necessary condition of homogeneity, confusion in the more intricate problems or radiation becomes inevitable. Thus if a molecule were .set into vibration at a specified time and oscillated according to the above equation during a finite period, it would not send out homogeneous vibrations. In interpreting the phenomena observed in a spectroscope, it is necessary to remember that the instrument, as pointed out by Lord Rayleigh, is itself a producer of homogeneity within the limits defined by its resolving power. A spectroscope may be compared to a mechanical harmonic analyser which when fed with an irregular function of one variable represented by a curve supplies us with the sine curves into which the original function may be resolved. This analogy is useful because the application of Fourier's analysis to the optical theory of spectroscopes has been doubted, and it may be urged in answer to the objections raised that the instrument acts in all respects like a mechanical analyser, 1 the applicability of which has never been called into question.

A limit to homogeneity of radiation is ultimately set by the so-called Doppler effect, which is the change of wave-length due to the translatory motion of the vibrating molecule from or towards the observer. If N be the frequency of a homogeneous vibration sent out by a molecule at rest, the apparent frequency will be N (i=*=/F), where V is the velocity of light and v is the velocity of the line of sight, taken as positive if the distance from the observer increases. If all molecules moved with the velocity of mean square, the line would be drawn out into a band having on the frequency scale a width 2Nv/V, where i) is now the velocity of mean square. According to Maxwell's law, however, the number of molecules having a velocity in the line of sight lying between v and v+dv is proportional to erPfdv, where |3 is equal to 3/2 2 ; for v=u, we have therefore the ratio in the number of molecules having velocity u to those having no velocity in the line of sight e~/' 2 = e-t = -22. We may therefcre still take 2Nu/V to be the width of the band if we define its edge to be the frequency at which its intensity has fallen to 22% of the central intensity. In the case of hydrogen rendered luminous in a vacuum tube we may put approximately u equal to 2000 metres per second, if the translatory motion of the luminous molecules is about the same as that at the ordinary temperature. In that case \u/V or the half width of the band measured in wave lengths would be f-io~ s X, or, for the red line, the half width would be 0-044 A. Michelson, who has compared the theoretical widening with that found experimentally by means of his interferometer, had to use a somewhat more complicated expression for the comparison, as his visibility curve does not directly give intensities for particular frequencies but an integral depending on a range of frequency. 2 He finds a remarkable agreement between the theoretical and experimental values, which it would be important to confirm with the more suitable instruments which are now at our disposal, as we might in this way get an estimate of the energy of translatory motion of the luminous molecules. If the motion were that of a body at white heat, or say a temperature of 1000, the velocity of mean square would be 3900 metres per second and the apparent width of the band would be doubled. Michelson's experiments therefore argue in favour of the view that the luminescence in a vacuum tube is similar to that produced by phosphorescence where the translatory energy does not correspond to the oscillatory energy but further experiments are desirable. The experimental verification of the change of wave-length due to a source moving in the line of sight has been realized in the laboratory by A. Belopolsky and Prince Galitzin, who substituted for the source an image formed of a stationary object in a rapidly moving mirror.

1 Phil. Mag. (1894), 37, p. 509.

J Cf. Rayleigh, Phil. Mag. (1899), 27, p. 298; Michelson, Mag. (1892), 34. P- 28 - Phil.

The homogeneity of vibration may also be diminished by molecular impacts, but the number of shocks in a given time depends on pressure and we may therefore expect to diminish the width of a line by diminishing the pressure. It is not, however, obvious that the sudden change of direction in the translatory motion, which is commonly called a molecular shock, necessarily also affects the phase of vibration. Experiments which will be discussed in 10 seem to show that there is a difference in this respect between the impacts of similar and those of dissimilar molecules. When the lines are obtained under circumstances which tend towards sharpness and homogeneity they are often found to possess complicated structures, single lines breaking up into two or more components of varying intensities. One of the most interesting examples is that furnished by the green mercury line, which when examined by a powerful echelon spectroscope splits up into a number of constituents which have been examined by several investigators. Six companions to the main lines are found with comparative ease and certainty and these have been carefully measured by Prince Galitzin, 3 H. Stansfield 4 and L. Janicki. 6 According to Stansfield there are three companion lines on either side of a central line, which consists of two lines of unequal brightness.

8. Distribution of Frequencies in Line Spectra. It is natural to consider the frequencies of vibrations of radiating molecules as analogous to the different notes sent out by an acoustical vibrator. The efforts which were consequently made in the early days of spectroscopy to discover some numerical relationship between the different wave lengths of the lines belonging to the same spectrum rather disregard the fact that even in acoustics the relationship of integer numbers holds only in special and very simple cases. Some corroboration of the simple law was apparently found by Johnstone Stoney, who first noted that the frequencies of three out of the four visible hydrogen lines are in the ratios 20 : 27 : 32. In other spectra such " harmonic " ratios were also discovered, but their search was abandoned when it was found that their number did not exceed that calculated by the laws of probability on the supposition of a chance distribution. 6 The next great step was made by J. J. Balmer, who showed that the four hydrogen lines in the visible part of the spectrum may be represented by the equation n = A(i- 4 /i), where n is the reciprocal of the wave-length and therefore proportional to the wave frequency, and j successively takes the values 3, 4, 5, 6. Balmer's formula received a striking confirmation when it was found to include the ultra-violet lines which were discovered by Sir William Huggins 7 in the photographic spectra of stars. The most complete hydrogen spectrum is that measured _ by Evershed 8 in the flash spectrum observed during a total solar eclipse, and contains thirty-one lines, all of which agree with considerable accuracy with the formula, if the frequency number n is calculated correctly by reducing the wave-length to vacuo. 9 It is a characteristic of Balmer's formula that the frequency approaches a definite limit as 5 is increased, and it was soon discovered that in several other spectra besides hydrogen, series of lines could be found, which gradually come nearer and nearer to each other as they become fainter, and approach a definite limit. Such series ought all to be capable of being represented by a formula resembling that of Balmer, but so far the exact form of the series has not been established with certainty.

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Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)

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