If we have parallel light falling on a slit, then, as before, we may divide the incident wave into half wave-length zones with reference to a point P. If the slit is at a considerable distance from the pole of P, it will include many zones, for at this distance from the pole the zones are very narrow, and the total effect of these zones will be zero. As the slit is moved nearer to the pole, the number of zones included in the portion of the wave which can pass through the slit decreases, and when there is an even number the zones very nearly neutralise each other's effect, and there is a minimum of illumination at P, while when the slit includes an odd number of zones, the illumination is a maximum. The illumination will, of course, be a maximum at a point immediately opposite the slit. On either side will be formed a number of alternate dark and bright lines, the intensity of the maxima rapidly decreasing as we go away from the central band.

CHAPTER VIII

EMISSION AND ABSORPTION OF LIGHT

381. Nature of the Light emitted by a Luminous Body-Spectra. -In § 368 we have referred to the spectrum obtained when sunlight is passed through a prism, we now have to examine the constitution of the light given out by other sources.

If a solid body, such as a piece of lime or of metal, is heated, it begins to glow with a dull red colour at a temperature of about 600° C., and if the light emitted is examined in a spectroscope only the red end of the spectrum will be seen. At a temperature of about 1000° the yellow will appear as well as the red, while at about 1600, the solid will glow with a white light, and the spectrum will stretch from the red to the violet.

The spectrum thus obtained with a glowing solid will differ from the solar spectrum in that there will be no dark bands, the spectrum being continuous from one end to the other.

The same character of spectrum is given by incandescent fluids, such as molten platinum.

When, however, the light given out by glowing gases or vapours is examined, the spectrum produced is of an entirely different character.

Thus, if a salt of either of the metals sodium, calcium, strontium, lithium, &c., is held in a colourless flame, such as that of a Bunsen burner, and the light is examined in a spectroscope, the spectrum will be found to be no longer continuous, but to consist of a number of bright lines in various parts of the spectrum. The position and number of these lines varies for the different metals, but does not depend either on the salt of the metal used (chloride, bromide, sulphate, &c.) or on the nature of the flame into which the salt is introduced. The number of lines visible with any given metal depends, to a certain extent, on the temperature of the flame, but although new lines may make their appearance as the temperature is raised, the position of the lines already present does not vary. FIG. 366. In the case of gases, the spectrum is obtained by passing the spark from an induction coil (§ 524) through the gas which is contained in a rarefied condition in a tube of the shape shown in Fig. 366. In addition to line spectra, under certain conditions of pressure and temperature, the spectra of some gases exhibit bands of light,

which with a small dispersion are generally sharply defined on one side, but shade off gradually on the other. With a high dispersion, these bands are seen to be composed of numerous lines packed close together. When, however, the temperature is raised, the band spectrum becomes changed into a line spectrum.

The character of the lines in the spectrum of a gas depends very much on the pressure to which the gas is subjected. Thus in the case of hydrogen, at low pressures, say below 1 mm. of mercury, the spectrum consists of three narrow lines, one in the violet, one in the blue, and one in the red, which are generally indicated by Hy, HB, and Ha. As the pressure is increased, first the line Hy, then Hs, and finally also Ha becomes wider, while under a pressure of about 36 cm. of mercury the spectrum is practically continuous. The explanation of these changes, if we accept the kinetic theory of gases, is comparatively easy. When a gas is under a low pressure, the mean free path (141) of the molecules is great, so that the interval between successive impacts of a molecule with another is comparatively great. Thus although during the impact the atoms will be set into all kinds of forced vibrations, yet all these vibrations, except those which correspond to the natural period of vibration of the atoms, will very rapidly die out, and for the greater part of the time the atoms will be vibrating in their own natural period. Hence, if we suppose that in a glowing gas the light emitted is due to the vibrations of the atoms, it is evident that at low pressures the gas will give out light of certain definite wavelengths, corresponding to the natural periods of the atoms. As the pressure increases the mean free path of the molecules decreases, and hence the impacts become more frequent. Under these circumstances the forced vibrations will begin to tell, and at first it will be those vibrations which are nearly of the same period as the natural period that will be most noticeable, so that the bands will widen out. When the pressure is further increased, the encounters between the molecules are so frequent that the forced vibrations persist from one encounter to the next, and hence vibrations of all periods will be taking place in the different molecules, and a continuous spectrum will be obtained.

382. Series of Spectral Lines.-If we assume that the frequency of the light vibrations given out by a luminous body is the same as the frequency of the vibrations set up within the molecules of the substance, we are led to the conclusion that the motion of even a gaseous molecule must be very complicated, for the spectrum of most substances contains quite a large number of bright lines, each line corresponding, on the above hypothesis, to a different mode of vibration.

Although at first sight the arrangement of the lines in the spectrum of a gas or vapour appears in general quite irregular, yet a study of this subject has shown that in many cases certain relations are found to hold between the frequencies of the various lines.

The first relation of this kind observed is due to Balmer, who noticed that the wave-lengths, A, of the lines in the hydrogen spectrum can be represented with great accuracy by the general expression

in which m is in succession given the values 3, 4, 5, &c., up to 16. The kind of agreement obtained between the observed values and those calculated from Balmer's formula is shown in the following table :

Another curious fact is that when there exists in the spectrum of an element a doublet or triplet, that is, two or three lines close together, there are also, in general, a number of other doublets or triplets, and the difference between the frequencies of the components of these doublets and triplets is the same for all those which occur in the spectrum of any one element. Thus, in the case of thallium, Kayser and Runge have found the following values for the reciprocals of the wavelengths of the components of the doublets. The reciprocal of the wave-length being proportional to the frequency of the vibrations, the differences will also be proportional to the differences of the frequencies.

If we plot the values of 1/A for the lines given in the above table as abscissæ, as shown in the upper line of Fig. 367, where, since the components of the doublets would be at a constant distance apart throughout, only one has been plotted, the lines do not appear regularly arranged. If, however, the fourth and sixth lines are omitted, the remaining lines can be arranged in two series as shown at B and C, each of which resembles the series of lines represented by Balmer's formula, and can be represented by a similar formula. The separation of the

lines into two series is further justified by the fact that each double line of the first series is accompanied, on its more refrangible side, by a strong line which is easily reversed, while the lines of the second series are not accompanied in this way. The further consideration of this subject is beyond the scope of this work, but sufficient has been said to indicate the direction in which modern work on the classification of the lines in the spectra of the different elements is proceeding.

383. Absorption of Light.-When light passes through a medium, this medium in general absorbs part of the radiation, and the amount of this absorption is generally different for light of different wave-lengths, or, in other words, most media exert a selective absorption on light.

In order to examine the character of the absorption, white light is passed through the given substance, and the transmitted light is examined spectroscopically. If then the substance absorbs light of any particular wave-lengths more strongly than it does light of other wave-lengths, the spectrum will be crossed by dark bands corresponding to the colours which have been absorbed. Thus if a dilute solution of permanganate of potash is used, the spectrum is crossed by five dark bands in the green, while a dilute solution of human blood produces well-marked absorption bands in the yellow and green.

In the case of solutions, the absorption bands are generally fairly wide, the width increasing with the strength of the solution. When light is absorbed by gases or vapours, however, the character of the absorption bands is very different, the bands are sharply defined, and in general consist of a number of fine narrow lines in various parts of the spectrum. Thus if white light from a very hot body, such as the electric