Prisms are nearly always used in the position of minimum deviation, but, if the collimator is properly adjusted, this is by no means a necessary condition for good definition. Prisms as generally cut, with an isosceles base, give the greatest resolving power in the position of minimum deviation, but the loss in resolving power is not great for a small displacement. The dispersion and magnifying power of a prism can be considerably altered by a change of its position, and a knowledge of this fact is of great value to an experienced observer. The use of a prism in a position different from that of minimum deviation is, however, a luxury which only those acquainted with the laws of optics can indulge in with safety.

Lord Rayleigh has given the theory of the spectroscope under Optics, and shown on what its resolving power depends. There is no connexion between resolving power and dispersion, any value of resolving power being consistent with any value of dispersion. To obtain large resolving power with small dispersion requires, however, the use of inconveniently large telescopes and prisms or gratings. It is easy, on the other hand, to obtain small resolving power together with large dispersion.

The following definitions would be found of general use if adopted. Resolving Power.— The unit resolving power of a spectroscope in any part of the spectrum is that resolving power which allows the separation of two lines differing by the thousandth part of their own wave-length or wave-number,—the wave-number being the number of waves in unit length. Purity.— The unit purity of a spectrum is that purity which allows the separation of two lines differing by the thousandth part of their own wave-length or wave-number. We speak of the resolving power of a spectroscope and of the purity of a spectrum. The resolving power is a constant for each spectroscope, and independent of the width of the slit. The purity of a spectrum, on the other hand, depends on the width of the slit, unless that width is small compared to a certain quantity presently to be mentioned. The resolving power of a spectroscope is numerically equal to the greatest purity of spectrum obtainable by it.

Adopting these definitions, we get from Lord Rayleigh’s equations for the resolving power R of a grating

1000 R=mn, where n is the total number of lines used on the grating and m the order of the spectrum. For a spectroscope with simple prisms we get

1000 R =-(t 2 - t 1 ) δμ / δλ , where t 2 and t 1 are the greatest and smallest lengths of paths in the dispersive medium. If we put for the refractive index of the medium μ = A + B /λ 2 we may write

1000 R =2 B (t 2 - t 1 )/ λ 3 ∙

It will be seen that, while the resolving power of a spectroscope with grating depends only on the order of the spectrum and is independent of the wave-length for each order, the resolving power of a spectroscope with prism will vary inversely as the third power of the wave-length λ, so that the resolving power will be about eight times as great in the violet as in the red (see Optics). If compound prisms are used we must write

1000 R =2(B 2 t 2 - B 1 t 1 )∕λ 3 , where t 2 is the greatest effective length of path in one medium, t 1 in the other medium, B 2 and B 1 being the dispersive constants for the two media.

The purity P of a spectrum is given by the equation P = λ / dψ + λ R , where d denotes the width of slit and ψ is the angle subtended by the collimator lens at the slit. If the slit is sufficiently narrowed, d ψ may be made small compared to λ, and in that case the purity of the spectrum is independent of the width of slit and equal to the resolving power. If, on the other hand, a wide slit is used, so that d ψ is large compared to λ, the purity becomes inversely proportional to the width of slit. In actual work the slit is generally of such width that neither term in the denominator of the expression for purity can be neglected.

There is a necessary limit to the resolving power of all optical instruments, depending on the fact that light consists of a series of groups of waves incapable of interfering with each other. If it is true, as is generally believed, but without sufficient reason, that a retardation of 50,000 wavelengths is sufficient to destroy the capability of interference—that is to say, that the groups consist on the average of approximately 50,000 waves—the maximum purity obtainable in any spectroscope is 50. The closest line resolved with a grating, as far as the present writer is aware, requires a resolving power of about 100. Professor Piazzi Smyth has with prisms realized a purity of 50. It would seem, therefore, that the theoretical limit of purity has very nearly been reached, for, though the estimate of 50,000 waves to the group is in all probability too small, there are other considerations which render it highly improbable that the total number of waves to the group should, for sunlight at any rate, be more than two or three times larger. The limit of possible purity will very likely depend on the temperature of the luminous body.

Almost the greatest practical difficulty which the spectroscopist has to contend with generally is the want of sufficient light. The following remarks apply to line spectra principally, but they hold also almost entirely for the spectra of fluted bands, which break up into lines under high resolving power. The maximum illumination for any line is obtained when the angular width of the slit is equal to the angle subtended by one wave-length at a distance equal to the collimator aperture. In that case dψ = λ and the purity is half the resolving power. Hence when light is a consideration we shall not, as a rule, realize more than half the resolving power of the spectroscope. If the visual impression depended only on the intensity of illumination, a further widening of the slit should not increase the visibility of a line. As a matter of fact spectroscopists generally work with slits wider than that which theoretically gives full illumination. The explanation of the fact is physiological, visibility depending on the apparent width of the object. If different spectroscopes have their slits of such width that the apparent width of a line as seen by the eye is the same, and if the magnifying power is such that the pupil is just filled with light, the purity of the spectrum is directly proportional to the resolving power. We come to the conclusion, therefore, that for both narrow and wide slits the efficiency of a spectroscope depends exclusively on its resolving power. It has been pointed out by Lord Rayleigh that, owing to the want of definition in the optical images on the retina when the full aperture of the pupil is used, the pencil must be contracted to a third or a quarter of its natural width, if full resolving power is to be obtained. This is accompanied with a serious loss of light, which can be partly obviated by contracting the horizontal aperture only (the refracting edge being supposed vertical). There are two ways of doing this. One consists in the use of magnifying half prisms. But the loss of light by reflexion in simple half prisms more than counterbalances the advantage; compound half prisms like those used by Christie may, however, be employed. We may also use prisms of three or four times the height of the effective horizontal aperture, with correspondingly large telescopes, and then by the eye-piece contract the beam until its vertical section fills the pupil. The latter plan, though theoretically best, involves more expensive apparatus and prisms of very homogeneous material.

The question of illumination is important also when photography is used for spectroscopic analysis. For a given intensity of the source of light the intensity of the image on the sensitive film will be directly proportional to the solid angle of the cone of light forming the last image, and will be independent of the arrangement of intermediate lenses. Hence lenses with as short a focus compared to aperture as is consistent with good definition should be used in the camera.

The methods of recording and reducing spectroscopic observations are described in all books and treatises on the subject and may therefore be passed over here.

A lens is often used to concentrate the light of the source on the slit. There is some loss of light due to reflexion from the surface of the lens, but its position, aperture, and focal length do not affect the luminosity of the spectrum seen as long as the whole collimator is filled with light.

Bodies are rendered luminous for spectroscopic investigation either by being placed in the Bunsen flame or by the help of the electric current. A little difficulty may arise where the body is given in solution and does not show its characteristic lines in the flame. Lecoq de Boisbaudran takes the spark from the surface of the solution. The present writer has found the tube sketched in the figure on the next page a great improvement on those commonly used, if a sufficient quantity of the solution is at hand; otherwise the method is too wasteful. The current is brought into the solution by a platinum wire, sealed into a small glass tube; the platinum wire reaches about to the level of the open end of the tube. A capillary of thick-walled glass tubing is placed over the platinum wire; the liquid rises in the capillary and sparks can be taken as from a solid. The lines due to the glass are easily eliminated.

If a small quantity of material only is avail able, the plan adopted by Bunsen and ex tensively used by Hartley seems the most successful. Pointed pieces of charcoal (Bun sen) or pieces of graphite pointed to a knife edge (Hartley) are impregnated with the liquid, and the spark is taken from them. Some substances, when introduced into a vacuum tube, especially near the negative pole, and under great exhaustion, show a characteristic phosphorescence. Becquerel was the first to examine the spectra shown under these circumstances, and Crookes has lately used the same method with great success.

Spectra of Metalloids.

A good deal of discussion has taken place on the spectra of the metalloids, owing to the fact that they seem to he able to give different spectra under different circumstances. Spectra have occasionally been assigned to the elements which on further investigation were found to belong to some compound present. According to the general opinion of spectroscopists at present, different spectra of the same elements are always due to different allotropic conditions. If a complex molecule breaks up into simpler molecules the breaking up is always accompanied by a change of spectrum.

Nitrogen. —(a ) The line spectrum appears whenever a strong spark (jar discharge) is taken in nitrogen gas. It is always present when metallic spectra are examined by the ordinary method of allowing the jar discharge to pass between metallic poles. Hartley (Phil. Brans., 1884, part i.) has measured the ultra-violet lines of the air spectrum, but has not separated the oxygen from the nitrogen lines, (b ) The band spectrum of the positive discharge, which is generally called the band spectrum of nitrogen, always appears when the discharge is sufficiently reduced in intensity. The spectrum consists of two sets of bands of different appearance, one in the less refrangible part and one in the more refrangible part of the spectrum, —the two sets of bands overlapping in the green. Hence some observers believe the spectrum to be made up of two distinct spectra. Plücker and Hittorf (Phil. Trans., 1865) give a coloured drawing of this spectrum, which is one of the most beautiful that can be observed. The most complete drawing of it is given by Piazzi Smyth (Trans. Roy. Soc. Edin., vol. xxxii. part iii.), and there is also a good drawing by Hasselberg (Mém. Acad. Imp. de St.Pétersb., vol. xxxii.). (c) The glow which surrounds the negative electrode in an exhausted tube shows in many cases a spectrum which, as a rule, is not seen in any other part of the tube. The memoir of Hasselberg contains a drawing of it. The spectrum seen when a weak spark is taken in a current of ammonia is neither that of nitrogen nor that of hydrogen, but must be due to a compound of these gases. When the pressure of the gas is reduced, a single band is seen having a wave-length from 5686 to 5627 X th metres (Nature , vi. p. 359). When a spark is taken from a liquid solution of ammonia a more complicated spectrum appears (Lecoq de Boisbaudran), and, if ammonia and hydrogen are burnt together either in air or oxygen, a complicated spectrum is obtained the chemical origin of which has not been satisfactorily explained. Drawings of it are given by Dibbits (Pogg. Ann., cxxii. p. 518) aud by Hofmann (Pogg. Anm., cxlvii. p. 95). The absorption spectrum of the red fumes of nitrogen tetroxide has often been mapped; the most perfect drawing is given by Dr B. Hasselberg (Mém. Acad. Imp. de St. Pét., xxvi.). According to Moser (Pogg. Ann., clx. p. 177), three bands close to the solar line C disappear when the vapour is heated. Recently Deslandes has obtained in vacuum tubes some ultraviolet bands which seem to be due to a compound of nitrogen and oxygen (C. R., chap. i. p. 1256, 1885).

Oxygen.—(a) The elementary line spectrum of oxygen is that which appears at the highest temperature to which we can subject oxygen, that is, whenever the jar and air break are introduced into the electric circuit. It consists of a great number of lines, especially in the more refrangible part of the spectrum, (b ) The compound belonging to sodium, with wave-lengths 8187 and 8199 (Proc. Roy. Soc., xxxii. p. 443, 1881). Becquerel finds lines in the infra-red at 11,420. The vapour of sodium and potassium heated up in a tube is coloured and shows a spectrum of fluted band; but in the ease of sodium the yellow line is always present at the same time. It is probable that the band spectrum belongs to the vapour, containing two atoms in each molecule, and that at higher temperatures the molecules are split up, the single atoms showing the line spectra. Both potassium and sodium show an additional absorption line (5510 for Na and 5730 for Ka) at the temperature at which the fluted bands appear. According to a suggestion of Liveing and Dewar, these lines may depend on the presence of hydrogen, which it is very difficult to exclude. These experimenters have also described interesting but complicated absorption phenomena depending on the simultaneous presence of two or more metals. Thus sodium and magnesium show a band in the green (λ=5300), which does not appear when sodium alone or magnesium alone is volatilized. Potassium and magnesium show similarly two lines in the red (Proc. Roy. Soc., xxvii. p. 350, 1878). If a spark is taken from potassium in an atmosphere of carbonic oxide a band appears (5700) depending probably on a combination between the potassium and the carbonic oxide. Lockyer has observed certain curious phenomena (Proc. Roy. Soc., vol. xxii. p. 378) taking place at the temperature at which the band spectrum of sodium changes into the line spectrum; these phenomena deserve a fuller investigation. Lithium furnishes a good example of a change in the relative intensity of lines at different temperatures. At the temperature of the flame the red line is the most powerful, an orange line being also seen. When a spark is taken from a liquid solution the orange line is far the strongest, and a blue line is seen, which in its turn rapidly gains in intensity as the temperature is raised. When the spark is taken from solutions of different strengths the more concentrated solution shows a change in relative intensity of lines in the direction in which an increase of temperature would act. Combination of the metals with transparent acids does not when in solution show any appreciable absorption in the visible part of the spectrum; but Soret has mapped their ultra-violet absorption.

Metals of Alkaline Earths.— Calcium, strontium, and barium are distinguished by the fact that their volatile compounds give fine spectra in the Bunsen flame. The more stable salts, as the phosphates and silicates, give the reaction only feebly or not at all. When a salt like the chloride of barium is introduced into the flame the spectrum is seen to change gradually; the spectrum seen at first is different according as the chloride, bromide, or iodide is used, while the spectrum which finally establishes itself is the same for the different salts of the same metal. Mitscherlich, who was the first to investigate carefully these phenomena (Pogg. Ann., cxxi. p. 459, 1864), ascribes the spectra seen at first to the compound placed in the flame, while gradually the oxide spectrum gets the upper hand. This explanation has always been accepted, and receives support from the fact that the bromide spectrum is strengthened by introducing bromine vapour into the flame, and the other compound spectra can be similarly strengthened by introducing suitable vapours. There is an observation, however, made by Professors Liveing and Dewar which in one case is not compatible with Mitscherlich's explanation. “A mixture of barium carbonate, aluminium filings, and lamp-black heated in a porcelain tube gave two absorption lines in the green, corresponding in position to bright lines seen when sparks are taken from a solution of barium chloride, at wave-lengths 5242 and 5136, marked a and β by Lecoq de Boisbaudran.” These two lines, or rather bands, are the brightest in the spectrum commonly ascribed to barium chloride. In addition to the compound spectra the brightest of the metallic lines seep at a low temperature appear in the flame. The metallic line is in the violet with calcium, in the blue with strontium, and in the green with barium. Sparks taken from a solution of the metallic salts show the compound spectra well, and in addition more of the true metallic lines than the flame. The best drawings of the compound spectra are those given in Lecoq de Boisbaudran’s Atlas ; but measurements with higher resolving powers are much wanted. When the salts are introduced into the voltaic arc numerous metallic lines appear which have been mapped by Thalén. Liveing and Dewar have investigated those lines which can be reversed and have also mapped the ultra-violet spectra. Captain Abney has mapped a pair of infra-red lines belonging to calcium between 8500 and 8600, and, according to Becquerel, with the help of a phosphorescent screen bands or lines appear of still lower refrangibility (8830 to 8880). Lockyer (Phil. Trans., clxiii. p. 253, 1873, and clxiv. p. 805, 1874) has measured and mapped as regards their length the lines of these as well as of many of the other metals.

Metals of Magnesium Group.— Beryllium presents comparatively simple spectroscopic phenomena, as far as it has hitherto been investigated. Two green lines were mapped by Thalén and five in the ultra-violet by Hartley (Jour. Chem. Soc., June 1883). The spectrum of magnesium is well known from its green triplet; but tħe vibrations of the metal seem very sensitive to a change of conditions....