701 



SPECTRUM. 



SPECULUM. 



702 



metallic woven spectacles for the free admission of air to the eyes, 

 while they serve as a screen against dust, insects, to., and also subdue 

 the light. 



SPECTRUM (in optics) is the name applied to the coloured image 

 of the sun, or a narrow luminous object, when the light proceeding 

 from it is transmitted through a prism, and either allowed to fall on a 

 screen at some distance, or received directly into the eye. [DISPER- 

 SION.] A similar coloured image, produced by diffraction, may be 

 obtained without a prism [DIFFRACTION OP LIGHT], and to it the 

 term tpettrum equally applies. 



The fiied lines of the solar spectrum have been already mentioned 

 in the former of the articles just quoted. Much light has recently 

 been thrown on their origin by the labours of Professor Kirchoif. 

 Fraunhofer long ago observed that the spectrum of a candle, or of a 

 spirit-lamp, exhibits a double bright line, which exactly coincides in 

 position with the double dark line D of the solar spectrum ; and Sir 

 David Brewster noticed a similar correspondence in the case of defla- 

 grating nitre. (' Report of the British Association," for 1842, p. 15.) 

 An imitation of the fixed lines of the solar spectrum, as to their general 

 character, is obtained by subjecting light to the absorbing action of 

 certain gasea, as was first discovered by Sir David Brewster, in the 

 case of nitrous acid gas. If the light of a lamp, which, if unmodified, 

 would give a continuous spectrum, be transmitted through this gas, 

 and then analysed, the spectrum is seen to be traversed by numerous 

 dark lines or narrow bands, which by their sharpness of definition, 

 narrowness, and apparently capricious arrangement, remind one of the 

 lines of the solar spectrum. That tome of the fixed lines of the spec- 

 trum seen when the sun is near the horizon are to be attributed to 

 absorption by the earth's atmosphere, is evident from the fact that 

 they are not seen when the sun is high ; but that all have not this 

 origin seems to follow from the fact, observed by Fraunhofer, that 

 different fixed stars have lines of their own, whereas were all the lines 

 due to absorption in the earth's atmosphere, the same system ought 

 to be seen whether the source of light were the sun or a fixed star. 



During the researches in which he was engaged, in common with 

 Professor Bunsen, on the application of the prismatic analysis of 

 flames to qualitative chemical analysis, Professor Kirchoff was led to 

 discover that flames which exhibit in their spectra bright lines of 

 certain definite refrangibilities at the same time absorb energetically 

 light of those precise degrees of refrangibility. (Poggendorffs ' Annalen,' 

 vol. ex., p. 161 ; or ' PhiL Mag.' for August, 1860.) He further connected 

 this phenomenon with Prevost's theory of exchanges. He found that 

 if behind a flame giving bright lines in its spectrum were placed 

 a brilliantly luminous body of higher temperature, giving itself alone 

 a continuous spectrum, the compound light, consisting partly of light 

 emitted by the flame, partly of light emitted by the luminous body 

 behind it and transmitted through the flame, exhibited on analysis 

 dark lines in the places of the bright lines given by the flame alone ; 

 the regions of those lines, as compared with the neighbouring regions, 

 Buffering more in luminosity by absorption of the light from the 

 luminous body than they gained by the light emitted by the flame. A 

 particular instance of this simultaneous emission and absorption oi 

 rays of definite refrangibility had been observed in the case of the 

 voltaic arc many years before by Foucault (' L'Institut,' for Feb. 7, 

 1849), who, however, had not further followed the observation, nor 

 connected it with the theory of exchanges. Now the outer portions oi 

 the atmosphere of the sun or a star, and the inner portions, or else 

 the solid or liquid body itself, may be conceived to be in the same 

 relative condition as the flame in the above experiment and the 

 luminous body behind it ; and thus we are led to connect the darl 

 lines seen in the spectra of light coming directly from the sun or a fixec 

 star, with the presence in their atmospheres, in a state of incandescence 

 of those elements, which, when present in flames, cause them to give 

 out bright lines of the same refrangibility. It is found that the intro 

 duction of small quantities of various metallic salts into a flame causes 

 its spectrum to exhibit bright lines, depending upon, and characteristic 

 of, the metal introduced ; and by comparing these lutes with the dark 

 lines of the solar spectrum we may infer the presence or absence o 

 such metals therein. Thus Professors Bunsen and Kirchoff have con 

 eluded that the solar atmosphere contains potassium and sodium, thai 

 lithium is absent, or present in comparatively small quantity, and sc 

 forth. 



SPE'CULUM, a name frequently given to a mirror used for anj 

 scientific purpose, as in a reflecting telescope. For the astronomica 

 bearings of the speculum we refer to TELESCOPE, but we here give the 

 first part of the simpler mathematical description of a pencil o 



mirror, to which we proceed, referring to Mr. Griffin's work on OPTICS 

 or further information. Let a pencil of rays fall on the spherical 



mirror A B from the point p, of which rays p B is one. Let p B bo 

 effected into Bp. It is supposed that p is in the radius o A, which is 

 tie axis of the mirror ; o being the centre of the sphere. Let A o = r, 

 . P = M, Ap = t>. The nearer B is taken to A, the more nearly does the 

 ioint p approach to a certain point F, at which the image of p is 



jaid to be formed : not that any rays are actually reflected to F, 

 lut because all the rays which are reflected from points near to 

 i fall exceedingly near to F, which is the cusp, and brightest point 

 if the CAUSTIC. If A F = w, the position of F is determined by the 

 quation 



1 2 1 



The point p however is always nearer to A, or lies between F and A, 

 and p F, or the longitudinal aberration, is thus found : let the length 

 of the arc A B be y ; then 



rays incident upon a mirror, BO as to make this article a counterpar 

 to LESS. 



The convex mirror is comparatively of no importance, and th 

 fonnuto for it may be [easily derived from those for the concav 



ery nearly, if y be not very great. And for the lateral aberration P t, 

 we have 



w /I l\a 



ft = -(- -) 3....(3). 

 r \r u/ y 



Again, there is for all the rays proceeding from P, after reflection, a 

 circle through which they all pass, as in LENS. The distance of this 

 circle of least aberration from the focus F toward A, is the following 

 expression : 



8 W'T /I IVi 



4 (r- -J "* 



1 Y be the whole semi-arc of the mirror : it ia therefore three-fourths 

 of the longitudinal aberration of the extreme ray. The diameter of 

 this circle of least aberration is 



1 WY 3 /I 1\2 



2 (F-;) - 



or one-half the lateral aberration of the extreme ray. 



When the r.iys fall parallel to each other on the mirror, it is infinite, 



and we have - r for the value of w, -L for the longitudinal aberration, 

 2 4r 



'L- for the lateral aberration, -L for the distance of the circle of 

 2C 2 IGr 



least aberration from 'the focus, and for its diameter. 



4r 



When u r, or the incident pencil is thrown from the centre, it is 

 returned again to the centre, and there are no aberrations. 



When u is less than r, or p is between o and A, F then falls beyond 

 o, and, as p approaches to the middle point of o A, recedes without 



limit. When u= _ ), or P is at the middle point of OA, all the 

 reflected rays are parallel to one another and to the axis of the mirror. 



And when is less than ), w becomes negative, or the focus is on 



2t 



the other side of the mirror, and the reflected rays diverge ; but only 

 (lie latitudinal aberration alters its sign. 



The formulae for a convex mirror may be found by making nega- 

 tive in those for a concave mirror. Hence w is always negative, or the 

 focus of every pencil is behind the mirror : the longitudinal aberra- 

 tions change sign, but not the latitudinal ones : and as w has also 

 changed sign, the effect is that p ia always nearer to the mirror than 

 F, as before. 



The image in a convex mirror is always upright ; and in a concave 

 one always inverted, except when the object falls between the principal 

 focus (or middle point of the radius) and the mirror. 



The astronomical value of the speculum depends on the quantity of 

 light that it can concentrate, and on the precision with which it forms 

 the optical image of a distant object. Hence the magnitude, the cur- 

 vature, and the surface polish are all of importance. The figure may 

 be parabolic, where every part has the same focus, or it may be an 

 ellipsoid, where the edge is of shorter focus than the centre, or if 

 longer an hyperboloid. The grinding and polishing of lenses in a 

 refracting telescope, to say nothing of the difficulty of obtaining good 

 optical glass, greatly limit the perfection of that form of telescope ; 

 but an amount of error that would be tolerated in the best lenses, 

 would be fatal in the speculum of a large reflecting telescope. The 

 difficulties of forming an accurate speculum constitute a problem of 

 the highest order, the solution of which has received the careful study 

 of first-rate astronomers and mechanicians. The reader who is 

 desirous of seeing how these difficulties have been overcome, will do 

 well to consult the memoir communicated to the Royal Society of 

 London in 1840 by t Lord Oxmantown (now Earl of Rosse) entitled ' An 

 Account of Experiments on the Reflecting Telescope." We may also 



