KLLIITIC POLARISATION'. 



ELM. 



8H 



to speik more precisely, partially pUiM-pokrisod light), on being 

 examined in thU way, ahnwi the well-known rin** of a imiaxal crystal, 

 diluted with a uniform light upread over the fit-Id ; whereas the light 

 obtained by reflecting plone-puUrised light from a metal, as above 

 described, abowi a syttom of ring* as vivid ai those produced by 

 pUne-poUuised light, but of a different character. 



Light is capable of receiving the same modification by total internal 

 reflexion. If plane-poUrised light be reflected internally from glass at 

 an angle of incidence exceeding the critical angle (or that t which 

 total reflexion begins), then, unlms either the plane of polarisation ! 

 parallel or perpaodicular to the plane of incidence, or the angle of inci- 

 dence be rery near one of the two limits, the critical angle mid 90, 

 the reflected light will ! found to he elliptically polarised, agreeing in 

 i(M characters with light which, having been previously plane-poUrised, 

 has been reflected from im-Ul. 



But elliptic polarisation may also be produced without reflexion, in 

 a manner which indicates at once its real nature. If plane-polarised 

 light be transmitted through a thin plate of mica or eelenite, then, 

 unless either the princi]*! axes of the plate are parallel and perpen- 

 dicular to the plane of primitive polarisation, or else the thickness of 

 the plane has one or other of a set of determinate values, the trans- 

 mitted light will be found to be elliptically polarised, having the same 

 characters as before. 



Now, in this case, we know that the primitive plane-polarised light is 

 divided in passing through the crystal into two pencils, which are polar- 

 ised respectively in the principal planes of the plate, and which after 

 emergence run on together, having been unequally retarded by pausing 

 tbrou.'h the plate. It appears, then, that elliptic polarisation, what- 

 ever it may be. is capable of being produced by the interference of two 

 plane-polarised beams, of which one is retarded relatively to the other. 



If, then, we adopt the undulatory theory of light, and the doctrine 

 of transversal vibrations, we shall be able to form a perfectly clear con- 

 ception of the nature of elliptically polarised light. According to this 

 doctrine, plane-polarised light consists of vibrations which are recti- 

 linear, and perpendicular to the ray (confining our attention to the 

 cose of propagation in ntfito, or in a singly refracting medium), and 

 which, like all the phenomena relating to such light, are symmetrical 

 with respect to the plane of polarisation, and are therefore either in or 

 perpendicular to that plane. Opticians are still divided in opinion on 

 the point last mentioned ; but for the explanation of the phenomena 

 with which we are at present concerned, it is a matter of perfect 

 indifference whether the vibrations are supposed to be parallel or per- 

 pendicular to the plane of polarisation, though, from considerations 

 into which we cannot here enter, the latter view appears the more 

 probable. 



Let the ether be referred to the rectangular axes of x, y, z, the axis 

 of x being measured in the direction of propagation, and those of y, z 

 along the principal planes of the plate ; and let the plane of primitive 

 polarisation be inclined at angles a, 90' a, and to the axes of y, z. 

 Then, if we represent the vibration by a sin p (vt a-), and take y, z to 

 denote the vibrations belonging to light polarised in the planes of x y 

 and x t, the resolved vibrations belonging to light polarised in the 

 principal planes of the plate will be represented by 



y = a cos a sin p (vl x) 

 = a sin a sin p (rt x). 



On emerging from the plate the phase of former vibration will be 

 accelerated or retarded relatively to the latter (suppose accelerated) by 

 8, and putting (f> for p (tt x) + a quantity the same for both, we may 

 represent the vibrations in the emergent light by 



y = a cos a sin (^ + !) 



t = a sin a sin <f. 



To 6nd the equation to the curve described by the ethereal particles 

 we must eliminate <f> from these equations, which gives 



(sin a.y cos aeon Sjf + cot? a sin 5 fj:- = a 5 sin 2 a cos 8 a sin" S, 



the equation of an ellipse, which, when 8 = 90 or an odd multiple of 

 90', and a= 45*, become* the circle 



(/+**-{ A 



Hence the ethereal particle* move in general in ellipses, which is 

 the reason why light thus modified is called by undulationists ellip- 

 tically polarised. It would lead us too far to follow into their details 

 the mathematical characters of the vibrations which, according to the 

 tmdulatory theory, constitute elliptically polarised light, for which the 

 reader is referred to Airj's ' Tracts.' or other standard works on 

 physical optics. 



We are led then to infer that, in the case of light reflected from a 



tel, /r totally reflected internally in gloss, the phase of vibration of 



the component of the reflected light which is polarised in the plane of 



inadenceiii changed relatively to that of the component polarised m 



w perpendicular plane. In the case of metallic reflexion the former 



rv.m|H,nent is accelerated, in the case of total internal reflexion 



etarded. relatively to the Utter. This is shown at once by the 



character of the rings of calcareous spar, observed as above explained, 



by noticing in which pair of opposite quadrants (whether the first and 



third or the second and fourth) the action of the spar, as a doubly re- 



fracting crystal, compensates the change of phase due to reflexion, 

 the spar being known to be a negative crystal. 



From his expressions far the intrnsity of reflected polarised liuht, 

 which in the case of total internal reflexion become imaginary, Fresnel 

 deduced mathematical expressions for the change of phase which 

 accompanies total internal reflexion. Guided by these expressions he 

 was led to construct a rhomb of glass (now known as Fresnel's rhomb), 

 action <>f which in i>f the form of a long parallelogram, the acute 

 ancles of which are determined by an equation involving the refractive 

 index of the glass, and which for the gloss which he employed come 

 out about 54* 37'. Light entering perpundicularly one of the HhrtT 

 faces emerges perpendicularly at the opposite, after suffering two total 

 internal reflexions at the long faces. The angle of the rhomb is deter- 

 mined liy the condition that the difference of phase of the components 

 polarisedin and pcr|Hmdicular to the plane of incidence is one-eight It 

 of an undulation for each reflexion, and therefore one-fourtli 

 unduliition for the two. Such a rhomb is much used in experiments 

 on polarisation ; but it is essential that the gloss should be thoroughly 

 annealed, a condition for want of which many rhombs made for the 

 purpose are worthless. If plane-polarised light is transmitted through 

 such a rhomb, the plane of reflexion in the rhomb being neither 

 parallel nor perpendicular to the plane of polarisation, the emergent 

 light is elliptically polarised ; if through two such rhombs placed with 

 their planes of reflexion parallel, the emergent light, in accordance 

 with the prediction of theory, is found to be plane-polarised, the plane 

 of polarisation being equally inclined with the plane of primitive 

 polarisation to the plane of reflection in the rhombs, but on the 

 opposite side. If, with a single rhomb, the plane of reflexion is placed 

 at 45 to the plane of primitive polarisation, the emergent light is of 

 the kind in which the ellipse of theory becomes a circle, and which is 

 called circularly polarised. Such light is characterised experimentally 

 by presenting the same appearance on analysation when the analyser 

 is turned round, while it differs from common light by presenting a 

 peculiar and perfectly vivid system of rings with calcareous spar, or, 

 if this mode of observation be preferred, by being converted into 

 plane-polarised light by transmission through a crystalline plate of 

 proper thickness, or through a Fresnel's rhomb. 



Whether the plane of reflexion in the rhomb be inclined 45 to the 

 right or to the left of the plane of primitive polarisation, we obtain 

 circularly polarised light ; but the light so obtained in the two cases 

 differs both theoretically and experimentally in a character of right- 

 handedness or left-handedness. Experimentally the difference is at once 

 recognised by means of a plate of calcareous spar and a Nicol's prism, 

 by noticing whether the rings of the first and third quadrant* are 

 pulled out, and those of the second and fourth pushed in, or rice vend. 

 Elliptically polarised light in like manner may be either right-handed 

 or left-handed. 



On the subject of metallic reflexion, the reader is referred to Sir 

 David Brewster's well-known paper in the ' Philosophical Transactions ' 

 for 1830 ; and to an elaborate memoir by M. Jamin, in the ' Annales 

 de Chimie,' ser. iii. torn. 19, p. 296. M. Jamin has also ('An. de Ch.,' 

 torn. 29, p. 263) investigated, in the cose of transparent substances in 

 general, the change of phase about the polarising angle, or, more 

 properly, the angle of maximum polarisation, which Mr. Airy had 

 observed in the case of the diamond. ('Cambridge Philosophical 

 Transactions,' vol. iv. p. 409.) 



ELLIPTIC REFLECTOR. If a pencil of light have its focus at 

 one of the foci of an ellipse, rays diverging from such focus striking 

 upon the ellipse, or on any surface with which the ellipse would co- 

 incide, would be reflected to the other focus. A mirror formed into 

 the figure of an ellipsoid, or portions thereof, acting on this principle 

 is called an elliptic reflector. [ LIGHT.] 



ELLIPTICITY, a term used in the theory of the figure of the 

 earth. It means the fraction whieh the excess of the axis major over 

 the axis minor of an ellipse is of the axis minor itself. Thus, if the 



o 

 axis major be 9 and the axis minor 7 the ellipticity is - . This term 



must not be confounded with the e.rcenlricity, a, word in much more 

 common use. If a and 6 be the semiaxes major and minor, and if e be 

 the excentricity and K the ellipticity, then 



0-6 



if b and a be nearly equal, e 2 = 2 E nearly. 



ELM, Economical Utet. The wood and other ports of the elm-tree 

 are applied to a great variety of useful purposes in the arts of life, both 

 domestic and trading. The timber, being hard and fine-grained, is 

 valuable for ship-building, such as in making the blocks and dead-eyes, 

 but especially the keels, which are made in one piece if the keel be not 

 very long. Elm is used for the naves of wheels ; in London for coffins ; 

 for water-pipes and troughs ; and for conveying the Cheshire brine 

 from the salt-springs to the evaporating pans. Knotted and twisted 

 varieties of the wood are much sought by cal>met-makeri! for ornamental 

 purposes. Elm veneers ore sometimes dyed to imitate mahogany, by 

 means of a dye of dragon's blood, alkanet root, aloes, and spirits of 

 wine. As fuel, and as a material for charcoal, the elm is rather inferior 

 to the beech. The ashes ore rich in alkali. The leaves and young 



