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refraction, and shall in general give them in the words of the author.

96. (1.) The objects seen through this crystalline prism appear sometimes, and in certain positions of the prism, double; where it is to be noted, that the distance between the two images is greater or less, according to the different bigness of the prism; insomuch that in thinner pieces this difference of the double image almost vanisheth.

97. (2.) The object appearing double, both images appear with a fainter color; and sometimes one part of the same species is obscurer

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98. (3.) To an attentive eye one of these images will appear higher than the other.

99. (4.) In a certain position the image of an object seen through this body appears but single, like as through any other transparent body.

100. (5.) We have also found a position wherein the object appears six-fold.

101. (6.) * If any of the obtuse angles of this prism be divided into two equal parts by a line, and the visual rays do pass from the eye to the object through that line or its parallel, both images will meet in that line, or in another parallel to it.

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102. (7.) Whereas objects seen through diaphanous bodies are wont to remain constantly in the same place, in what manner soever the transparent body be moved, nor the image on the surface move, except the body be moved; we have observed here that one of the images is moveable, the other remaining fixed; although there be a way also to make the fixed image moveable, and the moveable fixed in the same crystal, and another to make both moveable.

103. (8.) The moveable image doth not move at random, but always about the fixed, which while it turneth about, it never describeth a perfect circle but in one case.

104. (9.) Dioptrics teach, that a diaphanous body having one only surface, sends from one object but one image refracted to the eye, and, having more surfaces than one, it represents one image in each. But, whereas in our substance there occurs but one plain surperficies to the eye, and yet a double image of one object, it concerned us to consider whence this double image might be caused. Two ways offered themselves to us, reflection and refraction. How reflection could perform it, was difficult to find. For, having dulled the clearness of the two plain sides of our crystalline prism, thereby to make them unfit for reflecting the light, the rays being directed through its upper and lowermost superficies, the image still appeared double. Again, two species appearing through a great prism, upon breaking of the same into pieces, and so reducing it into divers smaller ones, it came to pass, that through each of these less portions the same object was seen always double. Whence I collected, that if it should be said that one of the images proceeded from the reflection of the plain sides, the former of these experiments would discountenance that assertion. But then if another should derive the cause from some internal reflection of the surfaces of this

body, certainly the same effect would not have been found in every one of its parts; but the double appearance that was exhibited in the smallest portion would have been multiplied in a greater bulk.

105. Reflection, therefore, not satisfying, we recurred to refraction. But whereas it is known that no image can pass through two diaphanous bodies of a different nature but by refraction, and that one image supposeth one refraction, it did follow that, if refraction were made the cause of this phenomenon, there would be a double refraction for a double image. And forasmuch as the appearances of our Iceland crystal are not of the same kind, but one of them is fixed, the other moveth, we shall distinguish the refractions themselves which refract the double rays arriving to the eye, and call the one which sends the fixed image refracted to our sight, usual; the other, which transmits the moveable to the eye, unusual. And hence, namely, from this peculiar and notable property of the double refraction in this Iceland-stone, we have not scrupled to call it dis— diaclastick.

106. This being supposed, it will not be irrational to suspect that these two refractions proceed from different principles. For, since it is commonly known from dioptrics that an object, by visual rays affecting the eye, exhibits some image on the superficies of the diaphanous bodies, which image is but one as long as the superficies is one, and the upper plain parallel to the lower; as also, that if, the eye remaining steady, the diaphanous body be moved, that image remains always fixed, as long as the object whence it comes remains unmoved; therefore, in this transparent substance, the image which appears fixed may proceed according to the ordinary laws of usual refraction; but that which moveth, and is carried about according to the motion of the diaphanous body, while the object remains unstirred, showeth an unusual kind of refraction, hitherto unobserved by dioptricians.

107. Hence, that I might examine the nature and difference of both, I put upon some object, as the point A, fig. 5, the prism of my double refracting crystal NPRQTBS, and, the eye M being perpendicularly posited over the upper plain of the prism NPRQ, I noted whether there was any refraction of the point A, for the usual laws of refraction teach that there is none. But the perpendicular ray of the eye was observed to pass not through the moveable but the fixed image, thereby being conformable to the rules of usual refraction, as striking the eye unrefracted, so that the eye, the image, and the object, were seen in the same line. But when in the same site of the eye, the object A did also exhibit the other image X, at no small distance from the former, I took notice that this object A was not seen unrefracted by the means of the image X, though the eye M remained perpendicular over the plain; and that, consequently, this unusual refraction is not subject to the received axiom of dioptrics, which imports that a ray, falling perpendicularly on the superficies of a diaphanous body, is not refracted, but passeth unrefracted.

108. 'Next I so placed the eye in O that the

ray from the object A arriving to the eye, might be parallel to the lines RT and QB of the plane RQT B, &c.; then it appeared that the rays were trajected from the object A without refraction, through the moveable image Q; the object A, the moveable image Z, and the eye O, being in the same line; and that the same object A did transmit to the eye O, remaining in the same position, yet another species Y, through the refracted ray A YO. Whence it was manifest to me that this unusual refraction had for its rule the parallel of the sides of this double refracting crystal, while the usual refraction was directed according to the perpendicular of the superficies. 109. But considering that the place of the point appearing through our diaphanous body cannot easily be determined, as being only obvious in the uppermost part, we shall add the way whereby we have found its diversity, by drawing on the subjacent table a straight line through that point; the place of which line will be determined by the one eye through this crystal, and by the other eye without the crystal. For, in the same figure, let through the object A be drawn upon the table a straight line BC. The eye being in M, that double line HD and IE will appear, the species being cast on the upper surface; and, if you will attend well, you will observe one of the images, viz. the fixed HD, to be congruent to the adjacent line BC, whilst the other, namely, the moveable EI, tendeth towards R. But if afterwards the eye be posited in O, the same object, I mean the line B C, will not only be represented double by the images K F and LG, but also the moveable image G L be congruent to the inferior line BC, while the fixed F K is not so, but tends towards N.'

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110. After describing these experiments, Bartholinus proceeds to measure the ratio of the angles of incidence and refraction in the ordinary image, and he finds it to be as five to three, which makes the index of refraction 1.667. He endeavours to account for the double refraction, by supposing that the Iceland crystal has two sets of pores; one, according to the ductus or direction of the sides, and parallel thereto; since it may be observed that, according to this disposition of the sides, it is broken, and the parts severed from one another, and that one of the images, namely the moveable, passeth through them. Next, besides these pores lying according to the parallelism of the sides, it has others, such as glass, water, and right crystals have, through which the right image is transmitted.' 111. Bartholinus next supposes that there are some directions in which the rays pass through the crystal unrefracted; and though, in ordinary diaphanous bodies, these directions are perpendicular to their surfaces, yet in other bodies they may have another position. He likewise supposes that half of the incident pencil is refracted usually, and the other half unusually; or, what is the same thing, that the usual and unusual refractions have the same power to refract the incident light.

112. From this account of Bartholinus's experiments, he appears to have discovered three important facts.

113. (1.) That Iceland spar has the property of double refraction.

114. (2.) That one of these refractions is performed according to a law which is common to all transparent sclids and fluids, while the other is performed according to an extraordinary law which had not previously been observed by philosophers; and,

115. (3.) That the incident light is equally divided between the ordinary and extraordinary pencils.

116. Bartholinus does not seem to have transmitted the ordinary and extraordinary pencils through a second piece of Iceland spar, and it was therefore reserved for the celebrated Huygens to discover, by means of this experiment, the remarkable properties which arise from the polarisation of these two pencils.

117. A few years after the publication of Bartholinus's work on Iceland crystal, the attention of Huygens was directed to the subject of double refraction. He was induced to begin this investigation principally with the view of obviating any objection that might be drawn from the facts discovered by Bartholinus, against his own theory of ordinary refraction; and he was led to the particular views which he has published from a desire to assimilate the two classes of phenomena.

118. His researches on the subject from the fifth chapter of his Traité de la Lumiere, which is entitled De l'Estrange Refraction du Cristal d'Islande. This work was composed about the year 1678, and read to several of the learned individuals who then composed the Academy of Sciences; but it was not published till the year 1690, when its author was resident in Holland.

119. After a few preliminary observations, in which he gives Bartholinus the credit of having discovered some of the principal phenomena, he supposes A B EF, fig. 6, to be a piece of Iceland crystal, and conceiving one of the three obtuse angles, which form the solid angle C, namely, ACB, to be bisected by CG, he calls the plane CGHF, which passes through this line, and the side C F, the principal section of the crystal.

120. If the surface A B is now exposed to the sun, being all covered but a small aperture K in C G, and if a ray I K is incident perpendicularly at K, it will be divided at the point K into two rays, one of which, K L, will be a continuation of IK; while the other, K M, will deviate from KL towards C, by an angle of 6° 40′, but will still be in the plane CGHF. This ray will emerge at M in the direction M Z parallel to IK. Hence, since the point M, by the extraordinary refraction, is seen by the refracted ray MKI, the eye being at I, any point or aperture at I, by the same refraction, will be seen by the refracted ray LKI, LK being parallel to M K, if I is very distant. The point L will consequently be seen in the direction IR S, and, as the same point is seen by the ordinary refraction in the direction IK, it will necessarily appear double.

121. If the ray now falls in the direction NO, in the plane CG HF, making an angle of 73° 20′ with C G, or nearly parallel to CF, which makes with F H an angle of 70° 57', it will be divided at O into two rays, one of which will be

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a continuation of NO, without refraction, while the other will be refracted in the direction OQ, both rays being in the plane CGHF. This is true of all planes parallel to the principal sec

tion.

122. In order to determine the law of the two refractions, Huygens drew upon a smooth surface a black line, A B, fig. 7, and two lines CED, K ML, perpendicular to it, and having their distance EM greater or less, according to the obliquity at which the refraction is to be examined. The crystal being placed upon E, so that A B is in, or parallel to, the principal section EG, place the eye above it, and the line AB will be seen single, but CD will be double. The ordinary image will be easily distinguished from the extraordinary image, from the latter being always more elevated, or from the former remaining fixed in turning the crystal, while the latter revolves round the ordinary image.

123. If the eye is now placed at I, perpendicular to AB, till it sees the ordinary image of CD coinciding with the part of C D without the crystal, let the point H be marked on the crystal where the intersection at E appears. Let the eye be now taken towards O, in the same perpendicular plane, till the ordinary image of CD coincides with K L, and let the point N, where the intersection E now appears, be marked upon the crystal. The lines N H, EM, and H E, the thickness of the crystal, being accurately measured, then, joining NE and N M, the ratio of refraction will be that of EN to NP, because these lines are as the sines of the angles of incidence and refraction N P H, NE P. In this way Huygens found the ratio to be that of five to three at all incidences, as Bartholinus had previously determined.

124. In order to find the extraordinary refraction, he next withdrew his eye to Q, till the extraordinary image of C D coincided with K L; he marked the point R, and consequently obtained by measurement the ratio of ER to ES, or the ratio of the sine of incidence to that of refraction. By numerous observations he found that this ratio was not constant, but changed with the inclination of the incident ray.

125. In continuing his observations on the extraordinary refraction, Huygens found that it observed the following law:-Let CGHF, fig. 8, be the principal section; and SK, VK, two incident rays equally inclined to the perpendicular IL; and KT, K X, the extraordinary rays af ter refraction; the distances TM and X M of these rays from the point M, where the refraction of the perpendicular ray I K cuts the base by F, will always be equal. This law is also true in the refraction of the other sections.

126. Having succeeded in explaining, in a very satisfactory manner, the refraction of ordinary transparent bodies, by means of spherical emanations of light, Huygens was naturally led to suppose that, as Iceland spar had two different refractions, it must also have two different emanations of waves of light, one of which might be propagated in a spherical form in the ethereal matter spread through the crystal. He conceives that this ethereal matter exists in greater quantity than the solid particles, and is alone capable of VOL. XVI.

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producing transparency. From these spherical undulations, which are propagated more slowly within the crystal than without it, proceed the phenomena of the ordinary refraction. other set of undulations, to which the irregular refraction is owing, he conceives to be elliptical or rather spheroidal, and to be propagated indifferently both through the ethereal matter and through the solid particles. Huygens considers that the regular arrangement of the particles may contribute to the formation of the spheroidal waves, as nothing more is required for this than that the light be propagated more quickly in one direction than another; and he was convinced that such an arrangement actually exists in Iceland spar.

127. In proceeding to explain his theory, Huygens supposes A B, fig. 1, plate II., to be the surface of Iceland spar, exposed to a beam of light; and as a perpendicular ray incident upon this surface from a distant luminary is, by the theory of undulation, no more than the incidence of a parcel of waves parallel to AB, he considers the line BC, parallel and equal to A B, to be a portion of the wave of light, of which the points R, H, h, C, meet A B at A, K, k, B. Instead of hemispherical waves, as in ordinary refractions, he supposes the waves to be now hemispheroids, whose major semi-axes are oblique to the plane A B. Hence S V I will represent an individual wave coming from the point A, after RC has arrived at A B. Now, as all the other points K, k, B, will propagate waves similar to S V I, in the same space of time that the point A did, the common tangent NQ of all these semi-ellipses will be the propagation of the wave RC in the transparent body, according to the above theory.

128. But the tangent N Q, which is equal and parallel to A B, is not directly opposite to A B, but comprehended between AN and B Q, conjugate diameters to those which are in the line AB. In this way,' says Huygens,' I have been able to conceive what appeared very difficult, how a perpendicular ray could suffer refraction in a transparent body,' the wave RC, instead of going straight on when it entered the surface AC, extending itself between the parallels A B and N Q.

129. In order to determine the form and situation of the spheroids in Iceland crystal, Huygens considered that all the six faces produced the same refraction, which were equally related to the principal sections shown in fig. 2, by dotted lines drawn from C. Hence he concluded that the spheroid which had the same relation to these three sections must have its axis coincident with the axis of the solid angle C, and therefore that the short diagonal of the rhomb determined the position of the axes of all the spheroidal waves, propagated from any point, taken either within or at the surface of the crystal, since all the spheroids ought to be similar, and have their axes parallel.

130. In the section GCF the angle C is 109° 3', and the angle F 70° 57'; and if we conceive a spheroidal wave round the centre C, its axis will be in the same plane. Let C S, fig. 3, be the half of this axis, then the angle GCS

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