# On the Refraction Observed in Iceland Spar

Besides the Refractions hitherto described, there is a refraction of another kind made in glass Island-glass, w^{ch} is a sort of Talc or pellucid stone \or pellucid \{&} fissile/ stone/ found in Island, in the form of an \{bounded} with six p/ /{illeg}\ parallelopiped, easily \clear as crystall/ splitting in p \glossy/ planes parallel to any of its \{six}/ sides, not fusible or not w^{th}out great difficulty \& enduring the \a violent/ fire w^{th}out fusion./ It has six plane sides bounded w^{th} in form of parallelograms whose \The/ obtuse angles are \of its {illeg} sides \or surfaces/ being/ 101 degr 52′, & \the/ acute ones 78 ^{degr} 8′ eat|c|h [It has eight solid angles two of w^{ch} opposite to one another are \each of them/ bounded w^{th} three of those obtuse angles, the other six w^{th} one obtuse & two acute ones.] This {illeg} strange substance w^{th} its wonderful refraction has been \was first/ described by Erasmus Bartholine & afterwards more exactly by Hugenius in he Treatise De la Lumiere \of light written in French./. Let ABFEHDCG represent the a piece of this glasse, [ABFE its parallelogram base whose opposi obtuse angles at B & E are 101 52 each & acute ones at A & F are 78 each & let ABCD, BCGF, GFEH & AEH be it four |parallelogram| sides standing up this base] bounded with six parallelogram sides AB {&} D, [ABFE, BCD, CBFG, GFEH, HEAD & DCGH,] each of w^{ch} whose obtuse angles \[ABF, AEF,/ DAB, DCB, BCG, BFG, FGH, FEH, HEA, HDA, \DCG, DHG]/ are all \each/ of them 101° 52′ & & {sic} their other angles \acute ones/ 78° 8′ each And let \let/ C & E \will/ be the \two opposite/ solid angles bounded each of them w^{th} three pl{a} of those obtuse angles Bisect with the line {illeg} CH bisect the solid \obtuse/ angle \the other six solid angles being bounded each w^{th} one obtuse & acute ones/ From one of those \two/ solid angles suppose (bisect \draw/ the line CH|K| bisecting the angle one of the obtuse angles \about it suppose/ DCG, & complete y^{e} parallelogram BCKL & let this parallelogram be called the principal section of this|e| Glass &] Le

If a beam of light fall perpendicularly upon any surface of this glass, this beam sh{illeg} \in passing through/ that {surface} shall part into two beams one of w^{ch} shall go perpendicularly through the glass {illeg} to do according to y^{e} ordina rules of Opticks & the other beam shall start {illeg}varicate from y^{e} former beam in an angle of about 6° 40′ & when it arrives {illeg} other side of the glass falling upon it obliquely in an angle of 83° 20′ it shall {illeg} perpendicularly out of the glass. And if the beame of light fall upon the {illeg} substance with its wonderfull first surface of y^{e} glass in any oblique {illeg} {this} beame shall always \there/ divide into two beames one of w^{ch} shall be refracted {according} to the known laws of Opticks the sine of incidence being to y^{e} sine of refraction {illeg}, & the other shall be refracted according to another law.

This {illeg} {instance} w^{th} its wonderfull refraction was first described by Erasmus Bartholine {illeg} more exactly by Hugenius in his book Treatise of light written {illeg} ABCDEF represent a p{illeg} bounded w^{th} six pgrā sides \or six {illeg}/ whose {obtuse} angles are each of them 101° 52′ & their acute ones 68° 8′. And let three of thi|e|s obtuse angles lye about the solid angle C & other three about the opposite solid angle E the other six solid angles being composed of \each of them with/ one obtuse & two acute ones And let the two biggest solid angles \C & E/ composed of {illeg}|three| obtuse ones be called the principal solid angles. And |& the plane w^{ch} is perpendicular to the refracting surfaces & bisects either of their obtuse angles be called the principal planes.| And let {illeg} ST represent a beam of light falling on y^{e} first surface of the glass AB at y^{e} point T{K} & being there refracted. This beam ST shall divide it self into two beams TV & TX some of the rays in the beam ST being refracted ac according to the known laws of Opticks & going in the beam TV to the place V in the second \further/ surface &|of| the glass & being there the sine of the refraction of these rays being to the sine of their incidence as 3 to 5. And the rest of the rays in the beam ST being refracted according to another law & going in the {illeg}|be|am TX to another place X w^{ch} in the further surface of the glass. In y^{e} w^{ch} place \X/ is thus found.

Find the line N w^{ch} is in such proportion to the thickness of the glass or distance between the two refracting surfaces as the sine of 6° 40′ is to y^{e} Radius. Then from the point V draw the lin upon the further surface of the glass draw he line VK equal to the line N & parallel to the lines w^{ch} bisect the obtuse angle \F/ of y^{e} further surface w^{ch} is opposite adacent {sic} to one of the lesser solid angles, & you will have to point X to w^{ch} the beam TX shal go.

Ph. 4|3| When these two beams of light TV & TX arrive at the further surface of |the glass| the beam TV w^{ch} was refracted at y^{e} first surface after the usual manner shall be again refracted \entirely/ after the usual manner at the second {f} surface & the beam \TX/ w^{ch} was refracted after the unusual manner in the first surface shall be again refracted \entirely/ after the \un/usuall manner \in the second/ so that both these beams shall emerge out of the second surface in lines parallel to the first incident beam ST.

Ph. 4 If two \or more/ pieces of Island glass be placed one after another in such manner y^{t} all the surfaces of the latter be parallel to all the corresponding surfaces of the f{illeg}|i|r{illeg}|s|t{illeg}, the rays w^{ch} are refracted regularly \after the usual manner/ in the first surface \of the first glass/ will be refacted {sic} regularly \after y^{e} usual manner/ in all the following surfaces & the rays w^{ch} are refracted after the unusual manner in the first surface will be refacted {sic} after y^{e} unusual manner in all the following surfaces. And {illeg} therefore there is a difference in the rays of light by means of w^{ch} one sort {illeg}|o|f rays is constantly refracted regularly & the after y^{e} usuall manner & the other sort \constantly/ after the unusual manner; & this difference was in the rays before their first refraction \as well as before the f{illeg}l latter refractions/ because it had the same effect upon them in all the refractions.

Ph. {illeg}|5| And tho the surfaces of the glasses are any ways inclined to one another yet if their planes of perpendicular refraction be parallel to one another the rays w^{ch} are refracted regularly \after y^{e} usual manner/ in the first surface are refracted regularly \after y^{e} usual manner/ in all the following surfaces & the rays w^{ch} are refracted after the unusual manner in the first surface shall be \are/ refracted after y^{e} unusuall manner in all the following surfaces.

Ph. 6. But if the planes of perpendicular refraction of the second glass be per at right angles w^{th} the planes of perpendicular refraction of y^{e} first glass: the rays w^{ch} are refracted after the usuall manner in passing through the first glass will all of them be refracted after the unusual manner in passing through the second glass & the rays w^{ch} are refracted after y^{e} unusual manner in passing through the first {illeg} glass will all of them be refracted after the unusual manner in passing through the second glass. And therefore there are not two sorts of rays \differing in nature from one another/ one of w^{ch} \is refracted/ constantly {illeg} /& in all positions\ after the usual manner & the other constantly \& in all positions/ after the unusual manner |The difference in the foregoing experiment was only in the position of the sides of the ray to the coast of unusual refraction For by this exp^{t} it appears that| but one & the same way is refracted sometimes regu in the usual & sometimes in the unsual manner according to the position w^{ch} it|s| hath \sides have/ to the glass. Let every ray be conceived to be distinguished into four quadrants by two planes crossing one another perpendicularly to |not according to y^{e} position or bigness of the angle of incidence but according to y^{e} position of the sides of y^{e} ray to the planes of perpendicular refraction of| the glass. [|L|et every ray be conceived to to {sic} have four sides or quadrants two of them opposite to one another {illeg} w^{ch} incline the ray to be refracted unusually & other two opposits] w^{ch} do not incline it to

And let the planes w^{ch} are perpendicular to y^{e} refracting plane \surfaces of the glass/ & parallel to the lines w^{ch} bisect the other {illeg}angles |of that plane surface parallelogram surface| be called the planes of perpendicular refraction. For if an {beam} of light fall perpendicularly upon any surface of this glass it shall divide at the point of incide{nce} {illeg} divide into two beames one of w^{ch} shall go perpendicularly into the glass \as it ought to do by the usual {illeg} laws of Opticks/ the other shall start aside & as is represented in the annexed scheme where represents \is/ the ray \Beam/ incident perpendicularly ray perpendicularly {illeg} \on/ y^{e} refracting surface, {illeg} the ray {illeg} going perpendicularly into y^{e} glass & the \refracted/ ray refracted divaricating from y^{e} perpendicular by an unusual refractiō the angle in an angle of 6° 40′] as it ought to do by the usua usual rules of Opticks, the other shall start aside & diaricate from the perpendicular ray making with it an angle of 6° 40′, & \&/ going \through y^{e} glass/ in the plane of perpendicular refraction & bending from the perpendicular towards the sides of the glass w^{ch} with the refracting plane comprehend one of the two begger solid angles. Let ST represent the beam incident \at T/ perpendicularly on the surface AC{illeg}BD, & TV TX the two be this beam at the point of incidence T shall become divided into {the} beame TV & TX one of w^{ch} TV shall go perpendicularly into y^{e} glass, the other TX shall decline from y^{e} perpendicular \shall go into it obliquely/ making with it \the perpendicular/ an angle {illeg} VTX of 6° 40′ & declining whose in the pl which [who{se} plane VTX is parallel to y^{e} planes of the perpendicular refraction] & {illeg} from it in the plane of perpendicular refraction VTX towards th{e} {illeg} of the glass AF & BF w^{ch} with the refracting plane surface AB {conteine} the one of the solid angle C w^{ch} is one of the two biggest solid angles. let the two rays TV & TX fall upon the further side of the glass EF at y^{e} points V & X & draw the line VX [& this line VX will be to y^{e} thickness of the glass or distance between the planes AB & EF as the tangent of 6 40 to y^{e} radius & be parallel to the lines w^{ch} bisect the obtuse angles E & F of that \further/ side of the glass]

Now let ST represent any \other/ beam of light incident obliquely on \{AB}/ y^{e} first surface of the glass AB & let the point of incidence be T & this beam shall {illeg} \also/ be divided at y^{e} point \of incidence/ T into two beams TV & TX one of w^{ch} TV shal be refracted after the usual manner, the sine of incidence being to the sine of refraction as five to three, & the Let this beame fall upon the further surface of the glass EF upon at the point V. & Draw the line VX equal & parallel to y^{e} line VX. Draw it the same way from V w^{ch} y^{e} line VX lies from V & joyning TX this line TX shall be the other beam of light carried by the unusual refraction from T to V.

When these two beams &c