Part 20

Chapter 204,086 wordsPublic domain

Nor is it material whether the Hair be encompassed with Air, or with any other pellucid Substance. For I wetted a polish'd Plate of Glass, and laid the Hair in the Water upon the Glass, and then laying another polish'd Plate of Glass upon it, so that the Water might fill up the space between the Glasses, I held them in the aforesaid beam of Light, so that the Light might pass through them perpendicularly, and the Shadow of the Hair was at the same distances as big as before. The Shadows of Scratches made in polish'd Plates of Glass were also much broader than they ought to be, and the Veins in polish'd Plates of Glass did also cast the like broad Shadows. And therefore the great breadth of these Shadows proceeds from some other cause than the Refraction of the Air.

Let the Circle X [in _Fig._ 1.] represent the middle of the Hair; ADG, BEH, CFI, three Rays passing by one side of the Hair at several distances; KNQ, LOR, MPS, three other Rays passing by the other side of the Hair at the like distances; D, E, F, and N, O, P, the places where the Rays are bent in their passage by the Hair; G, H, I, and Q, R, S, the places where the Rays fall on a Paper GQ; IS the breadth of the Shadow of the Hair cast on the Paper, and TI, VS, two Rays passing to the Points I and S without bending when the Hair is taken away. And it's manifest that all the Light between these two Rays TI and VS is bent in passing by the Hair, and turned aside from the Shadow IS, because if any part of this Light were not bent it would fall on the Paper within the Shadow, and there illuminate the Paper, contrary to experience. And because when the Paper is at a great distance from the Hair, the Shadow is broad, and therefore the Rays TI and VS are at a great distance from one another, it follows that the Hair acts upon the Rays of Light at a good distance in their passing by it. But the Action is strongest on the Rays which pass by at least distances, and grows weaker and weaker accordingly as the Rays pass by at distances greater and greater, as is represented in the Scheme: For thence it comes to pass, that the Shadow of the Hair is much broader in proportion to the distance of the Paper from the Hair, when the Paper is nearer the Hair, than when it is at a great distance from it.

_Obs._ 2. The Shadows of all Bodies (Metals, Stones, Glass, Wood, Horn, Ice, &c.) in this Light were border'd with three Parallel Fringes or Bands of colour'd Light, whereof that which was contiguous to the Shadow was broadest and most luminous, and that which was remotest from it was narrowest, and so faint, as not easily to be visible. It was difficult to distinguish the Colours, unless when the Light fell very obliquely upon a smooth Paper, or some other smooth white Body, so as to make them appear much broader than they would otherwise do. And then the Colours were plainly visible in this Order: The first or innermost Fringe was violet and deep blue next the Shadow, and then light blue, green, and yellow in the middle, and red without. The second Fringe was almost contiguous to the first, and the third to the second, and both were blue within, and yellow and red without, but their Colours were very faint, especially those of the third. The Colours therefore proceeded in this order from the Shadow; violet, indigo, pale blue, green, yellow, red; blue, yellow, red; pale blue, pale yellow and red. The Shadows made by Scratches and Bubbles in polish'd Plates of Glass were border'd with the like Fringes of colour'd Light. And if Plates of Looking-glass sloop'd off near the edges with a Diamond-cut, be held in the same beam of Light, the Light which passes through the parallel Planes of the Glass will be border'd with the like Fringes of Colours where those Planes meet with the Diamond-cut, and by this means there will sometimes appear four or five Fringes of Colours. Let AB, CD [in _Fig._ 2.] represent the parallel Planes of a Looking-glass, and BD the Plane of the Diamond-cut, making at B a very obtuse Angle with the Plane AB. And let all the Light between the Rays ENI and FBM pass directly through the parallel Planes of the Glass, and fall upon the Paper between I and M, and all the Light between the Rays GO and HD be refracted by the oblique Plane of the Diamond-cut BD, and fall upon the Paper between K and L; and the Light which passes directly through the parallel Planes of the Glass, and falls upon the Paper between I and M, will be border'd with three or more Fringes at M.

So by looking on the Sun through a Feather or black Ribband held close to the Eye, several Rain-bows will appear; the Shadows which the Fibres or Threds cast on the _Tunica Retina_, being border'd with the like Fringes of Colours.

_Obs._ 3. When the Hair was twelve Feet distant from this Hole, and its Shadow fell obliquely upon a flat white Scale of Inches and Parts of an Inch placed half a Foot beyond it, and also when the Shadow fell perpendicularly upon the same Scale placed nine Feet beyond it; I measured the breadth of the Shadow and Fringes as accurately as I could, and found them in Parts of an Inch as follows.

These Measures I took by letting the Shadow of the Hair, at half a Foot distance, fall so obliquely on the Scale, as to appear twelve times broader than when it fell perpendicularly on it at the same distance, and setting down in this Table the twelfth part of the Measures I then took.

_Obs._ 4. When the Shadow and Fringes were cast obliquely upon a smooth white Body, and that Body was removed farther and farther from the Hair, the first Fringe began to appear and look brighter than the rest of the Light at the distance of less than a quarter of an Inch from the Hair, and the dark Line or Shadow between that and the second Fringe began to appear at a less distance from the Hair than that of the third part of an Inch. The second Fringe began to appear at a distance from the Hair of less than half an Inch, and the Shadow between that and the third Fringe at a distance less than an inch, and the third Fringe at a distance less than three Inches. At greater distances they became much more sensible, but kept very nearly the same proportion of their breadths and intervals which they had at their first appearing. For the distance between the middle of the first, and middle of the second Fringe, was to the distance between the middle of the second and middle of the third Fringe, as three to two, or ten to seven. And the last of these two distances was equal to the breadth of the bright Light or luminous part of the first Fringe. And this breadth was to the breadth of the bright Light of the second Fringe as seven to four, and to the dark Interval of the first and second Fringe as three to two, and to the like dark Interval between the second and third as two to one. For the breadths of the Fringes seem'd to be in the progression of the Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the same progression with them; that is, the Fringes and their Intervals together to be in the continual progression of the Numbers 1, sqrt(1/2), sqrt(1/3), sqrt(1/4), sqrt(1/5), or thereabouts. And these Proportions held the same very nearly at all distances from the Hair; the dark Intervals of the Fringes being as broad in proportion to the breadth of the Fringes at their first appearance as afterwards at great distances from the Hair, though not so dark and distinct.

_Obs._ 5. The Sun shining into my darken'd Chamber through a hole a quarter of an Inch broad, I placed at the distance of two or three Feet from the Hole a Sheet of Pasteboard, which was black'd all over on both sides, and in the middle of it had a hole about three quarters of an Inch square for the Light to pass through. And behind the hole I fasten'd to the Pasteboard with Pitch the blade of a sharp Knife, to intercept some part of the Light which passed through the hole. The Planes of the Pasteboard and blade of the Knife were parallel to one another, and perpendicular to the Rays. And when they were so placed that none of the Sun's Light fell on the Pasteboard, but all of it passed through the hole to the Knife, and there part of it fell upon the blade of the Knife, and part of it passed by its edge; I let this part of the Light which passed by, fall on a white Paper two or three Feet beyond the Knife, and there saw two streams of faint Light shoot out both ways from the beam of Light into the shadow, like the Tails of Comets. But because the Sun's direct Light by its brightness upon the Paper obscured these faint streams, so that I could scarce see them, I made a little hole in the midst of the Paper for that Light to pass through and fall on a black Cloth behind it; and then I saw the two streams plainly. They were like one another, and pretty nearly equal in length, and breadth, and quantity of Light. Their Light at that end next the Sun's direct Light was pretty strong for the space of about a quarter of an Inch, or half an Inch, and in all its progress from that direct Light decreased gradually till it became insensible. The whole length of either of these streams measured upon the paper at the distance of three Feet from the Knife was about six or eight Inches; so that it subtended an Angle at the edge of the Knife of about 10 or 12, or at most 14 Degrees. Yet sometimes I thought I saw it shoot three or four Degrees farther, but with a Light so very faint that I could scarce perceive it, and suspected it might (in some measure at least) arise from some other cause than the two streams did. For placing my Eye in that Light beyond the end of that stream which was behind the Knife, and looking towards the Knife, I could see a line of Light upon its edge, and that not only when my Eye was in the line of the Streams, but also when it was without that line either towards the point of the Knife, or towards the handle. This line of Light appear'd contiguous to the edge of the Knife, and was narrower than the Light of the innermost Fringe, and narrowest when my Eye was farthest from the direct Light, and therefore seem'd to pass between the Light of that Fringe and the edge of the Knife, and that which passed nearest the edge to be most bent, though not all of it.

_Obs._ 6. I placed another Knife by this, so that their edges might be parallel, and look towards one another, and that the beam of Light might fall upon both the Knives, and some part of it pass between their edges. And when the distance of their edges was about the 400th part of an Inch, the stream parted in the middle, and left a Shadow between the two parts. This Shadow was so black and dark that all the Light which passed between the Knives seem'd to be bent, and turn'd aside to the one hand or to the other. And as the Knives still approach'd one another the Shadow grew broader, and the streams shorter at their inward ends which were next the Shadow, until upon the contact of the Knives the whole Light vanish'd, leaving its place to the Shadow.

And hence I gather that the Light which is least bent, and goes to the inward ends of the streams, passes by the edges of the Knives at the greatest distance, and this distance when the Shadow begins to appear between the streams, is about the 800th part of an Inch. And the Light which passes by the edges of the Knives at distances still less and less, is more and more bent, and goes to those parts of the streams which are farther and farther from the direct Light; because when the Knives approach one another till they touch, those parts of the streams vanish last which are farthest from the direct Light.

_Obs._ 7. In the fifth Observation the Fringes did not appear, but by reason of the breadth of the hole in the Window became so broad as to run into one another, and by joining, to make one continued Light in the beginning of the streams. But in the sixth, as the Knives approached one another, a little before the Shadow appeared between the two streams, the Fringes began to appear on the inner ends of the Streams on either side of the direct Light; three on one side made by the edge of one Knife, and three on the other side made by the edge of the other Knife. They were distinctest when the Knives were placed at the greatest distance from the hole in the Window, and still became more distinct by making the hole less, insomuch that I could sometimes see a faint lineament of a fourth Fringe beyond the three above mention'd. And as the Knives continually approach'd one another, the Fringes grew distincter and larger, until they vanish'd. The outmost Fringe vanish'd first, and the middlemost next, and the innermost last. And after they were all vanish'd, and the line of Light which was in the middle between them was grown very broad, enlarging it self on both sides into the streams of Light described in the fifth Observation, the above-mention'd Shadow began to appear in the middle of this line, and divide it along the middle into two lines of Light, and increased until the whole Light vanish'd. This enlargement of the Fringes was so great that the Rays which go to the innermost Fringe seem'd to be bent above twenty times more when this Fringe was ready to vanish, than when one of the Knives was taken away.

And from this and the former Observation compared, I gather, that the Light of the first Fringe passed by the edge of the Knife at a distance greater than the 800th part of an Inch, and the Light of the second Fringe passed by the edge of the Knife at a greater distance than the Light of the first Fringe did, and that of the third at a greater distance than that of the second, and that of the streams of Light described in the fifth and sixth Observations passed by the edges of the Knives at less distances than that of any of the Fringes.

_Obs._ 8. I caused the edges of two Knives to be ground truly strait, and pricking their points into a Board so that their edges might look towards one another, and meeting near their points contain a rectilinear Angle, I fasten'd their Handles together with Pitch to make this Angle invariable. The distance of the edges of the Knives from one another at the distance of four Inches from the angular Point, where the edges of the Knives met, was the eighth part of an Inch; and therefore the Angle contain'd by the edges was about one Degree 54: The Knives thus fix'd together I placed in a beam of the Sun's Light, let into my darken'd Chamber through a Hole the 42d Part of an Inch wide, at the distance of 10 or 15 Feet from the Hole, and let the Light which passed between their edges fall very obliquely upon a smooth white Ruler at the distance of half an Inch, or an Inch from the Knives, and there saw the Fringes by the two edges of the Knives run along the edges of the Shadows of the Knives in Lines parallel to those edges without growing sensibly broader, till they met in Angles equal to the Angle contained by the edges of the Knives, and where they met and joined they ended without crossing one another. But if the Ruler was held at a much greater distance from the Knives, the Fringes where they were farther from the Place of their Meeting, were a little narrower, and became something broader and broader as they approach'd nearer and nearer to one another, and after they met they cross'd one another, and then became much broader than before.

Whence I gather that the distances at which the Fringes pass by the Knives are not increased nor alter'd by the approach of the Knives, but the Angles in which the Rays are there bent are much increased by that approach; and that the Knife which is nearest any Ray determines which way the Ray shall be bent, and the other Knife increases the bent.

_Obs._ 9. When the Rays fell very obliquely upon the Ruler at the distance of the third Part of an Inch from the Knives, the dark Line between the first and second Fringe of the Shadow of one Knife, and the dark Line between the first and second Fringe of the Shadow of the other knife met with one another, at the distance of the fifth Part of an Inch from the end of the Light which passed between the Knives at the concourse of their edges. And therefore the distance of the edges of the Knives at the meeting of these dark Lines was the 160th Part of an Inch. For as four Inches to the eighth Part of an Inch, so is any Length of the edges of the Knives measured from the point of their concourse to the distance of the edges of the Knives at the end of that Length, and so is the fifth Part of an Inch to the 160th Part. So then the dark Lines above-mention'd meet in the middle of the Light which passes between the Knives where they are distant the 160th Part of an Inch, and the one half of that Light passes by the edge of one Knife at a distance not greater than the 320th Part of an Inch, and falling upon the Paper makes the Fringes of the Shadow of that Knife, and the other half passes by the edge of the other Knife, at a distance not greater than the 320th Part of an Inch, and falling upon the Paper makes the Fringes of the Shadow of the other Knife. But if the Paper be held at a distance from the Knives greater than the third Part of an Inch, the dark Lines above-mention'd meet at a greater distance than the fifth Part of an Inch from the end of the Light which passed between the Knives at the concourse of their edges; and therefore the Light which falls upon the Paper where those dark Lines meet passes between the Knives where the edges are distant above the 160th part of an Inch.

For at another time, when the two Knives were distant eight Feet and five Inches from the little hole in the Window, made with a small Pin as above, the Light which fell upon the Paper where the aforesaid dark lines met, passed between the Knives, where the distance between their edges was as in the following Table, when the distance of the Paper from the Knives was also as follows.

+------------------------------ | Distances between the edges Distances of the Paper | of the Knives in millesimal from the Knives in Inches. | parts of an Inch. -----------------------------+------------------------------ 1-1/2. | 0'012 3-1/3. | 0'020 8-3/5. | 0'034 32. | 0'057 96. | 0'081 131. | 0'087 _____________________________|______________________________

And hence I gather, that the Light which makes the Fringes upon the Paper is not the same Light at all distances of the Paper from the Knives, but when the Paper is held near the Knives, the Fringes are made by Light which passes by the edges of the Knives at a less distance, and is more bent than when the Paper is held at a greater distance from the Knives.

_Obs._ 10. When the Fringes of the Shadows of the Knives fell perpendicularly upon a Paper at a great distance from the Knives, they were in the form of Hyperbola's, and their Dimensions were as follows. Let CA, CB [in _Fig._ 3.] represent Lines drawn upon the Paper parallel to the edges of the Knives, and between which all the Light would fall, if it passed between the edges of the Knives without inflexion; DE a Right Line drawn through C making the Angles ACD, BCE, equal to one another, and terminating all the Light which falls upon the Paper from the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_, three hyperbolical Lines representing the Terminus of the Shadow of one of the Knives, the dark Line between the first and second Fringes of that Shadow, and the dark Line between the second and third Fringes of the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines representing the Terminus of the Shadow of the other Knife, the dark Line between the first and second Fringes of that Shadow, and the dark line between the second and third Fringes of the same Shadow. And conceive that these three Hyperbola's are like and equal to the former three, and cross them in the points _i_, _k_, and _l_, and that the Shadows of the Knives are terminated and distinguish'd from the first luminous Fringes by the lines _eis_ and _xip_, until the meeting and crossing of the Fringes, and then those lines cross the Fringes in the form of dark lines, terminating the first luminous Fringes within side, and distinguishing them from another Light which begins to appear at _i_, and illuminates all the triangular space _ip_DE_s_ comprehended by these dark lines, and the right line DE. Of these Hyperbola's one Asymptote is the line DE, and their other Asymptotes are parallel to the lines CA and CB. Let _rv_ represent a line drawn any where upon the Paper parallel to the Asymptote DE, and let this line cross the right lines AC in _m_, and BC in _n_, and the six dark hyperbolical lines in _p_, _q_, _r_; _s_, _t_, _v_; and by measuring the distances _ps_, _qt_, _rv_, and thence collecting the lengths of the Ordinates _np_, _nq_, _nr_ or _ms_, _mt_, _mv_, and doing this at several distances of the line _rv_ from the Asymptote DD, you may find as many points of these Hyperbola's as you please, and thereby know that these curve lines are Hyperbola's differing little from the conical Hyperbola. And by measuring the lines C_i_, C_k_, C_l_, you may find other points of these Curves.