Fig. 1.
Fig. 2.
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.
| At the Distance of | half a Foot | Nine Feet |
| The breadth of the Shadow | 1/54 | 1/9 |
| The breadth between the Middles of the brightest Light of the innermost Fringes on either side the Shadow | 1/38 or 1/39 | 7/50 |
| The breadth between the Middles of the brightest Light of the middlemost Fringes on either side the Shadow | 1/23-1/2 | 4/17 |
| The breadth between the Middles of the brightest Light of the outmost Fringes on either side the Shadow | 1/18 or 1/18-1/2 | 3/10 |
| The distance between the Middles of the brightest Light of the first and second Fringes | 1/120 | 1/21 |
| The distance between the Middles of the brightest Light of the second and third Fringes | 1/170 | 1/31 |
| The breadth of the luminous Part (green, white, yellow, and red) of the first Fringe | 1/170 | 1/32 |
| The breadth of the darker Space between the first and second Fringes | 1/240 | 1/45 |
| The breadth of the luminous Part of the second Fringe | 1/290 | 1/55 |
| The breadth of the darker Space between the second and third Fringes | 1/340 | 1/63 |
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, √(1/3), √(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, √(1/2), √(1/3), √(1/4), √(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.