When I observed and compared the deepest sensible red, and the Colour in the Confine of green and blue, which at the Rectilinear Sides of the Spectrum was distant from it half the Length of those Sides, the Focus where the Confine of green and blue cast the Species of the Lines distinctly on the Paper, was nearer to the Lens than the Focus, where the red cast those Lines distinctly on it by about 2-1/2 or 2-3/4 Inches. For sometimes the Measures were a little greater, sometimes a little less, but seldom varied from one another above 1/3 of an Inch. For it was very difficult to define the Places of the Foci, without some little Errors. Now, if the Colours distant half the Length of the Image, (measured at its Rectilinear Sides) give 2-1/2 or 2-3/4 Difference of the distances of their Foci from the Lens, then the Colours distant the whole Length ought to give 5 or 5-1/2 Inches difference of those distances.
But here it's to be noted, that I could not see the red to the full end of the Spectrum, but only to the Center of the Semicircle which bounded that end, or a little farther; and therefore I compared this red not with that Colour which was exactly in the middle of the Spectrum, or Confine of green and blue, but with that which verged a little more to the blue than to the green: And as I reckoned the whole Length of the Colours not to be the whole Length of the Spectrum, but the Length of its Rectilinear Sides, so compleating the semicircular Ends into Circles, when either of the observed Colours fell within those Circles, I measured the distance of that Colour from the semicircular End of the Spectrum, and subducting half this distance from the measured distance of the two Colours, I took the Remainder for their corrected distance; and in these Observations set down this corrected distance for the difference of the distances of their Foci from the Lens. For, as the Length of the Rectilinear Sides of the Spectrum would be the whole Length of all the Colours, were the Circles of which (as we shewed) that Spectrum consists contracted and reduced to Physical Points, so in that Case this corrected distance would be the real distance of the two observed Colours.
When therefore I farther observed the deepest sensible red, and that blue whose corrected distance from it was 7/12 Parts of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens was about 3-1/4 Inches, and as 7 to 12, so is 3-1/4 to 5-4/7.
When I observed the deepest sensible red, and that indigo whose corrected distance was 8/12 or 2/3 of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens, was about 3-2/3 Inches, and as 2 to 3, so is 3-2/3 to 5-1/2.
When I observed the deepest sensible red, and that deep indigo whose corrected distance from one another was 9/12 or 3/4 of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens was about 4 Inches; and as 3 to 4, so is 4 to 5-1/3.
When I observed the deepest sensible red, and that Part of the violet next the indigo, whose corrected distance from the red was 10/12 or 5/6 of the Length of the Rectilinear Sides of the Spectrum, the difference of the distances of their Foci from the Lens was about 4-1/2 Inches, and as 5 to 6, so is 4-1/2 to 5-2/5. For sometimes, when the Lens was advantageously placed, so that its Axis respected the blue, and all Things else were well ordered, and the Sun shone clear, and I held my Eye very near to the Paper on which the Lens cast the Species of the Lines, I could see pretty distinctly the Species of those Lines by that Part of the violet which was next the indigo; and sometimes I could see them by above half the violet, For in making these Experiments I had observed, that the Species of those Colours only appear distinct, which were in or near the Axis of the Lens: So that if the blue or indigo were in the Axis, I could see their Species distinctly; and then the red appeared much less distinct than before. Wherefore I contrived to make the Spectrum of Colours shorter than before, so that both its Ends might be nearer to the Axis of the Lens. And now its Length was about 2-1/2 Inches, and Breadth about 1/5 or 1/6 of an Inch. Also instead of the black Lines on which the Spectrum was cast, I made one black Line broader than those, that I might see its Species more easily; and this Line I divided by short cross Lines into equal Parts, for measuring the distances of the observed Colours. And now I could sometimes see the Species of this Line with its Divisions almost as far as the Center of the semicircular violet End of the Spectrum, and made these farther Observations.
When I observed the deepest sensible red, and that Part of the violet, whose corrected distance from it was about 8/9 Parts of the Rectilinear Sides of the Spectrum, the Difference of the distances of the Foci of those Colours from the Lens, was one time 4-2/3, another time 4-3/4, another time 4-7/8 Inches; and as 8 to 9, so are 4-2/3, 4-3/4, 4-7/8, to 5-1/4, 5-11/32, 5-31/64 respectively.
When I observed the deepest sensible red, and deepest sensible violet, (the corrected distance of which Colours, when all Things were ordered to the best Advantage, and the Sun shone very clear, was about 11/12 or 15/16 Parts of the Length of the Rectilinear Sides of the coloured Spectrum) I found the Difference of the distances of their Foci from the Lens sometimes 4-3/4 sometimes 5-1/4, and for the most part 5 Inches or thereabouts; and as 11 to 12, or 15 to 16, so is five Inches to 5-2/2 or 5-1/3 Inches.
And by this Progression of Experiments I satisfied my self, that had the Light at the very Ends of the Spectrum been strong enough to make the Species of the black Lines appear plainly on the Paper, the Focus of the deepest violet would have been found nearer to the Lens, than the Focus of the deepest red, by about 5-1/3 Inches at least. And this is a farther Evidence, that the Sines of Incidence and Refraction of the several sorts of Rays, hold the same Proportion to one another in the smallest Refractions which they do in the greatest.