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by the two Object-glasses; or by comparing two Bubbles of Water blown at distant Times, in the first of which the Whiteness appear'd, which succeeded all the Colours, and in the other, the Whiteness which preceded them all.

Obs. 24. When the two Object-glasses were lay'd upon one another, so as to make the Rings of the Colours appear, though with my naked Eye I could not discern above eight or nine of those Rings, yet by viewing them through a Prism I have seen a far greater Multitude, insomuch that I could number more than forty, besides many others, that were so very small and close together, that I could not keep my Eye steady on them severally so as to number them, but by their Extent I have sometimes estimated them to be more than an hundred. And I believe the Experiment may be improved to the Discovery of far greater Numbers. For they seem to be really unlimited, though visible only so far as they can be separated by the Refraction of the Prism, as I shall hereafter explain.

But it was but one side of these Rings, namely, that towards which the Refraction was made, which by that Refraction was render'd distinct, and the other side became more confused than when view'd by the naked Eye, insomuch that there I could not discern above, one or two, and sometimes none of those Rings, of which I could discern eight or nine with my naked Eye. And their Segments or Arcs, which on the other side appear'd so numerous, for the most part exceeded not the third Part of a Circle. If the Refraction was very great, or the

Prism very distant from the Object-glasses, the middle Part of those Arcs became also confufed, so as to disappear and constitute an even Whiteness, whilst oh either side their Ends, as also the whole Arcs farthest from the Center, became distincter than before, appearing in the Form as you fee them design'd in the fifth Figure.

The Arcs, where they seem'd distin&est, were only white and black successively, without any other Colours intermix'd. But in other Places there appeared Colours, whose Order was inverted by the Refraction in such manner, that if I first held the Prism very near the Object-glasses, and then gradually removed it farther off towards my Eye, the Colours of the 2d, 3d, 4th, and following Rings shrunk towards the white that emerged between them, until they wholly vanish'd into it at the middle of the Arcs, and afterwards emerged again in a contrary Order. But at the Ends of the Arcs they retain'd their Order unchanged.

I have sometimes so lay'd one Object-glass upon the other, that to the naked Eye they have all over seem'd uniformly white, without the least Appearance of any of the colour'd Rings; and yet by viewing them through a prism, great Multitudes of those Rings have discover'd themselves. And in like manner Plates of Muscovy Glass, and Bubbles of Glass blown at a Lamp-Furnace, which were not so thin as to exhibit any Colours to the naked Eye, have through the Prism exhibited a great Va-' riety of them ranged irregularly up and down in

the Form of Waves. And so Bubbles of Water, before they began to exhibit their Colours to the naked Eye of a By~stander, have appeared through a Prism, girded about with many parallel and horizontal Rings; to produce which Effect, it was necessary to hold the Prism parallel, or very nearly parallel to the Horizon, and to dispose it so that the Rays might be refracted upwards.

זין'

THE

THE

SECOND BOOK

of

OPTICKS.

PART II.

Remarks upon the foregoing Observations.

H

AVING given my Observations of these Colours, before I make use of them to unfold the Causes of the Colours of natural Bodies, it is convenient that by the simplest of them, such as are the 2d, 3d, 4th, 9th, 12th, 18th, 20th, and 24th, I first ex

0 4

plain

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2

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plain the more compounded. And first to shew how the Colours in the fourth and eighteenth Observations are produced, let there be taken in any Right Line from the Point Y, [in Fig.6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to one another, as the Cube-Roots of the Squares of the Numbers,,, ;, ;, ;, ¿1⁄2, 1, whereby the Lengths of a Musical Chord to found all the Notes in an eighth are represented; that is, in the Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243, 10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars Aα, Bβ, &c. be erected, by whose Intervals the Extent of the several Colours set underneath against them, is to be represented. Then divide the Line Aα in such Proportion as the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of Division denote. And through those Divisions from Y draw Lines 1 I, 2 K, 3L, 5 M, 6 N, 7O, &c.

Now, if A 2 be supposed to represent the Thickness of any thin transparent Body, at which the outniost Violet is most copiously reflected in the first Ring, or Series of Colours, then by the 13th Observation, HK will represent its Thickness, at which the utmost Red is most copiously reflected in the same Series. Also by the 5th and 16th Observations, A6 and HN will denote the Thicknesses at which those extreme Colours are most copiously reflected in the second Series, and A 10 and HQ the Thicknesses at which they are most copiously reflected in the third Series, and so on. And the Thickness at which any of the intermediate Co

lours

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