Among all the Observations there is none accompanied with so odd circumstances as the twenty-fourth. Of those the principal are, that in thin Plates, which to the naked Eye seem of an even and uniform transparent whiteness, without any terminations of Shadows, the Refraction of a Prism should make Rings of Colours appear, whereas it usually makes Objects appear colour'd only there where they are terminated with Shadows, or have parts unequally luminous; and that it should make those Rings exceedingly distinct and white, although it usually renders Objects confused and coloured. The Cause of these things you will understand by considering, that all the Rings of Colours are really in the Plate, when view'd with the naked Eye, although by reason of the great breadth of their Circumferences they so much interfere and are blended together, that they seem to constitute an uniform whiteness. But when the Rays pass through the Prism to the Eye, the Orbits of the several Colours in every Ring are refracted, some more than others, according to their degrees of Refrangibility: By which means the Colours on one side of the Ring (that is in the circumference on one side of its center), become more unfolded and dilated, and those on the other side more complicated and contracted. And where by a due Refraction they are so much contracted, that the several Rings become narrower than to interfere with one another, they must appear distinct, and also white, if the constituent Colours be so much contracted as to be wholly co-incident. But on the other side, where the Orbit of every Ring is made broader by the farther unfolding of its Colours, it must interfere more with other Rings than before, and so become less distinct.
To explain this a little farther, suppose the concentrick Circles AV, and BX, [in _Fig._ 7.] represent the red and violet of any Order, which, together with the intermediate Colours, constitute any one of these Rings. Now these being view'd through a Prism, the violet Circle BX, will, by a greater Refraction, be farther translated from its place than the red AV, and so approach nearer to it on that side of the Circles, towards which the Refractions are made. For instance, if the red be translated to _av_, the violet may be translated to _bx_, so as to approach nearer to it at _x_ than before; and if the red be farther translated to av, the violet may be so much farther translated to bx as to convene with it at x; and if the red be yet farther translated to [Greek: aY], the violet may be still so much farther translated to [Greek: bx] as to pass beyond it at [Greek: x], and convene with it at _e_ and _f_. And this being understood not only of the red and violet, but of all the other intermediate Colours, and also of every revolution of those Colours, you will easily perceive how those of the same revolution or order, by their nearness at _xv_ and [Greek: Yx], and their coincidence at xv, _e_ and _f_, ought to constitute pretty distinct Arcs of Circles, especially at xv, or at _e_ and _f_; and that they will appear severally at _x_[Greek: u] and at xv exhibit whiteness by their coincidence, and again appear severally at [Greek: Yx], but yet in a contrary order to that which they had before, and still retain beyond _e_ and _f_. But on the other side, at _ab_, ab, or [Greek: ab], these Colours must become much more confused by being dilated and spread so as to interfere with those of other Orders. And the same confusion will happen at [Greek: Ux] between _e_ and _f_, if the Refraction be very great, or the Prism very distant from the Object-glasses: In which case no parts of the Rings will be seen, save only two little Arcs at _e_ and _f_, whose distance from one another will be augmented by removing the Prism still farther from the Object-glasses: And these little Arcs must be distinctest and whitest at their middle, and at their ends, where they begin to grow confused, they must be colour'd. And the Colours at one end of every Arc must be in a contrary order to those at the other end, by reason that they cross in the intermediate white; namely, their ends, which verge towards [Greek: Ux], will be red and yellow on that side next the center, and blue and violet on the other side. But their other ends which verge from [Greek: Ux], will on the contrary be blue and violet on that side towards the center, and on the other side red and yellow.