that the Rays are not split or dilated, or otherways irregularly scatter'd by that Refraction, but that every Circle is by a regular and uniform Refraction translated entire into another Place, as the Circle AG by the greatest Refraction into the place _ag_, the Circle BH by a less Refraction into the place _bh_, the Circle CJ by a Refraction still less into the place _ci_, and so of the rest; by which means a new Spectrum _pt_ inclined to the former PT is in like manner composed of Circles lying in a right Line; and these Circles must be of the same bigness with the former, because the breadths of all the Spectrums Y, PT and _pt_ at equal distances from the Prisms are equal. I considered farther, that by the breadth of the hole F through which the Light enters into the dark Chamber, there is a Penumbra made in the Circuit of the Spectrum Y, and that Penumbra remains in the rectilinear Sides of the Spectrums PT and _pt_. I placed therefore at that hole a Lens or Object-glass of a Telescope which might cast the Image of the Sun distinctly on Y without any Penumbra at all, and found that the Penumbra of the rectilinear Sides of the oblong Spectrums PT and _pt_ was also thereby taken away, so that those Sides appeared as distinctly defined as did the Circumference of the first Image Y. Thus it happens if the Glass of the Prisms be free from Veins, and their sides be accurately plane and well polished without those numberless Waves or Curles which usually arise from Sand-holes a little smoothed in polishing with Putty. If the Glass be only well polished and free from Veins, and the Sides not accurately plane, but a little Convex or Concave, as it frequently happens; yet may the three Spectrums Y, PT and _pt_ want Penumbras, but not in equal distances from the Prisms. Now from this want of Penumbras, I knew more certainly that every one of the Circles was refracted according to some most regular, uniform and constant Law. For if there were any irregularity in the Refraction, the right Lines AE and GL, which all the Circles in the Spectrum PT do touch, could not by that Refraction be translated into the Lines _ae_ and _gl_ as distinct and straight as they were before, but there would arise in those translated Lines some Penumbra or Crookedness or Undulation, or other sensible Perturbation contrary to what is found by Experience. Whatsoever Penumbra or Perturbation should be made in the Circles by the cross Refraction of the second Prism, all that Penumbra or Perturbation would be conspicuous in the right Lines _ae_ and _gl_ which touch those Circles. And therefore since there is no such Penumbra or Perturbation in those right Lines, there must be none in the Circles. Since the distance between those Tangents or breadth of the Spectrum is not increased by the Refractions, the Diameters of the Circles are not increased thereby. Since those Tangents continue to be right Lines, every Circle which in the first Prism is more or less