And first, for the _Cartesian_, we have this to object against it, That whereas he says (_Meteorum Cap. 8. Sect. 5._) _Sed judicabam unicam (refractione scilicet) ad minimum requiri, & quidem talem ut ejus effectus aliâ contrariâ (refractione) non destruatur: Nam experientia docet si superficies _NM_ & _NP_ (nempe refringentes) Parallelæ forent, radios tantundem per alteram iterum erectos quantum per unam frangerentur, nullos colores depicturos_; This Principle of his holds true indeed in a prisme where the refracting surfaces are plain, but is contradicted by the Ball or Cylinder, whether of Water or Glass, where the refracting surfaces are Orbicular or Cylindrical. For if we examine the passage of any _Globule_ or Ray of the primary _Iris_, we shall find it to pass out of the Ball or Cylinder again, with the same inclination and refraction that it enter’d in withall, and that that last refraction by means of the _intermediate_ reflection shall be the same as if without any reflection at all the Ray had been twice refracted by two Parallel surfaces. And that this is true, not onely in one, but in every Ray that goes to the constitution of the Primary Iris; nay, in every Ray, that suffers only two refractions, and one reflection, by the surface of the round body, we shall presently see most evident, if we repeat the _Cartesian Scheme_, mentioned in the tenth _Section_ of the eighth _Chapter_ of his _Meteors_, where EFKNP in the third Figure[9] is one of the Rays of the Primary Iris, twice refracted at F and N, and once reflected at K by the surface of the Water-ball. For, first it is evident, that KF and KN are equal, because KN being the reflected part of KF they have both the same inclination on the surface K that is the angles FKT, and NKV made by the two Rays and the Tangent of K are equal, which is evident by the Laws of reflection; whence it will follow also, that KN has the same inclination on the surface N, or the Tangent of it XN that the Ray KF has to the surface F, or the Tangent of it FY, whence it must necessarily follow, that the refractions at F and N are equal, that is, KFE and KNP are equal. Now, that the surface N is by the reflection at K made parallel to the surface at F, is evident from the principles of reflection; for reflection being nothing but an inverting of the Rays, if we re-invert the Ray KNP, and make the same inclinations below the line TKV that it has above, it will be most evident, that KH the inverse of KN will be the continuation of the line FK, and that LHI the inverse of OX is parallel to FY. And HM the inverse of NP is Parallel to EF for the angle KHI is equal to KNO which is equal to KFY, and the angle KHM is equal to KNP which is equal to KFE which was to be prov’d.