Hypothesis of emanations of Light, within Iceland Crystal, of spheroidal form, for the Irregular Refraction. How a perpendicular ray can suffer Refraction. How the position and form of the spheroidal emanations in this Crystal can be defined. Explanation of the Irregular Refraction by these spheroidal emanations. Easy way to find the Irregular Refraction of each incident ray. Demonstration of the oblique ray which traverses the Crystal without being refracted. Other irregularities of Refraction explained. That an object placed beneath the Crystal appears double, in two images of different heights. Why the apparent heights of one of the images change on changing the position of the eyes above the Crystal. Of the different sections of this Crystal which produce yet other refractions, and confirm all this Theory. Particular way of polishing the surfaces after it has been cut. Surprising phenomenon touching the rays which pass through two separated pieces; the cause of which is not explained. Probable conjecture on the internal composition of Iceland Crystal, and of what figure its particles are. Tests to confirm this conjecture. Calculations which have been supposed in this Chapter. CHAPTER VI. On the Figures of transparent bodies which serve for Refraction and for Reflexion. General and easy rule to find these Figures. Invention of the Ovals of Mr. Des Cartes for Dioptrics. How he was able to find these Lines. Way of finding the surface of a glass for perfect refraction, when the other surface is given. Remark on what happens to rays refracted at a spherical surface. Remark on the curved line which is formed by reflexion in a spherical concave mirror. CHAPTER I ON RAYS PROPAGATED IN STRAIGHT LINES As happens in all the sciences in which Geometry is applied to matter, the demonstrations concerning Optics are founded on truths drawn from experience. Such are that the rays of light are propagated in straight lines; that the angles of reflexion and of incidence are equal; and that in refraction the ray is bent according to the law of sines, now so well known, and which is no less certain than the preceding laws.