(22.) But even such results as these, striking as they are, yet fall short of the force with which conviction is urged upon us when, through the medium of reasoning too abstract for common apprehension, we arrive at conclusions which outrun experience, and describe beforehand what will happen under new combinations, or even correct imperfect experiments, and lead us to a knowledge of facts contrary to received analogies drawn from an experience wrongly interpreted or overhastily generalised. To give an example:--every body knows that objects viewed through a transparent medium, such as water or glass, appear distorted or displaced. Thus, a stick in water appears bent, and an object seen through a prism or wedge of glass seems to be thrown aside from its true place. This effect is owing to what is called the _refraction_ of light; and a simple rule discovered by Willebrod Snell enables any one to say exactly _how much_ the stick will be bent, and _how far_, and in what _direction_, the apparent situation of an object seen through the glass will deviate from the real one. If a shilling be laid at the bottom of a basin of water and viewed obliquely, it will appear to be raised by the water; if instead of water spirits of wine be used it will appear more raised; if oil, still more:--but in none of these cases will it appear to be thrown _aside_ to the _right_ or _left_ of its true place, however the eye be situated. The _plane_, in which are contained the eye, the object, and the point in the surface of the liquid at which the object is seen, is an upright or _vertical_ plane; and this is one of the principal characters in the _ordinary refraction_ of light, viz. that the ray by which we see an object through a refracting surface, although it undergoes a bending, and is, as it were, broken at the surface, yet, in pursuing its course to the eye, does not _quit a plane perpendicular to the refracting surface_. But there are again other substances, such as rock-crystal, and especially Iceland spar, which possess the singular property of _doubling_ the image or appearance of an object seen through them in certain directions; so that instead of seeing one object we see two, side by side, when such a crystal or spar is interposed between the object and the eye; and if a ray or small sunbeam be thrown upon a surface of either of these substances, it will be split into two, making an angle with each other, and each pursuing its own separate course,--this is called _double refraction_. Now, of these images or doubly refracted rays, one always follows the same rule as if the substance were glass or water: its deviation can be correctly calculated by Snell’s law above mentioned, and it does not quit the plane perpendicular to the refracting surface. The other ray, on the contrary, (which is therefore said to have undergone _extraordinary refraction_) _does_ quit that plane, and the amount of