If one sets in the path of a luminous cone a glass-walled trough filled with water, then, if both water and surrounding air are slightly clouded, the cone is seen to make a more acute angle within the water than outside it (Fig. 13). Here in an external phenomenon we meet the same weakening in the light's tendency to expand that we recognized in the shortening of our experience of depth on looking through a dense medium. Obviously, we expect the externally observable narrowing of the light-cone and the subjectively experienced change of optical depth to show the same ratio. In order to compare the rate of expansion of a luminous cone inside and outside water, we must measure by how much less the width of the cone increases within the water than it does outside. (To be comparable, the measurements must be based upon the same distances on the edge of the cone, because this is the length of the way the light actually travels.) In Fig. 13 this is shown by the two distances, a-b and a'-b'. Their ratio is the same as that by which the bottom of a vessel appears to be raised when the vessel is filled with water (4:3). Thus by means of pure observation we have arrived at nothing less than what is known to physical optics as Snell's Law of Refraction. This law was itself the result of pure observation, but was clothed in a conceptual form devoid of reality. In this form it states that a ray of light in transition between two media of different densities is refracted at their boundary surface so that the ratio of the angle which is formed by the ray in either medium with a line at right angles to the boundary surface is such that the quotient of the sines of both angles is for these media a constant factor. In symbols sin α / sin β = c. It will be clear to the reader familiar with trigonometry that this ratio of the two sines is nothing else but the ratio of the two distances which served us as a measure for the respective apertures of the cone. But whereas the measurement of these two distances is concerned with something quite real (since they express an actual dynamic alteration of the light), the measuring of the angle between the ray of light and the perpendicular is founded on nothing real. It is now clear that the concept of the ray, as it figures in the usual picture of refraction, is in reality the boundary between the luminous space and its surroundings. Evidently the concept of the perpendicular on the boundary between the two media is in itself a complete abstraction, since nothing happens dynamically in its direction.