a similar defect, and from this, and other causes, it arises that when the naked light from fifty cells is looked at the blur of light upon the retina is sufficient to destroy the definition of the retinal image of the carbons. A long list of indictments might indeed be brought against the eye—its opacity, its want of symmetry, its lack of achromatism, its partial blindness. All these taken together caused Helmholt to say that, if any optician sent him an instrument so defective, he would be justified in sending it back with the severest censure. But the eye is not to be judged from the standpoint of theory. It is not perfect, but is on its way to perfection. As a practical instrument, and taking the adjustments by which its defects are neutralized into account, it must ever remain a marvel to the reflecting mind.
§ 3. Rectilineal Propagation of Light. Elementary Experiments. Law of Reflection.
The ancients were aware of the rectilineal propagation of light. They knew that an opaque body, placed between the eye and a point of light, intercepted the light of the point. Possibly the terms 'ray' and 'beam' may have been suggested by those straight spokes of light which, in certain states of the atmosphere, dart from the sun at his rising and his setting. The rectilineal propagation of light may be illustrated by permitting the solar light to enter, through a small aperture in a window-shutter, a dark room in which a little smoke has been diffused. In pure air you cannot see the beam, but in smoky air you can, because the light, which passes unseen through the air, is scattered and revealed by the smoke particles, among which the beam pursues a straight course.
The following instructive experiment depends on the rectilineal propagation of light. Make a small hole in a closed window-shutter, before which stands a house or a tree, and place within the darkened room a white screen at some distance from the orifice. Every straight ray proceeding from the house, or tree, stamps its colour upon the screen, and the sum of all the rays will, therefore, be an image of the object. But, as the rays cross each other at the orifice, the image is inverted. At present we may illustrate and expand the subject thus: In front of our camera is a large opening (L, fig. 2), from which the lens has been removed, and which is closed at present by a sheet of tin-foil. Pricking by means of a common sewing-needle a small aperture in the tin-foil, an inverted image of the carbon-points starts forth upon the screen. A dozen apertures will give a dozen images, a hundred a hundred, a thousand a thousand. But, as the apertures come closer to each other, that is to say, as the tin-foil between the apertures vanishes, the images overlap more and more. Removing the tin-foil altogether, the screen becomes uniformly illuminated. Hence the light upon the screen may be regarded as the overlapping of innumerable images of the carbon-points. In like manner the light upon every white wall, on a cloudless day, may be regarded as produced by the superposition of innumerable images of the sun.
The law that the angle of incidence is equal to the angle of reflection has a bearing upon theory, to be subsequently mentioned, which renders its simple illustration here desirable. A straight lath (pointing to the figure 5 on the arc in fig. 3) is fixed as an index perpendicular to a small looking-glass (M), capable of rotation. We begin by receiving a beam of light upon the glass which is reflected back along the line of its incidence. The index being then turned, the mirror turns with it, and at each side of the index the incident and the reflected beams (L o, o R) track themselves through the dust of the room. The mere inspection of the two angles enclosed between the index and the two beams suffices to show their equality; while if the graduated arc be consulted, the arc from 5 to m is found accurately equal to the arc from 5 to n. The complete expression of the law of reflection is, not only that the angles of incidence and reflection are equal, but that the incident and reflected rays always lie in a plane perpendicular to the reflecting surface.
This simple apparatus enables us to illustrate another law of great practical importance, namely, that when a mirror rotates, the angular velocity of a beam reflected from it is twice that of the reflecting mirror. A simple experiment will make this plain. The arc (m n, fig. 3) before you is divided into ten equal parts, and when the incident beam and the index cross the zero of the graduation, both the incident and reflected beams are horizontal. Moving the index of the mirror to 1, the reflected beam cuts the arc at 2; moving the index to 2, the arc is cut at 4; moving the index to 3, the arc is cut at 6; moving the index at 4, the arc is cut at 8; finally, moving the index to 5, the arc is cut at 10 (as in the figure). In every case the reflected beam moves through twice the angle passed over by the mirror.
One of the principal problems of science is to help the senses of man, by carrying them into regions which could never be attained without that help. Thus we arm the eye with the telescope when we want to sound the depths of space, and with the microscope when we want to explore motion and structure in their infinitesimal dimensions. Now, this law of angular reflection, coupled with the fact that a beam of light possesses no weight, gives us the means of magnifying small motions to an extraordinary degree. Thus, by attaching mirrors to his suspended magnets, and by watching the images of divided scales reflected from the mirrors, the celebrated Gauss was able to detect the slightest thrill of variation on the part of the earth's magnetic force. By a similar arrangement the feeble attractions and repulsions of the diamagnetic force have been made manifest. The minute elongation of a bar of metal, by the mere warmth of the hand, may be so magnified by this method, as to cause the index-beam to move through 20 or 30 feet. The lengthening of a bar of iron when it is magnetized may be also thus demonstrated. Helmholtz long ago employed this method of rendering evident to his students the classical experiments of Du Bois Raymond on animal electricity; while in Sir William Thomson's reflecting galvanometer the principle receives one of its latest and most important applications.
§ 4. The Refraction of Light. Total Reflection.
For more than a thousand years no step was taken in optics beyond this law of reflection. The men of the Middle Ages, in fact, endeavoured, on the one hand, to develop the laws of the universe à priori out of their own consciousness, while many of them were so occupied with the concerns of a future world that they looked with a lofty scorn on all things pertaining to this one. Speaking of the natural philosophers of his time, Eusebius says, 'It is not through ignorance of the things admired by them, but through contempt of their useless labour, that we think little of these matters, turning our souls to the exercise of better things.' So also Lactantius—'To search for the causes of things; to inquire whether the sun be as large as he seems; whether the moon is convex or concave; whether the stars are fixed in the sky, or float freely in the air; of what size and of what material are the heavens; whether they be at rest or in motion; what is the magnitude of the earth; on what foundations is it suspended or balanced;—to dispute and conjecture upon such matters is just as if we chose to discuss what we think of a city in a remote country, of which we never heard but the name.'
As regards the refraction of light, the course of real inquiry was resumed in 1100 by an Arabian philosopher named Alhazen. Then it was taken up in succession by Roger Bacon, Vitellio, and Kepler. One of the most important occupations of science is the determination, by precise measurements, of the quantitative relations of phenomena; the value of such measurements depending greatly upon the skill and conscientiousness of the man who makes them. Vitellio appears to have been both skilful and conscientious, while Kepler's habit was to rummage through the observations of his predecessors, to look at them in all lights, and thus distil from them the principles which united them. He had done this with the
