THE BETRAYED. I KNEW thee in our childhood's hours, Thrilled with more joy, than our young strain; Than life held out to tempt us twain. Yes! while we shared each childish game, I knew thee in thy youth's fair pride, Yes! when thy hand was clasped in mine, I loved thee then-I love thee now! And when thy treachery sealed my doom, Was all that now could yield relief; I loved thee then-I love thee now! And oh! let her, thy bride, forbear To mock these foolish tears of mine; Which waits the loss of love like thine. I loved thee then-I love thee now! 564 (Continued from page 262). CENSUS OF SCIENTIFIC THEORIES. No. 3. THE UNDULATORY THEORY OF LIGHT. BY CHARLES TOOGOOD DOWNING, M.R.C.S.-Author of the “Fanqui in China,” &c. It will be perceived that the undulatory theories of refraction and reflection which have been just explained are extremely accurate and beautiful, and we will now proceed to the consideration of the theory of the interference of light. This is a subject of the highest interest, and has justly entailed honour on the memory of its discoverer. As it is considered the great bulwark of the doctrine of Huygens, and is of such an interesting character, we propose to devote a short space to a kind of historical notice of the progress of our knowledge of the inflection or diffraction of light. cone. So early as the year 1665, there was published at Bologna, the posthumous work of a learned Italian jesuit of the name of Grimaldi, in which this curious phenomenon is described. Having closed the shutters, he admitted a ray of light into the darkened room through a very small aperture. He observed that it was diffused in the form of a Upon placing bodies in this divergent light, he noticed that their shadows always were larger than they would have been, had the light passed in a rectilinear direction past their edges. Viewing this curious property with more consideration, he discovered that the shadow was surrounded by three circles or fringes of coloured light, the fringes growing narrower as they receded from the body, and the colours, consisting chiefly of blue and red, becoming more and more faint. He also observed similar fringes of coloured light within the shadows, especially when the light was strong, and the shadow was received at some distance from the screen. From these facts, Grimaldi concluded that light was inflected or bent from its rectilinear course in passing near bodies. By another series of experiments he arrived at the conclusion, "that a body actually illuminated may become more obscure by adding a new light to that which it already receives." This apparently paradoxical proposition he demonstrated by admitting two cones of light into a dark chamber, through two very small apertures placed at such a distance from each other, that the cones do not begin to penetrate each other until they arrive at a certain distance from the aperture. When thus managed, it may be observed, that the mutual interferences of the rays act upon each other, in such a manner, that the spot illuminated by their joint influence is more obscure than when it was illuminated by either of them singly. It was a singular circumstance, but certainly does not stand alone in the list of coincidences which appear almost to prove that the minds of men collectively march onwards in the path of science, as it were simultaneously, that our own countryman Dr. Hooke made nearly the same discoveries without knowing what had been done by the Italian. The results of his observations were read before the Royal Society in the years 1672 and 1675. Sir Isaac Newton devoted a considerable share of his attention to this subject, and by experiments with human hair, horn, ice, and various other substances added considerably to the knowledge of the laws of inflection, and attempted to explain the phenomena of the corpuscular doctrine. His observations being left in an unfinished state, various authors have written on the subject, but with no great success, with the exception of Dr. Thomas Young. This great philosopher, directed his attention to the inflection of light during the course of his enquiries respecting light and colours. He found that when he interposed an opaque screen either a few inches before or a few inches behind an inflecting body, so as to intercept all the light on that side by receiving the edge of the shadow on the screen, then all the fringes in the shadow constantly disappeared, although the light still passed by the other edge of the body as freely as before. Dr. Young, therefore, considered that these fringes were the joint effects of the portions of light passing on each side of substances, and inflected into the shadow, and that the light which passed on both sides was necessary to the production of the fringes. In order to show that the extinction of the fringes was not occasioned by want of light, in consequence of the interposition of the screen, he reduced the intensity of the light to one-tenth, or even one-twentieth, and still found that the fringes were seen distinctly in this attenuated light when the screen was not interposed. Dr. Young thus obtained an experimental demonstration of the law of interference, which in this case led to the conclusion, that the fringes within the shadow were produced by the interference of the rays bent into the shadow by one side of the body, with the rays bent into the shadow by the other side. This law is now universally admitted as a principle in optics, although at the time it was neglected by some and opposed by others. Like other productions of genius, it has finally triumphed over all opposition. That the law of interference may be well understood, and its direct accordance with the theory of undulation explained familiarly, let us suppose two pencils of light to radiate from two points very close to each other; and that a piece of paper is held parallel to the line which joins the two points, so that the light may fall upon a spot, which is directly opposite the point which bisects the distance between the two radiant points. This spot will be illuminated with the sum of the light of the two rays; because the pencils would cross each other at that spot, if the paper were removed, so as to allow them to diverge. In this case, the two rays may be said to interfere with each other as the length of the paths of the two rays is exactly the same, the spot on the paper being exactly distant from both the radiant points. If, as has been proved by experiment, there is a certain minute, but well defined difference between the lengths of the paths of the two pencils of light, the spot upon the paper where the two pencils of light interfere with each other is still a bright spot as it is still illuminated by the sum of the two lights. We may designate this difference in the lengths of the paths d, and it will be found that when the difference in the length of the paths is d, 2 d, 3d, 4 d, &c., the spot which is formed by the interference of the two pencils will be bright. But it will excite some little surprise when it is demonstrated, that when the two pencils of light interfere at intermediate points, or when the difference in the lengths of the paths isd, 1 d, 2 d, 34 d, &c. the rays instead of producing a double brilliancy equal to the sum of the light, will destroy each other, and produce a black spot. It will now easily be perceived how the doctrine of interference is in complete accordance with the undulatory theory. When the waves of light are similarly combined, so that the elevations and depressions of the one coincide with those of the other, a wave of double magnitude will be produced. On the contrary, when the elevations of the one coincide or meet with the depressions of the other, both systems of waves will be annihilated. The similarity between the theories of light and sound will now be apparent. When two musical strings which are in unison, are struck, the effect of the two sounds is equal to the sum of their separate intensities, but when they are not in unison, the cessation of sound between the beats announces that the sonorous waves have destroyed each other. Illustrative examples in other media of the law of interference are afforded by Dr. Young himself. "The spring and neap tides derived from the combination of the simple soli-lunar tides, afford a magnificent example of the interference of two immense waves with each other; the spring tide being the joint result of the combination when they coincide in time and place, and the neap tide when they succeed each other at the distance of half an interval, so as to leave the effect of their difference only sensible. The tides of the port of Batsha, as described and explained by Halley and Newton, exhibit a different modification of the same opposition of undulations; the ordinary periods of high and low water being altogether superseded on account of the different lengths of the two channels by which the tides arrive, affording exactly the half interval, which causes the disappearance of the alternation. It may also be very easily observed, by merely throwing two equal stones into a piece of stagnant water, that the circles of waves which they occasion, obliterate each other and leave the surface of the water smooth in certain lines of a hyperbolic form, while in other neighbouring parts the surface exhibits the agitation belonging to both series united." According to the Huygenian doctrine, the quantity or difference d, above mentioned is equal to the breadth of a wave of light, and it is obvious that this is no imaginary quantity, but a real absolute magnitude. It is demonstrable, that one half of it is opposed in its properties to the other half, if we judge by the phenomena produced. For if two anterior or two posterior halves of this magnitude combine, or interfere in a similar manner, the effect is doubled, but if the anterior half combines accurately with the posterior half, or interferes with it in this manner under a small angle, the effect which would have been produced by each separately is destroyed. As all the phenomena of interference are dependent upon the quantity d, it becomes interesting to ascertain its exact magnitude for the different coloured rays. These were calculated by Sir Isaac Newton with a precision which did him great honour. They are, perhaps, the most minute measurements of time and space ever effected by man; and, as they are real bona fide existences, they fill us with wonder and astonishment. We extract from Mr. Herschel's Table the measurements of the three primary rays; although Newton prepared this for the seven colours and intermediate spaces of his spectrum. It would occupy far too great a space were we to consider all the minute and beautiful phenomena which can be satisfactorily explained by the law of interference applied to the undulatory theory. A slight sketch of the principal of these is all that remains to be given. From the table above, it will be perceived that each of the coloured rays differs from the rest in the length and size of its waves, and also in the number which is propelled in a second of time. The phenomena of the inflection of light can now be easily understood. The fringes of coloured light which are observed in the shadow, and called the interior fringes, depend upon the interference of the rays which come on either side of the inflecting body. It is clear, that as the middle of the shadow is at the same distance from both edges of this inflecting body, there should be a narrow white strip illumined by the sum of the two inflected pencils, because there is no difference in the lengths of the paths of the two pencils coming from each side of the body; but at a point at such a distance from the centre of the shadow, that the difference of the two paths of the pencils from each side of the body is equal to d, the two pencils will destroy each other, and give a dark stripe : consequently, on each side of the central bright stripe there will be a dark one. For the same reasons, it may be shown that at a point at such a distance from the centre of the shadow that the difference in the lengths of the paths is 2d; 3 d, there will be bright stripes: and at intermediate points, when the difference in the lengths of the paths is 1d; 2} d, there will be dark stripes. This is exactly the case in point of fact. With respect to those rings of coloured light which are observed on the edges of the inflecting body, and called the exterior fringes, some little difference of opinion exists; and certainly they cannot be explained in so satisfactory a manner. Dr. Thomas Young believed that they were occasioned by the interference of the direct rays with those which are reflected from the edge of the screen. M. Fresnal, who has pursued these investigations with the greatest skill and nicety, found, from observations made with various-shaped bodies, that this was not exactly the case. He believed that those rays which pass at a sensible distance from the inflecting body, assists also in producing this phenomenon, by deviating from their original direction, and interfering with the others. One of the most successful applications of the law of interference is in the explanations of the colours of thin plates. This is a subject which has engaged the attention of such men as Boyle, Newton, Hooke, Bre |