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in water; so that light is motion, and therefore subject to the laws of dynamics and mathematical analysis. Although the progressive motion of light is known by experience to be uniform and in a straight line, the vibrations of the particles are always at right angles to the direction of the ray. The propagation of light is like the spreading of waves in water; but, if one ray alone be considered, its motion may be conceived by supposing a rope of indefinite length stretched horizontally, one end of which is held in the hand. If it be agitated to and fro at regular intervals, with a motion perpendicular to its length, a series of similar and equal tremors or waves will be propagated along it; and if the regular impulses be given in a variety of planes, as up and down, from right to left, and also in oblique directions, the successive undulations will take place in every possible plane. An analogous motion in the ether, when communicated to the optic nerves, would produce the sensation of common light. It is evident that the waves which flow from end to end of the cord in a serpentine form are altogether different from the perpendicular vibratory motion of each particle of the rope, which never deviates far from a state of rest. So, in ether, each particle vibrates perpendicularly to the direction of the ray; but these vibrations are totally different from and independent of the undulations which are transmitted through it, in the same manner as the vibrations of each particular ear of corn are independent of the waves that rush from end to end of a harvest-field when agitated by the wind.
The intensity of light depends upon the amplitude or extent of the vibrations of the particles of ether, while its colour depends upon their frequency. The time of the vibration of a particle of ether is, by theory, as the length of a wave directly, and inversely as its velocity. Now, as the velocity of light is known to be 190,000 miles in a second, if the lengths of the waves of the different coloured rays could be measured, the number of vibrations in a second corresponding to each could be computed. That has been accomplished as follows:-All transparent substances of a certain thickness, with parallel surfaces, reflect and transmit white light; but, if they be extremely thin, both the reflected and transmitted light is coloured. The vivid hues on soap-bubbles, the iridescent colours produced by heat on polished steel and copper, the fringes of colour between the lamina of
Iceland spar and sulphate of lime, all consist of a succession of hues disposed in the same order, totally independent of the colour of the substance, and determined solely by its greater or less thickness-a circumstance which affords the means of ascertaining the length of the waves of each coloured ray, and the frequency of the vibrations of the particles producing them. If a plate of glass be laid upon a lens of almost imperceptible curvature, before an open window, when they are pressed toge ther a black spot will be seen in the point of contact, surrounded by seven rings of vivid colours, all differing from one another (N. 199). In the first ring, estimated from the black spot, the colours succeed each other in the following order :-black, very faint blue, brilliant white, yellow, orange, and red. They are quite different in the other rings, and in the seventh the only colours are pale bluish green and very pale pink. That these rings are formed between the two surfaces in apparent contact may be proved by laying a prism on the lens instead of the plate of glass, and viewing the rings through the inclined side of it that is next to the eye, which arrangement prevents the light reflected from the upper surface mixing with that from the surfaces in contact, so that the intervals between the rings appear perfectly black-one of the strongest circumstances in favour of the undulatory theory; for, although the phenomena of the rings can be explained by either hypothesis, there is this material difference, that, according to the undulatory theory, the intervals between the rings ought to be absolutely black, which is confirmed by experiment; whereas, by the doctrine of emanation, they ought to be half illuminated, which is not found to be the case. M. Fresnel, whose opinion is of the first authority, thought this test conclusive. It may therefore be concluded that the rings arise entirely from the interference of the rays: the light reflected from each of the surfaces in apparent contact reaches the eye by paths of different lengths, and produces coloured and dark rings alternately, according as the reflected waves coincide or destroy one another. The breadths of the rings are unequal; they decrease in width, and the colours become more crowded, as.they recede from the centre. Coloured rings are also produced by transmitting light through the same apparatus; but the colours are less vivid, and are complementary to those reflected, consequently the central spot is white.
The size of the rings increases with the obliquity of the incident light, the same colour requiring a greater thickness or space between the glasses to produce it than when the light falls perpendicularly upon them. Now, if the apparatus be placed in homogeneous instead of white light, the rings will all be of the same colour with that of the light employed, that is to say, if the light be red, the rings will be red, divided by black intervals. The size of the rings varies with the colour of the light. They are largest in red, and decrease in magnitude with the succeeding prismatic colours, being smallest in violet light.
Since one of the glasses is plane and the other spherical, it is evident that from the point of contact the space between them gradually increases in thickness all round, so that a certain thickness of air corresponds to each colour, which in the undulatory system measures the length of the wave producing it (N. 200). By actual measurement Sir Isaac Newton found that the squares of the diameters of the brightest part of each ring are as the odd numbers, 1, 3, 5, 7, &c.; and that the squares of the diameters of the darkest parts are as the even numbers, 0, 2, 4, 6, &c. Consequently, the intervals between the glasses at these points are in the same proportion. If, then, the thickness of the air corresponding to any one colour could be found, its thickness for all the others would be known. Now, as Sir Isaac Newton knew the radius of curvature of the lens, and the actual breadth of the rings in parts of an inch, it was easy to compute that the thickness of air at the darkest part of the first ring is the part of an inch, whence all the others have been deduced. As these intervals determine the length of the waves on the undulatory hypothesis, it appears that the length of a wave of the extreme red of the solar spectrum is equal to the 0.0000266th part of an inch; that the length of a wave of the extreme violet is equal to the 0·0000167th part of an inch; and, as the time of a vibration of a particle of ether producing any particular colour is directly as the length of a wave of that colour, and inversely as the velocity of light, it follows that the molecules of ether producing the extreme red of the solar spectrum perform 458 millions of millions of vibrations in a second; and that those producing the extreme violet accomplish 727 millions of millions of vibrations in the same time. The lengths of the waves of the intermediate colours, and the number of their vibrations, being intermediate between these two, white light,
which consists of all the colours, is consequently a mixture of waves of all lengths between the limits of the extreme red and violet. The determination of these minute portions of time and space, both of which have a real existence, being the actual results of measurement, do as much honour to the genius of Newton as that of the law of gravitation.
The number of advancing waves of light in an inch is known to be from 37,600 to 59,880, and the number of lateral vibrations is from 458 to 727 billions in a second, but the extent of these lateral vibrations of the particles of the ethereal medium is not known, though both their extent and velocity are probably very small compared with the length of the advancing waves and the velocity of propagation. Colour is identified with the number of vibrations; but whether reflection, refraction, absorption, &c., have any relations to the lateral vibrations, or whether they are dependent in part upon some physical action of the ethereal medium unknown and unsuspected, are points as yet undetermined. To ascertain these circumstances, Dr. Faraday instituted a series of the most refined experiments upon the relation of the minute particles of metals to the vibrations of light.
Gold acts powerfully on light, and possesses a real transparency, transmitting green rays when very thin; and being capable of extreme division by solvents without losing its metallic character, its particles transmit rays of various colours according to their size; those that transmit the rose-colour in Bohemian glass are of inconceivable minuteness. The progressive waves of the ether are so long compared with the dimensions of the molecules to which gold can be reduced, that it seemed probable to Dr. Faraday when the latter were placed in a sunbeam that some effective relation might be discovered between them and the smaller vibrations of the ethereal medium; in which case, if reflection, refraction, &c., depended upon such relations, there was reason to expect that these functions would change sensibly by the substitution of different sized particles of the gold for one another. At one time Dr. Faraday hoped he had changed one colour into another by means of gold, which would have been equivalent to a change in the number of vibrations; but although he has not yet confirmed that result, his researches are of the greatest interest.*
* Bakerian Lecture, by Michael Faraday, Esq. Phil. Trans. 1857.
The phenomenon of the coloured rings takes place in vacuo as well as in air, which proves that it is the distance between the lenses alone, and not the air, which produces the colours. However, if water or oil be put between them, the rings contract, but no other change ensues; and Newton found that the thickness of different media at which a given tint is seen is in the inverse ratio of their refractive indices, so that the thickness of laminæ which could not otherwise be measured may be known by their colour; and, as the position of the colours in the rings is invariable, they form a fixed standard of comparison, well known as Newton's scale of colours; each tint being estimated according to the ring to which it belongs from the central spot inclusively. Not only the periodical colours which have been described, but the colours seen in thick plates of transparent substances, the variable hues of feathers, of insects' wings, mother-of-pearl, and of striated substances, all depend upon the same principle. To these may be added the coloured fringes surrounding the shadows of all bodies held in an extremely small beam of light, and the coloured rings surrounding the small beam itself when received
on a screen.
When a very slender sunbeam, passing through a small pinhole into a dark room, is received on a white screen, or plate of ground-glass, at the distance of a little more than six feet, the spot of light on the screen is larger than the pin-hole: and, instead of being bounded by shadow, it is surrounded by a series of coloured rings separated by obscure intervals. The rings are more distinct in proportion to the smallness of the beam (N. 201). When the light is white there are seven rings, which dilate or contract with the distance of the screen from the hole. As the distance of the screen diminishes, the white central spot contracts to a point and vanishes; and, on approaching still nearer, the rings gradually close in upon it, so that the centre assumes successively the most intense and vivid hues. When the light is homogeneous-red, for example-the rings are alternately red and black, and more numerous; and their breadth varies with the colour, being broadest in red light and narrowest in violet. The tints of the coloured fringes from white light, and their obliteration after the seventh ring, arise from the superposition of the different sets of fringes of all the coloured rays. The shadows of objects are also bordered by coloured fringes when held in this