Sine

“ The Excesses of the Sines of Refraction of several sorts of Rays above their common Sine of Incidence when the Refractions are made out of divers denser Mediums immediately into one and the same rarer Medium, suppose of Air, are to one another in a given Proportion. ”

“ Assuming that the intensity of light varies directly as the sine of the angle under which it strikes an illuminated surface, and inversely as the square of its distance from the surface, how high should the light he hung in order that the best possible light shall fall on a walk along the circumference of the plot? ”

“ If two lines of incidence, having equal inclination, be one in a thinner the other in a thicker medium, the sine of the angle of inclination will be a mean proportional between the two sines of the refracted angles. ”

“ The rays of light are straight lines. The angles of incidence and reflexion are in the same plane and equal. The angles of incidence and refraction are in the same plane, and their sines bear an invariable ratio to one another for the same medium. ”

“ Sines.
1.GIven two sides & the contained angle, to find the third side.
⁠From the half-versed sine of the sum of the sides subtract the half-versed sine of their difference; multiply the remainder by the half-versed sine of the contained angle; divide the product by radius; to this add the half-versed sine of the difference of the sides, and you have the half-versed sine of the required base. ”

“ Let us then take instead of the tangents of the angles to the radius and which are to each other as the sines of the angles that is, as and
We have then M x RQ [errata 2] , that is, if squaring both sides,
It appears then that is in general greater than its ultimate value by the quantity supposing the angle to be small. ”

“ Therefore the parts of the medium that lie nearest to the tremulous body move to and fro by turns, in like manner as the parts of the tremulous body itself do; and for the same cause that the parts of this body agitate these parts of the medium, these parts, being agitated by like tremors, will in their turn agitate others next to themselves; and these others, agitated in like manner, will agitate those that lie beyond them, and so on in infinitum. ”

“ The system of Physics which I have for many years inculcated, in the hope of removing from Philosophy the equivocal word attraction, supposes that space is filled with an elastic medium,—that this medium permeates bodies in proportion to their quantities of matter,—that resistance or re-action takes place between the universal medium of space and the novel arrangements of matter in bodies,—that this action and re-action diverge in the medium of space from the surfaces of bodies,—and that, like all diverging forces, they act inversely as the squares of the distances. ”

“ Each particle of each substance draws and is drawn by each other particle of every substance. And each body in the Universe, from a grain of sand to a sun, draws and is drawn by each other body, whether far or near. All these drawings are in obedience to that mysterious something—that force, or power, or influence—which has been named Attraction or Gravitation. ”

“ If we wished to represent to ourselves, by the mechanical properties of a medium filling the whole of the universe, all luminous, electric, and gravitation phenomena, we should be led to attribute to this medium very strange and almost contradictory characteristics ”

“ Why the concurrence of every favorable condition is requisite for success in such inquiries may be readily comprehended. The object in view is to discern, singly, sparkling points, small as the point of a needle, and close as the particles of a handful of sand; so that it needs but the smallest unsteadiness in the air, or imperfection in the shape of the reflecting surface, to scatter the light of each point, to merge them into each other, and present them as one mass. ”

“ Reflexion.—When rays of light fall upon a plane surface, as the flat surface of the mirror, a greater or less number of them are reflected, and this according to a definite law, by which the angle of incidence, or that formed by the incident ray with the perpendicular, is equal to the angle of reflexion, or that formed by the reflected ray with the same. ”

“ Through the medium of another set of sense-perceptions, which some regard as belonging to a different category, we distinguish between bodies that feel "hot" and those that feel "cold;" and in this manner we arrive at the notion of differences of temperature. And it is through the medium of our tactile sense, without any aid from vision, that we first gain the idea of solid form, or the three dimensions of space. ”

“ Let ABC abc [in Fig. 16.] represent a Prism, by which the Sun's Light let into a dark Chamber through the Hole F, may be refracted towards the Lens MN, and paint upon it at p, q, r, s, and t, the usual Colours violet, blue, green, yellow, and red, and let the diverging Rays by the Refraction of this Lens converge again towards X, and there, by the mixture of all those their Colours, compound a white according to what was shewn above. ”

“ IN speaking of the Ancient History of Physics, we have already noticed that the optical philosophers of antiquity had satisfied themselves that vision is performed in straight lines;—that they had fixed their attention upon those straight lines, or rays, as the proper object of the science;—they had ascertained that rays reflected from a bright surface make the angle of reflection equal to the angle of incidence;—and they had drawn several consequences from these principles. ”

“ Stand before a mirror; hold your arms in precisely the same position at each side, your head upright, your body straight; divide your hair exactly in the middle and get it as nearly as you can into exactly the same shape over each ear; and you will see the effect of accurate symmetry: you will see, no less, how all grace and power in the human form result from the interference of motion and life with symmetry, and from the reconciliation of its balance with its changefulness. Your position, as seen in the mirror, is the highest type of symmetry as understood by modern architects. ”

“ For we can give transparent bodies such form and position with respect to the eye and the object that the rays are refracted and bent to where we like, so that we, under any angle, see the objects near or far, and in that manner we can, at a great distance, read the smallest letters, and we can count atoms and sand-grains, on account of the greatness of the angle under which they are seen. ”

“ Do you admit that at a point in the universe that is far away from all material masses a moving object left to itself must follow a straight line? If so, you recognise the existence of privileged observers—those for whom the line is straight. ”

“ You see, we cannot look into the middle of a body like this piece of glass. We perceive the outside form, and the inside form, and we look through it; but we cannot well find out how these forms become so, and I want you, therefore, to take a lesson in the way in which we use a ray of light for the purpose of seeing what is in the interior of bodies. ”

“ My own experience and investigation are, of course, limited, but so far I have only been able to discover one, namely, the larger mass and the smaller mass: the larger mass dominating the centre of interest, which catches your eye instantly at first sight of a picture, and the smaller or less interesting object which next attracts your eye, and so relieves the vision and spares you the monotony of looking at a single object long and steadily, thus fatiguing the eye and dissipating the interest. ”

“ Anything that invalidates our seeing, as a source of knowledge concerning physical reality, invalidates also the whole of physics and physiology. And yet, starting from a common-sense acceptance of our seeing, physics has been led step by step to the construction of the causal chain in which our seeing is the last link, and the immediate object which we see cannot be regarded as that initial cause which we believe to be ninety-three million miles away, and which we are inclined to regard as the "real" sun. ”

“ For as Sound in a Bell or musical String, or other sounding Body, is nothing but a trembling Motion, and in the Air nothing but that Motion propagated from the Object, and in the Sensorium 'tis a Sense of that Motion under the Form of Sound; so Colours in the Object are nothing but a Disposition to reflect this or that sort of Rays more copiously than the rest; in the Rays they are nothing but their Dispositions to propagate this or that Motion into the Sensorium, and in the Sensorium they are Sensations of those Motions under the Forms of Colours. ”

“ Continuous degrees are related like the degrees of the waning of a light from its bright blaze to darkness, or like the degrees of the decrease of vision from objects in the light to those in the shade, or like degrees of purity in the atmosphere from bottom to top. ”

“ If now we suppose a consciousness connected with the film in such a way that the intersection of the spiral with the film gives rise to a conscious experience, we see that we shall have in the film a point moving in a circle, conscious of its motion, knowing nothing of that real spiral the record of the successive intersections of which by the film is the motion of the point. ”

“ DYNAMICS OF A PARTICLE.
Particles are logically divided according to Genius and Speeches.
Genius is the higher classification, and this, combined with Differentia, (i.e. difference of opinion,) produces Speeches. These again naturally divide themselves into three heads.
Particles belonging to the great order of Genius are called 'able' or 'enlightened.' ”

“ A manual treating of physics will best explain the reason of our false impression. When a ray of light is transmitted from one medium to another of different density, as from air to water, a change of direction is impressed on the ray, making the straight line appear broken ”

“ When both the object and the eye are fixed without the least motion, and the medium unchanged, we expect that the object should appear to rest, and keep the same place: yet in the second and fourth experiments, when both the eye and the object are at rest, and the medium unchanged, we make the object appear to move upward or downward, or in any direction we please. ”

“ We have therefore reason to believe, from the phenomena of light and heat, that there is an æthereal medium filling space and permeating bodies capable of being set in motion, and of transmitting that motion to gross matter, so as to heat it and affect it in various ways.... ”

“ Firstly, where gravity, with its tendency to individualize, is absent, no such sharp distinctions exist between one form of perception and another as are found in the sphere of the physical senses.6 Secondly, even in ordinary sense-perception a certain overlapping of visual and aural experiences is known to us. We need only think how common it is to give musical attributes, such as 'consonant' and 'dissonant' to colours, and to describe tones as 'light' and 'dark'. ”

“ The stuff of the world, so far as we have experience of it, consists, on the view that I am advocating, of innumerable transient particulars such as occur in seeing, hearing, etc., together with images more or less resembling these, of which I shall speak shortly. If physics is true, there are, besides the particulars that we experience, others, probably equally (or almost equally) transient, which make up that part of the material world that does not come into the sort of contact with a living body that is required to turn it into a sensation. ”

“ What an infinitely complex play of subtle waves having their origin in our [58] minds may spread itself over the gross lower realm of action, perceptible to the outward eye and ear, like the fine ripples on the large waves of a pond, or the flat designs on the surface of a closely woven carpet, which takes from them its whole beauty and higher meaning. The physicist, however, recognizes and follows only the action of the lower exterior order, and does not concern himself with the finer, which he does not perceive. ”

“ Reflexion and refraction are therefore the essential and indispensable properties of light; and so far as we can understand, it appears that it was necessary that light should possess such properties, in order that it might form a medium of communication between man and the external world. ”

“ Far, too, as her splendors shine, system on system shooting like rays, upward, downward, without centre, without circumference,—in the mass and in the particle, nature hastens to render account of herself to the mind. ”

“ A single line may contain the elements of the motions of all the heavenly bodies; and the eye of science, taking its stand-point at the center of gravity of the system, will see in the equation the harmonious revolutions of all the bodies which circle the heavens. ”

“ The eye moves through a series of angles toward the angle which contains the greatest number of attractions. The reader can hardly fail to feel the successive axes of symmetry as a retarding element in this Rhythm.
46. Sixth. Symmetrical relations of position may be repeated in progressions of scale and of intervals. In that case we get two movements, one caused by a gradual increase in the number of attractions in successive angles of vision, the other being due to a gradual crowding together and convergence of attractions in the same series of angles. ”

“ The phenomena discernible by the sense of sight are explained, but only by bringing into the range of a purer and more piercing vision phenomena infinitely more wonderful. If one could see through some amazing extension of visual power, or if even the imagination could adequately picture, the rush of light waves of all orders of length upon the line of crystal breakers, their deflection in all directions, their separation into their various orders of wave-length ”

“ Now what absurdity to say that a law of nature, say gravity, or electricity, or magnetism has such knowledge of the principles of mechanics as the eye proclaims its Former to have—that it could make a choice among multitudes of shapes of eyes and kinds of joints, and this choice the very best for our convenience ”