REFRACTION
, in Mechanics, is the deviation of a moving body from its direct course, by reason of the different density of the medium it moves in; or a flexion and change of determination, occasioned by a body's passing obliquely out of one medium into another of a different density.
Thus a ball A, moving in the air in the line AB, and falling obliquely on the surface of the water CD, does not proceed straight in the same direction, as to E, but deviates or is deflected to F. Again, if the ball move in water in the line AB, and fall obliquely on a surface of air CD; it will in this case also deviate from the same continued direction BE, but now the contrary way, and will go to G, on the other side of it. Now the deflection in either case is called the Refraction, the Refraction being towards the denser surface BD in the former case, but from it in the latter.
These Refractions are supposed to arise from hence; that the ball arriving at B, in the first case finds more resistance or opposition on the one side O, or from the side of the water, than it did from the side P, or that of the air; and in the latter more resistance from the side P, which is now the side of the water, than the side O, which is that of the air. And so for any other different media: a visible instance of which is often perceived in the falling of shot or shells into the earth, as clay &c, when the perforation is found to rise a little upwards, toward the surface. However another reason is assigned for the Refraction of the rays of light, whose Refractions lie the contrary way to those above, as will be seen in what follows, viz, that water by its greater attraction accelerates the motion of the rays of light more than air does.
Refraction of Light, in Optics, is an inflection or deviation of the rays from their rectilinear course on passing obliquely out of one medium into another, of a different density.
That a body may be refracted, it is necessary that it should fall obliquely on the second medium: in perpendicular incidence there is no Refraction. Yet Voscius and Snellius imagined they had observed a perpendicular ray of light undergo a Refraction; a perpendicular object appearing in the water nearer than it really was: but this was attributing that to a Refraction of the perpendicular rays, which was owing to the divergency of the oblique rays after refraction, from a nearer point. Yet there is a manifest Refraction even of perpendicular rays found in island crystal.
Rohault adds, that though an oblique incidence be necessary in all other mediums we know of, yet the obliquity must not exceed a certain degree; if it do, the body will not penetrate the medium, but will be reflected instead of being refracted. Thus, cannon-balls, in sea engagements, falling very obliquely on the surface of the water, are observed to bound or rise from it, and to sweep the men from off the enemy's decks. And the same thing happens to the little stones with which children make their ducks and drakes along the surface of the water.
The ancients confounded Refraction with Reflection; and it was Newton who first taught the true difference between them. He shews however that there is a good deal of analogy between them, and particularly in the case of light.
The laws of Refraction of the rays of light in mediums differently terminated, i. e. whose surfaces are plane, concave, and convex, make the subject of Dioptrics.—By Refraction it is, that convex glasses, or lenses, collect the rays, magnify objects, burn, &c; and hence the foundation of microscopes, telescopes, &c.—And by Refraction it is, that all remote objects are seen out of their real places; particularly, that the heavenly bodies are apparently higher than they are in reality. The Refraction of the air has many times so uncertain an influence on the places of celestial objects, near the horizon, that wherever Refraction is concerned, the conclusions deduced from observations that are much affected by it, will always remain doubtful, and sometimes too precarious to be relied on. See Dr. Bradley in Philos. Trans. number 485.
As to the cause of Refraction, it does not appear that any person before Des Cartes attempted to explain it; this he undertook to do by the resolution of forces, on the principles of mechanics; in consequence of which, he was obliged to suppose that light passes with more ease through a dense medium than a rare one: thus, the ray AC falling obliquely on a denser medium at C is supposed to be acted on by two forces, one of them impelling it in the direction AL, and the other in AK, which alone can be affected by the change of medium: and since, after the ray has entered the denser medium, it approaches the perpendicular CI, it is plain that this force must have received an increase, whilst the other continued the same.
The first person who questioned the truth of this explanation of the cause of Refraction, was Fermat; he asserted, contrary to Des Cartes, that light suffers greater resistance in water than in air, and greater in glass than in water; and h<*> maintained that the resistance of different mediums, with respect to light, is in proportion to their densities. Leibnitz also adopted the same general idea; and they reasoned upon the subject in the following manner. Nature, say they, accomplishes her ends by the shortest methods; and therefore light ought to pass from one point to another, either by the shortest course, or by that in which the least time is required. But it is plain that the path in which light passes, when it falls obliquely upon a den- | ser medium, is not the most direct or the shortest; and therefore it must be that in which the least time is spent. And whereas it is demonstrable, that light falling obliquely upon a denser medium (in order to take up the least time possible, in passing from a point in one medium to a point in the other) must be refracted in such a manner, that the sine of the angles of incidence and Refraction must be to one another, as the different facilities with which light is transmitted in those mediums; it follows that, since light approaches the perpendicular when it passes obliquely from air into water, the facility with which water suffers light to pass through it, is less than that of the air; so that the light meets with greater resistance in water than in air.
This method of arguing from final causes could not satisfy philosophers. Dr. Smith observes, that it agrees only to the case of Refraction at a plane surface; and that the hypothesis is altogether arbitrary.
Dechales, in explaining the law of Refraction, supposes that every ray of light is composed of several smaller rays, which adhere to one another; and that they are refracted towards the perpendicular, in passing into a denser medium, because one part of the ray meets with more resistance than another part; so that the former traverses a smaller space than the latter; in consequence of which the ray must necessarily bend a little towards the perpendicular. This hypothesis was adopted by the celebrated Dr. Barrow, and indeed some say, he was the author of it. On this hypothesis it is plain, that mediums of a greater refractive power, must give a greater resistance to the passage of the rays of light, than mediums of a less refractive power; which is contrary to fact.
The Bernoullis, both father and son, have attempted to explain the cause of Refraction on mechanical principles; the former on the equilibrium of forces, and the latter on the same principles with the supposition of etherial vortices: but neither of these hypotheses have gained much credit.
M. Mairan supposes a subtle fluid, filling the pores of all bodies, and extending, like an atmosphere, to a small distance beyond their surfaces; and then he supposes that the Refraction of light is nothing more than a necessary and mechanical effect of the incidence of a small body in those circumstances. There is more, he says, of the refracting fluid, in water than in air, more in glass than in water, and in general more in a dense medium than in one that is rarer.
Maupertuis supposes that the course which every ray takes, in passing out of one medium into another, is that which requires the least quantity of action, which depends upon the velocity of the body and the space it passes over; so that it is in proportion to the sum of the products arising from the spaces multiplied by the velocities with which bodies pass over them. From this principle he deduces the necessity of the sine of the angle of incidence being in a constant proportion to that of Refraction; and also all the other laws relating to the propagation and reflection of light.
Dr. Smith (in his Optics, Remarks, p. 70) observes, that all other theories for explaining the reflection and Refraction of light, except that of Newton, suppose that it strikes upon bodies and is resisted by them; which has never been proved by any deduction from experience. On the contrary, it appears by various considerations, and might be shewn by the observations of Mr. Molyneux and Dr. Bradley on the parallax of the sixed stars, that their rays are not at all impeded by the rapid motion of the earth's atmosphere, nor by the object glass of the telescope, through which they pass. And by Newton's theory of Refraction, which is grounded on experience only, it appears that light is so far from being resisted and retarded by Refraction into any dense medium, that it is swifter there than in vacuo in the ratio of the sine of incidence in vacuo to the sine of Refraction into the dense medium. Priestley's Hist. of Light, &c, p. 102 and 333.
Newton shews that the Refraction of light is not performed by the rays salling on the very surface of bodies; but that it is effected, without any contact, by the action of some power belonging to bodies, and extending to a certain distance beyond their surfaces; by which same power, acting in other circumstances, they are also emitted and reflected.
The manner in which Refraction is performed by mere attraction, without contact, may be thus accounted for: Suppose HI the boundary of two mediums, N and O; the first the rarer, ex. gr. air; the second the denser, ex. gr. glass; the attraction of the mediums here will be as their densities. Suppose p S to be the distance to which the attracting force of the denser medium exerts itself within the rarer. Now let a ray of light Aa fall obliquely on the surface which separates the mediums, or rather on the surface pS, where the action of the second and more resisting medium commences: as the ray arrives at a, it will begin to be turned out of its rectilinear course by a superior force, with which it is attracted by the medium O, more than by the medium N; hence the ray is bent out of its right line in every point of its passage between pS and RT, within which distance the attraction acts; and therefore between these lines it describes a curve aBb; but beyond RT, being out of the sphere of attraction of the medium N, it will proceed uniformly in a right line, according to the direction of the curve in the point b.
Again, suppose N the denser and more attracting medium, O the rarer, and HI the boundary as before; and let RT be the distance to which the denser medium exerts its attractive force within the rarer: even when the ray has passed the point B, it will be within the sphere of the superior attraction of the denser medium; but that attraction acting in lines perpendicular to its surface, the ray will be continually drawn from its straight course BM perpendicularly towards HI: thus, having two forces or directions, it will have a compound motion, by which, instead of BM, it will describe Bm, which Bm will in strictness be a curve. Lastly, after it has arrived at m, being out of the influence of the medium N, it will persist uniformly, in a right line, in the direction in which the extremity of | the curve leaves it.—Thus we see how Refraction is performed, both towards the perpendicular DE, and from it.
Refraction in Dioptrics, is the inflexion or bending of the rays of light, in passing the surfaces of glasses, lenses, and other transparent bodies of different densities. Thus, a ray, as AB, falling obliquely from the radiant A, upon a point B, in a diaphanous surface HI, rarer or denser than the medium along which it was propagated from the radiant, has its direction there altered by the action of the new medium; and instead of proceeding to M, it deviates, as for ex. to C.
This deviation is called the Refraction of the ray; BC the refracted ray, or line of Refraction; and B the point of Refraction.—The line AB is also called the line of incidence; and in respect of it, B is also called the point of incidence. The plane in which both the incident and refracted ray are found, is called the plane of Refraction; also a right line BE drawn in the refracting medium perpendicular to the refracting surface at the point of Refraction B, is called the axis of Refraction; and its continuation DB along the medium through which the ray falls, is called the axis of incidence.—Farther, the angle ABI, made by the incident ray and the refracting surface, is usually called the angle of incidence; and the angle ABD, between the incident ray and the axis of incidence, is the angle of inclination. Moreover, the angle MBC, between the refracted and incident rays, is called the angle of Refraction; and the angle CBE, between the refracted ray and the axis of Refraction, is the refracted angle. But it is also very common to call the angles ABD and CBE made by the perpendicular with the incident and refracted rays, the angles of incidence and Refraction.
General Laws of Refraction.—I. A ray of light in its passage out of a rarer medium into a denser, ex. gr. out of air into water or into glass, is refracted towards the perpendicular, i. e. towards the axis of Refraction. Hence, the refracted angle is less than the angle of inclination; and the angle of Refraction less than that of incidence; as they would be equal were the ray to proceed straight from A to M.
II. The ratio of the sines of the angles ABD, CBE, made by the perpendicular with the incident and refracted rays, is a constant and fixed ratio; whatever be the obliquity of the-incident ray, the mediums remaining. Thus, the Refraction out of air, into water, is nearly as 4 to 3, and into glass it is nearly as 3 to 2. As to air in particular, it is shewn by Newton, that a ray of light, in traversing quite through the atmosphere, is refracted the same as it would be, were it to pass with the same obliquity out of a vacuum immediately into air of equal density with that in the lowest part of the atmosphere.
The true law of Refraction was first discovered by Willebrord Snell, professor of Mathematics at Leyden; who found by experiment that the cosecants of the angles of incidence and Refraction, are always in the same ratio. It was commonly attributed however to Des Cartes; who, having seen it in a MS. of Snell's, first published it in his Dioptrics, without naming Snellius, as Huygens asserts; Des Cartes having only altered the form of the law, from the ratio of the cosecants, to that of the sines, which is the same thing.
It is to be observed however, that as the rays of light are not all of the same degree of refrangibility, this constant ratio must be different in different kinds: so that the ratio mentioned by authors, is to be understood of rays of the mean refrangibility, i. e. of green rays. The difference of Refraction between the least and most refrangible rays, that is, between violet and red rays, Newton shews, is about the 2/55 of the whole Refraction of the mean refrangible; which difference, he allows, is so small, that it seldom needs to be regarded.
Different transparent substances have indeed very different degrees of Refraction, and those not according to any regular law; as appears by many experiments of Newton, Euler, Hawksbee, &c. See Newton's Optics, 3d edit. pa. 247; Hawksbee's Experim. pa. 292; Act. Berlin. 1762, pa. 302; Priestley's Hist. of Light &c. pa. 479.
Whence the different refractive powers in different fluids arise, has not been determined. Newton shews, that in many bodies, as glass, crystal, selenites, pseudo-topaz, &c, the refractive power is indeed proportionable to their densities; whilst in sulphureous bodies, as camphor, linseed, and olive oil, amber, spirit of turpentine, &c, the power is two or three times greater than in other bodies of equal density; and yet even these have the refractive power with respect to each other, nearly as their densities. Water has a refractive power in a medium degree between those two kinds of substances; whilst salts and vitriols have refractive powers in a middle degree between those of earthy substances and water, and accordingly are composed of those two sorts of matter. Spirit of wine has a refractive power in a middle degree between those of water and oily substances; and accordingly it seems to be composed of both, united by fermentation. It appears therefore, that all bodies seem to have their refractive powers nearly proportional to their densities, excepting so far as they partake more or less of sulphureous oily particles, by which those powers are altered.
Newton suspected that different degrees of heat might have some effect on the refractive power of bodies; but his method of determining the general Refraction was not sufficiently accurate to ascertain this circumstance. Euler's method however was well adapted to this purpose: from his experiments he insers, that the focal distance of a single lens of glass diminishes with the heat communicated to it; which diminution is owing to a change in the refractive power of the glass itself, which is probably increased by heat, and diminished by cold, as well probably as that of all other translucent substances.
From the law above laid down it follows, that one angle of inclination, and its corresponding refracted angle, being found by observation, the refracted angles corresponding to the several other angles of inclination are thence easily computed. Now, Zahnius and Kircher have found, that if the angle of inclination be 70°, the refracted angle, out of air into glass, will be 38° 50′; on which principle Zahnius has constructed a table of those Refractions for the several degrees of the | angle of inclination; a specimen of which here follows:
| Angle of In- | Refracted | Angle of Re- | ||||
| clination. | Angle. | fraction. | ||||
| ° | ° | ′ | ″ | ° | ′ | ″ |
| 1 | 0 | 40 | 5 | 0 | 19 | 55 |
| 2 | 1 | 20 | 6 | 0 | 39 | 54 |
| 3 | 2 | 0 | 4 | 0 | 59 | 56 |
| 4 | 2 | 40 | 5 | 1 | 19 | 55 |
| 5 | 3 | 20 | 3 | 1 | 39 | 57 |
| 10 | 6 | 39 | 16 | 3 | 20 | 44 |
| 20 | 13 | 11 | 35 | 6 | 48 | 25 |
| 30 | 19 | 29 | 29 | 10 | 30 | 31 |
| 45 | 28 | 9 | 19 | 16 | 50 | 41 |
| 90 | 41 | 51 | 40 | 48 | 8 | 20 |
Hence it appears, that if the angle of inclination be less than 20°, the angle of Refraction out of air into glass is almost 1/3 of the angle of inclination; and therefore a ray is refracted to the axis of Refraction by almost a third part of the quantity of its angle of inclination. And on this principle it is that Kepler, and most other dioptrical writers, demonstrate the Refractions in glasses; though in estimating the law of these Refractions he followed the example of Alhazen and Vitello, and sought to discover it in the proportion of the angles, and not in that of the sines, or cosecants, as discovered by Snellius, as mentioned above.
The refractive powers of several substances, as determined by different philosophers, may be seen in the following tables; in which the ray is supposed to pass out of air into each of the substances, and the annexed numbers shew the proportion to unity or 1, between the sines of the angles of incidence and Refraction.
| 1. By Sir Isaac Newton's Observations. | |
| Air | 0.9997 |
| Rain water | 1.3358 |
| Spirit of wine | 1.3698 |
| Oil of vitriol | 1.4285 |
| Alum | 1.4577 |
| Oil olive | 1.4666 |
| Borax | 1.4667 |
| Gum Arabic | 1.4771 |
| Linseed oil | 1.4814 |
| Selenites | 1.4878 |
| Camphor | 1.5000 |
| Dantzick vitriol | 1.5000 |
| Nitre | 1.5238 |
| Sal gem | 1.5455 |
| Glass | 1.5500 |
| Amber | 1.5556 |
| Rock crystal | 1.5620 |
| Spirit of turpentine | 1.5625 |
| A yellow pseudo-topaz | 1.6429 |
| Island crystal | 1.6666 |
| Glass of antimony | 1.8889 |
| A Diamond | 2.4390 |
| 2. By Mr. Hawksbee. | |
| Water | 1.3359 |
| Spirit of honey | 1.3359 |
| Oil of amber | 1.3377 |
| Human urine | 1.3419 |
| White of an egg | 1.3511 |
| French brandy | 1.3625 |
| Spirit of wine | 1.3721 |
| Distilled vinegar | 1.3721 |
| Gum ammoniac | 1.3723 |
| Aqua regia | 1.3898 |
| Aqua fortis | 1.4044 |
| Spirit of nitre | 1.4076 |
| Crystalline humour of an ox's eye | 1.4635 |
| Oil of vitriol | 1.4262 |
| Oil of turpentine | 1.4833 |
| Oil of amber | 1.5010 |
| Oil of cloves | 1.5136 |
| Oil of cinnamon | 1.5340 |
| 3. By Mr. Euler, junior. | |
| Rain or distilled water | 1.3358 |
| Well water | 1.3362 |
| Distilled vinegar | 1.3442 |
| French wine | 1.3458 |
| A solution of gum arabic | 1.3467 |
| French brandy | 1.3600 |
| Ditto a stronger kind | 1.3618 |
| Spirit of wine rectified | 1.3683 |
| Ditto more highly rectified | 1.3706 |
| White of an egg | 1.3685 |
| Spirit of nitre | 1.4025 |
| Oil of Provence | 1.4651 |
| Oil of turpentine | 1.4822 |
III. When a ray passes out of a denser medium into a rarer, it is refracted from the perpendicular, or from the axis of Refraction.
This is exactly the reverse of the 2d law, and the quantity of Refraction is equal in both cases, or both forwards and backwards; so that a ray would take the same course back, by which another passed forward, viz, if a ray would pass from A by B to C, another would pass from C by B to A. Hence, in this case, the angle of Refraction is greater than the angle of inclination. Hence also, if the angle of inclination be less than 30°, MBC is nearly equal to 1/3 of MBE; therefore MBC is 1/2 of CBE; consequently, if the Refraction be out of glass into air, and the angle of inclination less than 30°, the ray is refracted from the axis of Refraction by almost the half of the angle of inclination. And this is the other dioptrical principle used by most authors after Kepler, to demonstrate the Refractions of glasses.
If the Refraction be out of air into glass, the ratio of the sines of inclination and Refraction is as 3 to 2, or more accurately as 17 to 11; if out of air into water as 4 to 3; therefore if the course be the contrary way, viz, out of glass or water into air, the ratio of the sines will be, in the former case as 2 to 3 or 11 to 17, and in the latter as 3 to 4. So that, if the Refraction be from water or glass into air, and the angle of inci- | dence or inclination be greater than about 48 1/2 degrees in water, or greater than about 40° in glass, the ray will not be refracted into air; but will be reflected into a line which makes the angle of reflection equal to the angle of incidence; because the sines of 48 1/2 and 40° are to the radius, as 3 to 4, and as 11 to 17 nearly; and therefore when the sine has a greater proportion to the radius than above, the ray will not be refracted.
IV. A ray falling on a curve surface, whether concave or convex, is refracted after the same manner as if it fell on a plane which is a tangent to the curve in the point of incidence. Because the curve and its tangent have the point of contact common to both, where the ray is refracted.
1. If parallel rays, AB and CD, be refracted out of one transparent medium into another of a different density, they will continue parallel after Refraction, as BE and DF. Hence a glass that is plane on both sides, being turned either directly or obliquely to the sun, &c, the light passing through it will be propagated in the same manner as if the glass were away.
2. If two rays CD and CP, proceeding from the same radiant C, and falling on a plane surface of a different density, so that the points of Refraction D and P be equally distant from the perpendicular of incidence GK, the refracted rays DF and PQ have the same virtual focus, or the same point of dispersion G.— Hence, when refracted rays, falling on the eye placed out of the perpendicular of incidence, are either equally distant from the perpendicular, or very near each other, they will flow upon the eye as if they came to it from the point G; consequently the point C will be seen by the refracted rays as in G. And hence also, if the eye be placed in a dense medium, objects in a rarer will appear more remote than they are; and the place of the image, in any case, may be determined from the ratio of Refraction: Thus, to fishes swimming under water, objects out of the water must appear farther distant than in reality they are. But, on the contrary, if the eye at E be placed in a rarer medium, then an object G placed in a denser, appears, at C, nearer than it is; and the place of the image may be determined in any given case by the ratio of Refraction: and thus the bottom of a vessel full of water is raised by Refraction a third part of its depth, with respect to an eye placed perpendicularly over the refracting surface; and thus also fishes and other bodies, under water, appear nearer than they really are.
3. If the eye be placed in a rarer medium; then an object seen in a denser, by a ray refracted in a plane surface, will appear larger than it really is. But if the eye be in a denser medium, and the object in a rarer, the object will appear less than it is. And, in each case, the apparent magnitude FQ is to the real one EH, as the rectangle CK . GL to GK . CL, or in the compound ratio of the distance CK of the point to which the rays tend before Refraction, from the refracting surface DP, to the distance GK of the eye from the same, and of the distance GL of the object EH from the eye, to its distance CL from the point to which the rays tend before Refraction.—Hence, if the object be very remote, CL will be physically equal to GL; and then the real magnitude EL is to the apparent maguitude FL, as GK to CK, or as the distance of the eye G from the refracting plane, to the distance of the point of convergence F from the same plane. And hence also, objects under water, to an eye in the air, appear larger than they are; and to fishes under water, objects in the air appear less than they are.
1. A ray of light DE, parallel to the axis, after a single refraction at E, meets the axis in the point F, beyond the centre C.
2. Also in that case, the semidiameter CB or CE will be to the refracted ray EF, as the sine of the angle of refraction to the sine of the angle of inclination BCE. But the distance of the focus, or point of concurrence from the centre, CF, is to the refracted ray EF, as the sine of the refracted angle to the sine of the angle of inclination.
3. Hence also, in this case, the distance BF of the focus from the refracting surface, must be to CF its distance from the centre, in a ratio greater than that of the sine of the angle of inclination to the sine of the refracted angle. But those ratios will be nearly equal when the rays are very near the axis, and the angle of inclination BCE is only of a few degrees. And when the Refraction is out of air into glass, then
| For rays near the axis, | For more distant rays, |
| BF:FC::3:2, | BF:FC > 3:2, |
| BC:BF::1:3. | BC:BF < 1:3. |
| For rays near the axis, | For more distant rays, |
| BF:FC::4:3, | BF:FC > 4:3, |
| BC:BF::1:4, | BC:BF < 1:4. |
Hence, as the sun's rays are parallel as to sense, if they fall on the surface of a solid glass sphere, or of a sphere full of water, they will not meet the axis within the sphere: so that Vitello was mistaken when he imagined that the sun's rays, falling on the surface of a crystalline sphere, were refracted to the centre.
4. If a ray HE fall parallel to the axis FA, out of a rarer medium, on the concave spherical surface BE of a denser one; the refracted ray EN will diverge from the point of the axis F, so that FE will be to FC, in the ratio of the sine of the angle of inclination, to the sine of the refracted angle. Consequently FB to FC is in a greater ratio than that; unless when the rays are very near the axis, and the angle BCE is very small, | for then FB will be to FC nearly in that ratio. And hence, in the cases of Refraction out of air into water or glass, the ratios of BC, BF and CF, will be the same as specified in the last article.
5. If a ray DE, parallel to the axis FC, pass out of a denser into a rarer spherical convex medium, it will diverge from the axis after Refraction; and the distance FC of the point of dispersion, or of the virtual focus F, from the centre of the sphere, will be to its semidiameter CE or CB, as the sine of the refracted angle is to the sine of the angle of Refraction; but to the portion of the refracted ray drawn back, FE, it will be in the ratio of the sine of the refracted angle to the sine of the angle of inclination. Consequently FC will be to FB, in a greater ratio than this last one: unless when the rays DE fall very near the axis FC, for then FC to FB will be very nearly in that ratio.
Hence, when the Refraction is out of glass into air; then,
| For rays near the axis, | For more distant rays, |
| FC:FB::3:2, | FC:FB > 3:2, |
| BC:BF::1:2. | BC:BF > 1:2, |
| For rays near the axis, | For more distant rays, |
| FC:FB::4:3, | FC:FB > 4:3, |
| BC:BF::1:3. | BC:BF > 1:3. |
6. If the ray HE fall parallel to the axis CF, from a denser medium, upon the surface of a spherically concave rarer one; the refracted ray will meet with the axis in the point F, so that the distance CF from the centre, will be to the refracted ray FE, as the sine of the refracted angle, to the sine of the angle of inclination. Consequently FC will be to FB, in a greater ratio than that above mentioned: unless when the rays are very near the axis, for then FC is to FB very nearly in that ratio; and the three FB, FC, BC are, in the cases of air, water and glass, in the numeral ratios as specified at the end of the last article. See Wolsius, Elem. Mathes. tom. 3 p. 179 &c.
ABC being the transverse section of a prism; if a ray of light DE fall obliquely upon it out of the air; instead of proceeding straight on to F, being refracted towards the perpendicular IE, it will decline to G. Again, since the ray EG, passing out of glass into air, falls obliquely on BC, it will be refracted to M, so as to recede from the perpendicular GO. And hence arise the various phenomena of the prism. See Colour.
If parallel rays, AB, CD, EF, fall on the surface of a convex lens XBZ (the last fig. above); the perpendicular ray AB will pass unrefracted to K, where emerging, as before, perpendicularly, into air, it will proceed straight on to G. But the rays CD and EF, falling obliquely out of air into glass, at D and F, will be refracted towards the axis of Refraction, or towards the perpendiculars at D and F, and so decline to Q and P: where emerging again obliquely out of the glass into the surface of the air, they will be refracted from the perpendicular, and proceed in the directions QG and PG, meeting in G. And thus also will all the other rays be refracted so as to meet the rest near the place G. See Focus and Lens.—Hence the great property of convex glasses; viz, that they collect parallel rays, or make them converge into a point.
Parallel rays AB, CD, EF, falling on a concave lens GBHIMK, the ray AB falling perpendicularly on the glass at B, will pass unrefracted to M; where, being still perpendicular, it will pass into the air to L, with- out Refraction. But the ray CD, falling obliquely on the surface of the glass, will be refracted towards the perpendicular at D, and proceed to Q; where again falling obliquely out of the glass upon the surface of air, it will be refracted from the perpendicular at Q, and proceed to V. After the same manner the ray EF is first refracted to Y, and thence to Z.—Hence the great property of concave glasses; viz, that they disperse parallel rays, or make them diverge. See Lens.
If parallel rays EF, GH, IK, (the last fig. above) fall obliquely on a plane glass ABCD; the obliquity being the same in all, by reason of their parallelism, they will be all equally refracted towards the perpendicular; and accordingly, being still parallel at M, O, and Q, they will pass out into the air equally refracted again from the perpendicular, and still parallel. Thus will the rays EF, GH, and IK, at their entering the glass, be inflected towards the right; and in their going out as much inflected to the left; so that the first Refraction is here undone by the second, thereby causing the rays on their emerging from the glass, to be parallel to their first direction before they entered it; though not so as that the object is seen in its true place; for the ray RQ, being produced back again, will not coincide with the ray IK, but will fall to the left of it; and this the more as the glass is thicker; however, as | to the colour, the second Refraction does really undo the first. See Colour.
Refraction in Astronomy, or Refraction of the Stars, is an inflexion of the rays of those luminaries, in passing through our atmosphere; by which the apparent altitudes of the heavenly bodies are increased.
This Refraction arises from hence, that the atmosphere is unequally dense in different stages or regions; rarest of all at the top, and densest of all at the bottom; which inequality in the same medium, makes it equivalent to several unequal mediums, by which the course of the ray of light is continually bent into a continued curve line. See Atmosphere.—And Sir Isaac Newton has shewn, that a ray of light, in passing from the highest and rarest part of the atmosphere, down to the lowest and densest, undergoes the same quantity of Refraction that it would do in passing immediately, at the same obliquity, out of a vacuum into air of equal density with that in the lowest part of the atmosphere.
The effect of this Refraction may be thus conceived. Suppose ZV a quadrant of a vertical circle described from the centre of the earth T, under which is AB a quadrant of a circle on the surface of the earth, and GH a quadrant of the surface of the atmosphere. Then suppose SE a ray of light emitted by a star at S, and falling on the atmosphere at E: this ray coming out of the ethereal medium, which is much rarer than our air, or perhaps out of a perfect vacuum, and falling on the surface of the atmosphere, will be refracted towards the perpendicular, or inclined down more towards the earth; and since the upper air is again rarer than that near the earth, and grows still denser as it approaches the earth's surface, the ray in its progress will be continually refracted, so as to arrive at the eye in the curve line EA. Then supposing the right line AF to be a tangent to the arch at A, the ray will enter the eye at A in the direction of AF; and therefore the star will appear in the heavens at Q, instead of S, higher or nearer the zenith than the star really is.
Hence arise the phenomena of the crepusculum or twilight; and hence also it is that the moon is sometimes seen eclipsed, when she is really below the horizon, and the sun above it.
That there is a real Refraction of the stars &c, is deduced not only from physical considerations, and from arguments a priori, and a similitudine, but also from precise astronomical observation: for there are numberless observations by which it appears that the sun, moon, and stars rise much sooner, and appear higher, than they should do according to astronomical calculations. Hence it is argued, that as light is propagated in right lines, no rays could reach the eye from a luminary below the horizon, unless they were deflected out of their course, at their entrance into the atmosphere; and therefore it appears that the rays are refracted in passing through the atmosphere.
Hence the stars appear higher by Refraction than they really are; so that to bring the observed or apparent altitudes to the true ones, the quantity of Refraction must be subtracted. And hence, the ancients, as they were not acquainted with this Refraction, reckoned their altitudes too great, so that it is no wonder they sometimes committed considerable errors. Hence also, Refraction lengthens the day, and shortens the night, by making the sun appear above the horizon a little before his rising, and a little after his setting. Refraction also makes the moon and stars appear to rise sooner and set later than they really do. The apparent diameter of the sun or moon is about 32′; the horizontal refraction is about 33′; whence the sun and moon appear wholly above the horizon when they are entirely below it. Also, from observations it appears that the Refractions are greater nearer the pole than at lesser latitudes, causing the sun to appear some days above the horizon, when he is really below it; doubtless from the greater density of the atmosphere, and the greater obliquity of the incidence.
Stars in the zenith are not subject to any Refraction: those in the horizon have the greatest of all: from the horizon, the Refraction continually decreases to the zenith. All which follows from hence, that in the first case, the rays are perpendicular to the medium; in the second, their obliquity is the greatest, and they pass through the largest space of the lower and denser part of the air, and through the thickest vapours; and in the third, the obliquity is continually decreasing.
The air is condensed, and consequently Refraction is increased, by cold; for which reason it is greater in cold countries than in hot ones. It is also greater in cold weather than in hot, in the same country; and the morning Refraction is greater than that of the evening, because the air is rarefied by the heat of the sun in the day, and condensed by the coldness of the night. Refraction is also subject to some small variation at the same time of the day in the finest weather.
At the same altitudes, the sun, moon, and stars all undergo the same Refraction: for at equal altitudes the incident rays have the same inclinations; and the sines of the refracted angles are as the sines of the angles of inclination, &c.
Indeed Tycho Brahe, who first deduced the Refractions of the sun, moon, and stars, from observation, and whose table of the Refraction of the stars is not much different from those of Flamsteed and Newton, except near the horizon, makes the solar Refractions about 4′ greater than those of the fixed stars; and the lunar Refractions also sometimes greater than those of the stars, and sometimes less. But the theory of Refractions, found out by Snellius, was not fully understood in his time.
The horizontal Refraction, being the greatest, is the cause that the sun and moon appear of an oval form at their rising and setting; for the lower edge of each being more refracted than the upper edge, the perpendicular diameter is shortened, and the under edge appears more flatted also.—Hence also, if we take with an instrument the distance of two stars when they are in the same vertical and near the horizon, we shall find it considerably less than if we measure it when they are both at such a height as to suffer little or no Refraction; because the lower star is more elevated than the higher. There is also another alteration made by Refraction in the apparent distance of stars: when two stars are in the same almicantar, or parallel of declination, their ap- | parent distance is less than the true; for since Refraction makes each of them higher in the azimuth or vertical in which they appear, it must bring them into parts of the vertical where they come nearer to each other; because all vertical circles converge and meet in the zenith. This contraction of distance, according to Dr. Halley (Philos. Trans. numb. 368) is at the rate of at least one second in a degree; so that, if the distance between two stars in a position parallel to the horizon measure 30°, it is at most to be reckoned only 29° 59′ 30″.
The quantity of the Refraction at every altitude, from the horizon, where it is greatest, to the zenith where it is nothing, has been determined by observation, by many astronomers; those of Dr. Bradley and Mr. Mayer are esteemed the most correct of any, being nearly alike, and are now used by most astronomers. Doctor Bradley, from his observations, deduced this very simple and general rule for the Refraction r at any altitude a whatever; viz, as rad. 1 : cotang. the Refraction in seconds.
This rule, of Dr. Bradley's, is adapted to these states of the barometer and thermometer, viz, either 29.6 inc. barom. and 50° thermometer, or 30 — barom. and 55 thermometer, for both which states it answers equally the same. But for any other states of the barometer and thermometer, the Refraction above-found is to be corrected in this manner; viz, if b denote any other height of the barometer in inches, and t the degrees of the thermometer, r being the Refraction uncorrected, as found in the manner above. Then as 29.6:b::r:R the Refraction corrected on account of the barometer, and 400:450 t::R: the Refraction corrected both on account of the barometer and thermometer; which sinal corrected Refraction is therefore . Or, to correct the same Refraction r by means of the latter state, viz, barom. 30 and therm. 55, it will be as , and the correct Refraction.
From Dr. Bradley's rule, , the following Table of the mean astronom. Refrac. is computed.
| Mean Astronomical Refractions in Altitude. | |||||||||||||||||
| Apparent | Refraction. | Apparent | Refraction. | Apparent | Refraction. | Apparent | Refraction. | Apparent | Refraction. | ||||||||
| Altitude. | Altitude. | Altitude. | Altitude. | Altitude. | |||||||||||||
| 0° | 0′ | 33′ | 0″ | 3° | 0′ | 14′ | 36″ | 8° | 30′ | 6′ | 8″ | 20° | 0′ | 2′ | 35″ | 54° | 41″ |
| 0 | 5 | 32 | 10 | 3 | 5 | 14 | 20 | 8 | 40 | 6 | 1 | 20 | 30 | 2 | 31 | 55 | 40 |
| 0 | 10 | 31 | 22 | 3 | 10 | 14 | 4 | 8 | 50 | 5 | 55 | 21 | 0 | 2 | 27 | 56 | 38 |
| 0 | 15 | 30 | 35 | 3 | 15 | 13 | 49 | 9 | 0 | 5 | 48 | 21 | 30 | 2 | 24 | 57 | 37 |
| 0 | 20 | 29 | 50 | 3 | 20 | 13 | 34 | 9 | 10 | 5 | 42 | 22 | 0 | 2 | 20 | 58 | 35 |
| 0 | 25 | 29 | 6 | 3 | 25 | 13 | 20 | 9 | 20 | 5 | 36 | 23 | - | 2 | 14 | 59 | 34 |
| 0 | 30 | 28 | 22 | 3 | 30 | 13 | 6 | 9 | 30 | 5 | 31 | 24 | - | 2 | 7 | 60 | 33 |
| 0 | 35 | 27 | 41 | 3 | 40 | 12 | 40 | 9 | 40 | 5 | 25 | 25 | - | 2 | 2 | 61 | 31 |
| 0 | 40 | 27 | 0 | 3 | 50 | 12 | 15 | 9 | 50 | 5 | 20 | 26 | - | 1 | 56 | 62 | 30 |
| 0 | 45 | 26 | 20 | 4 | 0 | 11 | 51 | 10 | 0 | 5 | 15 | 27 | - | 1 | 51 | 63 | 29 |
| 0 | 50 | 25 | 42 | 4 | 10 | 11 | 29 | 10 | 15 | 5 | 7 | 28 | - | 1 | 47 | 64 | 28 |
| 0 | 55 | 25 | 5 | 4 | 20 | 11 | 8 | 10 | 30 | 5 | 0 | 29 | - | 1 | 42 | 65 | 26 |
| 1 | 0 | 24 | 29 | 4 | 30 | 10 | 48 | 10 | 45 | 4 | 53 | 30 | - | 1 | 38 | 66 | 25 |
| 1 | 5 | 23 | 54 | 4 | 40 | 10 | 29 | 11 | 0 | 4 | 47 | 31 | - | 1 | 35 | 67 | 24 |
| 1 | 10 | 23 | 20 | 4 | 50 | 10 | 11 | 11 | 15 | 4 | 40 | 32 | - | 1 | 31 | 68 | 23 |
| 1 | 15 | 22 | 47 | 5 | 0 | 9 | 54 | 11 | 30 | 4 | 34 | 33 | - | 1 | 28 | 69 | 22 |
| 1 | 20 | 22 | 15 | 5 | 10 | 9 | 38 | 11 | 45 | 4 | 29 | 34 | - | 1 | 24 | 70 | 21 |
| 1 | 25 | 21 | 44 | 5 | 20 | 9 | 23 | 12 | 0 | 4 | 23 | 35 | - | 1 | 21 | 71 | 19 |
| 1 | 30 | 21 | 15 | 5 | 30 | 9 | 8 | 12 | 20 | 4 | 16 | 36 | - | 1 | 18 | 72 | 18 |
| 1 | 35 | 20 | 46 | 5 | 40 | 8 | 54 | 12 | 40 | 4 | 9 | 37 | - | 1 | 16 | 73 | 17 |
| 1 | 40 | 20 | 18 | 5 | 50 | 8 | 41 | 13 | 0 | 4 | 3 | 38 | - | 1 | 13 | 74 | 16 |
| 1 | 45 | 19 | 51 | 6 | 0 | 8 | 28 | 13 | 20 | 3 | 57 | 39 | - | 1 | 10 | 75 | 15 |
| 1 | 50 | 19 | 25 | 6 | 10 | 8 | 15 | 13 | 40 | 3 | 51 | 40 | - | 1 | 8 | 76 | 14 |
| 1 | 55 | 19 | 0 | 6 | 20 | 8 | 3 | 14 | 0 | 3 | 45 | 41 | - | 1 | 5 | 77 | 13 |
| 2 | 0 | 18 | 35 | 6 | 30 | 7 | 51 | 14 | 20 | 3 | 40 | 42 | - | 1 | 3 | 78 | 12 |
| 2 | 5 | 18 | 11 | 6 | 40 | 7 | 40 | 14 | 40 | 3 | 35 | 43 | - | 1 | 1 | 79 | 11 |
| 2 | 10 | 17 | 48 | 6 | 50 | 7 | 30 | 15 | 0 | 3 | 30 | 44 | - | 0 | 59 | 80 | 10 |
| 2 | 15 | 17 | 26 | 7 | 0 | 7 | 20 | 15 | 30 | 3 | 24 | 45 | - | - | 57 | 81 | 9 |
| 2 | 20 | 17 | 4 | 7 | 10 | 7 | 11 | 16 | 0 | 3 | 17 | 46 | - | - | 55 | 82 | 8 |
| 2 | 25 | 16 | 44 | 7 | 20 | 7 | 2 | 16 | 30 | 3 | 10 | 47 | - | - | 53 | 83 | 7 |
| 2 | 30 | 16 | 24 | 7 | 30 | 6 | 53 | 17 | 0 | 3 | 4 | 48 | - | - | 51 | 84 | 6 |
| 2 | 35 | 16 | 4 | 7 | 40 | 6 | 45 | 17 | 30 | 2 | 59 | 49 | - | - | 49 | 85 | 5 |
| 2 | 40 | 15 | 45 | 7 | 50 | 6 | 37 | 18 | 0 | 2 | 54 | 50 | - | - | 48 | 86 | 4 |
| 2 | 45 | 15 | 27 | 8 | 0 | 6 | 29 | 18 | 30 | 2 | 49 | 51 | - | - | 46 | 87 | 3 |
| 2 | 50 | 15 | 9 | 8 | 10 | 6 | 22 | 19 | 0 | 2 | 45 | 52 | - | - | 44 | 88 | 2 |
| 2 | 55 | 14 | 52 | 8 | 20 | 6 | 15 | 19 | 30 | 2 | 39 | 53 | - | - | 43 | 89 | 1 |
Mr. Mayer says his rule was deduced from theory, and, when reduced from French measure and Reaumur's thermometer, to English measure and Fahrenheit's thermometer, it is this, the Refraction in seconds, corrected for both barometer and thermometer: where the letters denote the same things as before, except A, which denotes the angle whose tangent is .
Mr. Simpson too (Dissert. pa. 46 &c) has ingeniously determined by theory the astronomical Refractions, from which he brings out this rule, viz, As 1 to .9986 or as radius to sine of 86° 58′ 30″, so is the sine of any given zenith distance, to the sine of an arc; then 2/11 of the difference between this arc and the zenith distance, is the Refraction sought for that zenith distance. And by this rule Mr. Simpson computed a Table of the mean Refractions, which are not much different from those of Dr. Bradley and Mr. Mayer, and are as in the following Table.
| Mr. Simpson's Table of Mean Refractions. | ||||||||
| Appa- | Appa- | Appa- | ||||||
| rent | Refrac- | rent | Refrac- | rent | Refrac- | |||
| Alti- | tion. | Alti- | tion. | Alti- | tion. | |||
| tude. | tude. | tude. | ||||||
| 0° | 33 | 0″ | 17° | 2′ | 50″ | 38° | 1′ | 7″ |
| 1 | 23 | 50 | 18 | 2 | 40 | 40 | 1 | 2 |
| 2 | 17 | 43 | 19 | 2 | 31 | 42 | 0 | 58 |
| 3 | 13 | 44 | 20 | 2 | 23 | 44 | 0 | 54 |
| 4 | 11 | 5 | 21 | 2 | 16 | 46 | 0 | 50 |
| 5 | 9 | 10 | 22 | 2 | 9 | 48 | 0 | 47 |
| 6 | 7 | 49 | 23 | 2 | 3 | 50 | 0 | 44 |
| 7 | 6 | 48 | 24 | 1 | 57 | 52 | 0 | 41 |
| 8 | 5 | 59 | 25 | 1 | 52 | 54 | 0 | 38 |
| 9 | 5 | 21 | 26 | 1 | 47 | 56 | 0 | 35 |
| 10 | 4 | 50 | 27 | 1 | 42 | 58 | 0 | 32 |
| 11 | 4 | 24 | 28 | 1 | 38 | 60 | 0 | 30 |
| 12 | 4 | 2 | 29 | 1 | 34 | 65 | 0 | 24 |
| 13 | 3 | 43 | 30 | 1 | 30 | 70 | 0 | 19 |
| 14 | 3 | 27 | 32 | 1 | 23 | 75 | 0 | 14 |
| 15 | 3 | 13 | 34 | 1 | 17 | 80 | 0 | 9 |
| 16 | 3 | 1 | 36 | 1 | 12 | 85 | 0 | 4 1/2 |
It is evident that all observed altitudes of the heavenly bodies ought to be diminished by the numbers taken out of the foregoing Table. It is also evident that the Refraction diminishes the right and oblique ascensions of a star, and increases the descensions: it increases the northern declination and latitude, but decreases the southern: in the eastern part of the heavens it diminishes the longitude of a star, but in the western part of the heavens it increases the same.
Refraction of Altitude, is an arc of a vertical circle, as AB, by which the altitude of a star AC is increased by the Refraction.
Refraction of Ascension and Descension, is an arc DE of the equator, by which the ascension and descension of a star, whether right or oblique, is increased or diminished by the Refraction.
Refraction of Declination, is an arc BF of a circle of declination, by which the declination of a star DA or EF is increased or diminished by Refraction.
Refraction of Latitude is an arc AG of a circle of latitude, by which the latitude of a star AH is increased or diminished by the Refraction.
Refraction of Longitude is an arc 1H of the ecliptic, by which the longitude of a star is increased or diminished by means of the Refraction.
Terrestrial Refraction, is that by which terrestrial objects appear to be raised higher than they really are, in observing their altitudes. The quantity of this Refraction is estimated by Dr. Maskelyne at one-tenth of the distance of the object observed, expressed in degrees of a great circle. So, if the distance be 10000 fathoms, its 10th part 1000 fathoms, is the 60th part of a degree of a great circle on the earth, or 1′, which therefore is the Refraction in the altitude of the object at that distance. (Requisite Tables, 1766, pa. 134).
But M. Le Gendre is induced, he says, by several experiments, to allow only 1/14th part of the distance for the Refraction in altitude. So that, upon the distance of 10000 fathoms, the 14th part of which is 714 fathoms, he allows only 44″ of terrestrial Refraction, so many being contained in the 714 fathoms. See his Memoir concerning the Trigonometrical operations, &c.
Again, M. de Lambre, an ingenious French astronomer, makes the quantity of the Terrestrial Refraction to be the 11th part of the arch of distance. But the English measurers, Col. Edw. Williams, Capt. Mudge, and Mr. Dalby, from a multitude of exact observations made by them, determine the quantity of the medium Refraction to be the 12th part of the said distance.
The quantity of this Refraction, however, is found to vary considerably, with the different states of the weather and atmosphere, from the 15th part of the distance, to the 9th part of the same; the medium of which is the 12th part, as above mentioned.
Some whimsical effects of this Refraction are also related, arising from peculiar situations and circumstances. Thus, it is said, any person standing by the side of the river Thames at Greenwich, when it is high- | water there, he can see the cattle grazing on the Isle of Dogs, which is the marshy meadow on the other side of the river at that place; but when it is low-water there, he cannot see any thing of them, as they are hid from his view by the land wall or bank on the other side, which is raised higher than the marsh, to keep out the waters of the river. This curious effect is probably owing to the moist and dense vapours, just above and rising from the surface of the water, being raised higher or lifted up with the surface of the water at the time of high tide, through which the rays pass, and are the more refracted.
Again, a similar instance is related in a letter to me, from an ingenious friend, Mr. Abr. Crocker of Frome in Somersetshire, dated January 12, 1795. “My Devonshire friend,” says he, (whose seat is in the vicinity of the town of Modbury, 12 miles in a geographical line from Maker tower near Plymouth) “being on a pleasure spot in his garden, on the 4th of December 1793, with some friends, viewing the surrounding country, with an achromatic telescope, descried an object like a perpendicular pole standing up in the chasm of a hedge which bounded their view at about 9 miles distance; which, from its direction, was conjectured to be the flagstaff on Maker tower.—Directing the glass, on the morning of the next day, to the same part of the horizon, a flag was perceived on the pole; which corroborated the conjecture of the preceding day. This day's view also discovered the pinnacles and part of the shaft of the tower.—Viewing the same spot at 8 in the morning on the 9th of January 1794, the whole tower and part of the roof of the church, with other remote objects not before noticed, became visible.
“It is necessary to give you the state of the weather there, on those days.
| 1793. | Barometer. | Thermom. | Wind | |
| Dec. 4 | 29.93, rising | 36.0 | N.E. | Frosty morning, |
| a mist over the | ||||
| land below. | ||||
| 5 | 29.97, rising | 35.2 | W. | Ditto. |
| 1794. | ||||
| Jan. 9 | 30.01, falling | 29.8 | W. | Hardwhitefrost, |
| a fog over the | ||||
| lowlands; clear | ||||
| in the surround- | ||||
| ing country. |
“The singularity of this phenomenon has occasioned repeated observations on it; from all which it appears that the summer season, and wet windy weather, are unfavourable to this refracted elevation; but that calm frosty weather, with the absence of the sun, are favourable to it.
“From hence a question arises; what is the principal or most general cause of atmospheric Refraction, which produces such extraordinary appearances?”
The following is also a copy of a letter to Mr. Crocker on this curious phenomenon, from his friend above mentioned, viz, Mr. John Andrews, of Traine, near Modbury, dated the 1st of February 1795.
“My good Friend,
“Finding, by your favour of last Sunday, the pro- ceedings which are going on in respect to my observations on the phenomenon of Looming, I have thought it necessary to bestow about half this day in preparing, what I am obliged to call, in my way, drawings, illustrative of those observations.—I have endeavoured to distinguish, by different tints and shades, the grounds which lie nearer or more remote; but this will perhaps be better explained by the letters of reference, which I have inserted as they may be serviceable in future correspondence.—I believe the drawings, rough as they are, give a tolerably exact representation of the scenes: they may be properly copied to send to London by one of your ingenious sons.—I have been attentive in my observations, or rather in looking out for observations, during the late hard frosts, which you will be surprised to learn, have (except on one or two days) been very unpropitious to the phenomenon; but they have compensated for that disappointment, by a discovery, that a dry frost, though ever so intense, has no tendency to produce it. A hoar frost, or that kind of dewy vapour which, in a sufficient degree of cold, occasions a hoar frost, appears essentially necessary. This took place pretty favourably on the 6th of January, when the elevation was equal to that represented in the third drawing (see plate 25, fig. 3), much like what it was on the 9th of January 1794, and confirmed me as to the certainty of some peculiar appearances, hinted at in my letter of the 14th of that month, but not there described. What I allude to, was a fluctuating appearance of two horizons, one above the other, with a complete vacancy between them, exactly like what may be often observed looking through an uneven pane of glass. Divers instances of this were seen by my brother and myself on the 6th of last January; continually varying and intermitting, but not rapidly, so that they were capable of distinct observation.—Till that day I had formed, as I thought, a plausible theory, to account for, as well this latter, as all the other phenomena; but now, unless my imagination deceives me, I am left in impenetrable darkness. The vacant line of separation, you will take notice, would often increase so much in breadth, as to efface entirely the upper of the two horizons; forming then a kind of dent or gap in the remaining horizon, which horizon at the places contiguous to the extremities of the vacancy, seemed of the same height as the upper horizon was, before effaced. This vacancy was several times seen to approach and take in the tower, and immediately to admit a view of the whole or most part of its body (like that in the third drawing) which was not the case before: exactly, to all appearance, as if it had opened a gap for that purpose in the intercepted ground.—It remains therefore to be determined by future observations, whether the separation is effected by an elevation of the upper, or depression of the lower horizon; and if the latter, why the vacancy does not cause the tower to disappear, as well as the intervening ground?—As an opportunity for this purpose may not soon occur, I hope you will not wait for it, in your communications to him who is, Dear Sir, yours very truly, John Andrews.”
See the representations in plate 25, of the appearances, in three different states of the atmosphere, with the explanations of them. |
REFRANGIBILITY of Light, the disposition of the rays to be refracted. And a greater or less Refrangibility, is a disposition to be more or less refracted, in passing at equal angles of incidence into the same medium.
That the rays of light are differently refrangible, is the foundation of Newton's whole theory of light and colours; and the truth and circumstances of the principle he evinced from such experiments as the following.
Let EG represent the window-shutter of a dark room, and F a hole in it, through which the light passes, from the luminous object S, to the glass prism ABC within the room, which refracts it towards the opposite side, or a screen, at PT, where it appears of an oblong form; its length being about five times the breadth, and exhibiting the various colours of the rainbow; whereas without the interposition of the prism, the ray of light would have proceeded on in its first direction to D. Hence then it follows,
1. That the rays of light are refrangible. This appears by the ray being refracted from its original direction SHD, into another one, HP or HT, by passing through a different medium.
2. That the ray SFH is a compound one, which, by means of the prism, is decompounded or separated into its parts, HP, HT, &c, which it hence appears are all endued with different degrees of Refrangibility, as they are transmitted to all the intermediate points from T to P, and there painting all the different colours.
From this, and a great variety of other experiments, Newton proved, that the blue rays are more refracted than the red ones, and that there is likewise unequal refraction in the intermediate rays; and upon the whole it appears that the sun's rays have not all the same Refrangibility, and consequently are not of the same nature. It is also observed that those rays which are most refrangible, are also most reflexible. See REFLEXIBILITY; also Newton's Optics, pa. 22 &c, 3d edit.
The difference between Refrangibility and reflexibility was first discovered by Sir Isaac Newton, in 1671-2, and communicated to the Royal Society, in a letter dated Feb. 6 of that year, which was published in the Philos. Trans. numb. 80, pa. 3075; and from that time it was vindicated by him, from the objections of several authors; particularly Pardies, Mariotte, Linus or Lin, and other gentlemen of the English college at Liege; and at length it was more fully laid down, illustrated, and confirmed, by a great variety of experiments, in his excellent treatise on Optics.
But farther, as not only these colours of light produced by refraction in a prism, but also those reflected from opaque bodies, have their different degrees of Refrangibility and reflexibility; and as a white light arises from a mixture of the several coloured rays together, the same great author concluded that all homogeneous light has its proper colour, corresponding to its degree of Refrangibility, and not capable of being changed by any reflexions, or any refractions; that the sun's light is composed of all the primary colours; and that all compound colours arise from the mixture of the primary ones, &c.
The different degrees of Refrangibility, he conjectures to arise from the different magnitude of the particles composing the different rays. Thus, the most refrangible rays, that is the red ones, he supposes may consist of the largest particles; the least refrangible, i. e. the violet rays, of the smallest particles; and the intermediate rays, yellow, green, and blue, of particles of intermediate sizes. See Colour.
For the method of correcting the effect of the different Refrangibility of the rays of light in glasse, see ABERRATION and Telescope.
