Chapter XVII: Introduction (13)

7. OUR great author teaches in the next place how from the refraction of the most refrangible and least refrangible rays to find the refraction of all the intermediate ones[315]. The method is this: if the sine of incidence be to the sine of refraction in the least refrangible rays as A to B C, (in fig. 133) and to the sine of refraction in the most refrangible as A to B D; if C E be taken equal to C D, and then E D be so divided in F, G, H, I, K, L, that E D, E F, E G, E H, E I, E K, E L, E C, shall be proportional to the eight lengths of musical chords, which found the notes in an octave, E D being the length of the key, E F the length of the tone above that key, E G the length of the lesser third, E H of the fourth, E I of the fifth, E K of the greater sixth, E L of the seventh, and E C of the octave above that key; that is if the lines E D, E F, E G, E H, E I, E K, E L, and E C bear the same proportion as the numbers, 1, 9/8, 5/6, ¾, ⅓, ¾, 9/61, ½, respectively then shall B D, B F, be the two limits of the sines of refraction of the violet-making rays, that is the violet-making rays shall not all of them have precisely the same sine of refraction, but none of them shall have a greater sine than B D, nor a less than B F, though there are violet-making rays which answer to any sine of refraction that can be taken between these two. In the same manner B F and B G are the limits of the sines of refraction of the indigo-making rays; B G, B H are the limits belonging to the blue-making rays; B H, B I the limits pertaining to the green-making rays, B I, B K the limits for the yellow-making rays; B K, B L the limits for the orange-making rays; and lastly, B L and B C the extreme limits of the sines of refraction belonging to the red-making rays. These are the proportions by which the heterogeneous rays of light are separated from each other in refraction.

8. WHEN light passes out of glass into air, our author found A to B C as 50 to 77, and the same A to B D as 50 to 78. And when it goes out of any other refracting substance into air, the excess of the sine of refraction of any one species of rays above its sine of incidence bears a constant proportion, which holds the same in each species, to the excess of the sine of refraction of the same sort of rays above the sine of incidence into the air out of glass; provided the sines of incidence both in glass and the other substance are equal. This our author verified by transmitting the light through prisms of glass included within a prismatic vessel of water; and draws from those experiments the following observations: that whenever the light in passing through so many surfaces parting diverse transparent substances is by contrary refractions made to emerge into the air in a direction parallel to that of its incidence, it will appear afterwards white at any distance from the prisms, where you shall please to examine it; but if the direction of its emergence be oblique to its incidence, in receding from the place of emergence its edges shall appear tinged with colours: which proves that in the first case there is no inequality in the refractions of each species of rays, but that when any one species is so refracted as to emerge parallel to the incident rays, every sort of rays after refraction shall likewise be parallel to the same incident rays, and to each other; whereas on the contrary, if the rays of any one sort are oblique to the incident light, the several species shall be oblique to each other, and be gradually separated by that obliquity. From hence he deduces both the forementioned theorem, and also this other; that in each sort of rays the proportion of the sine of incidence to the sine of refraction, in the passage of the ray out of any refracting substance into another, is compounded of the proportion to which the sine of incidence would have to the sine of refraction in the passage of that ray out of the first substance into any third, and of the proportion which the sine of incidence would have to the sine of refraction in the passage of the ray out of that third substance into the second. From so simple and plain an experiment has our most judicious author deduced these important theorems, by which we may learn how very exact and circumspect he has been in this whole work of his optics; that notwithstanding his great particularity in explaining his doctrine, and the numerous collection of experiments he has made to clear up every doubt which could arise, yet at the same time he has used the greatest caution to make out every thing by the simplest and easiest means possible.

9. OUR author adds but one remark more upon refraction, which is, that if refraction be performed in the manner he has supposed from the light’s being pressed by the refracting power perpendicularly toward the surface of the refracting body, and consequently be made to move swifter in the body than before its incidence; whether this power act equally at all distances or otherwise, provided only its power in the same body at the same distances remain without variation the same in one inclination of the incident rays as well as another; he observes that the refracting powers in different bodies will be in the duplicate proportion of the tangents of the lead angles, which the refracted light can make with the surfaces of the refracting bodies[316]. This observation may be explained thus. When the light passes into any refracting substance, it has been shewn above that the sine of incidence bears a constant proportion to the sine of refraction. Suppose the light to pass to the refracting body A B C D (in fig. 134) in the line E F, and to fall upon it at the point F, and then to proceed within the body in the line F G. Let H I be drawn through F perpendicular to the surface A B, and any circle K L M N be described to the center F. Then from the points O and P where this circle cuts the incident and refracted ray, the perpendiculars O Q, P R being drawn, the proportion of O Q to P R will remain the same in all the different obliquities, in which the same ray of light can fall on the surface A B. Now O Q is less than F L the semidiameter of the circle K L M N, but the more the ray E F is inclined down toward the surface A B, the greater will O Q be, and will approach nearer to the magnitude of F L. But the proportion of O Q to P R remaining always the same, when O Q, is largest, P R will also be greatest; so that the more the incident ray E F is inclined toward the surface A B, the more the ray F G after refraction will be inclined toward the same. Now if the line F S T be so drawn, that S V being perpendicular to F I shall be to F L the semidiameter of the circle in the constant proportion of P R to O Q; then the angle under N F T is that which I meant by the least of all that can be made by the refracted ray with this surface, for the ray after refraction would proceed in this line, if it were to come to the point F lying on the very surface A B; for if the incident ray came to the point F in any line between A F and F H, the ray after refraction would proceed forward in some line between F T and F I. Here if N W be drawn perpendicular to F N, this line N W in the circle K L M N is called the tangent of the angle under N F S. Thus much being premised, the sense of the forementioned proposition is this. Let there be two refracting substances (in fig. 135) A B C D, and E F G H. Take a point, as I, in the surface A B, and to the center I with any semidiameter describe the circle K L M. In like manner on the surface E F take some point N, as a center, and describe with the same semidiameter the circle O P Q. Let the angle under B I R be the least which the refracted light can make with the surface A B, and the angle under F N S the least which the refracted light can make with the surface E F. Then if L T be drawn perpendicular to A B, and P V perpendicular to E F; the whole power, wherewith the substance A B C D acts on the light, will bear to the whole power wherewith the substance E F G H acts on, the light, a proportion, which is duplicate of the proportion, which L T bears to P V.

10. UPON comparing according to this rule the refractive powers of a great many bodies it is found, that unctuous bodies which abound most with sulphureous parts refract the light two or three times more in proportion to their density than others: but that those bodies, which seem to receive in their composition like proportions of sulphureous parts, have their refractive powers proportional to their densities; as appears beyond contradiction by comparing the refractive power of so rare a substance as the air with that of common glass or rock crystal, though these substances are 2000 times denser than air; nay the same proportion is found to hold without sensible difference in comparing air with pseudo-topar and glass of antimony, though the pseudo-topar be 3500 times denser than air, and glass of antimony no less than 4400 times denser. This power in other substances, as salts, common water, spirit of wine, &c. seems to bear a greater proportion to their densities than these last named, according as they abound with sulphurs more than these; which makes our author conclude it probable, that bodies act upon the light chiefly, if not altogether, by means of the sulphurs in them; which kind of substances it is likely enters in some degree the composition of all bodies. Of all the substances examined by our author, none has so great a refractive power, in respect of its density, as a diamond.

11. OUR author finishes these remarks, and all he offers relating to refraction, with observing, that the action between light and bodies is mutual, since sulphureous bodies, which are most readily set on fire by the sun’s light, when collected upon them with a burning glass, act more upon light in refracting it, than other bodies of the same density do. And farther, that the densest bodies, which have been now shewn to act most upon light, contract the greatest heat by being exposed to the summer sun.

12. HAVING thus dispatched what relates to refraction, we must address ourselves to discourse of the other operation of bodies upon light in reflecting it. When light passes through a surface, which divides two transparent bodies differing in density, part of it only is transmitted, another part being reflected. And if the light pass out of the denser body into the rarer, by being much inclined to the foresaid surface at length no part of it shall pass through, but be totally reflected. Now that part of the light, which suffers the greatest refraction, shall be wholly reflected with a less obliquity of the rays, than the parts of the light which undergo a less degree of refraction; as is evident from the last experiment recited in the first chapter; where, as the prisms D E F, G H I, (in fig. 129.) were turned about, the violet light was first totally reflected, and then the blue, next to that the green, and so of the rest. In consequence of which our author lays down this proportion; that the sun’s light differs in reflexibility, those rays being most reflexible, which are most refrangible. And collects from this, in conjunction with other arguments, that the refraction and reflection, of light are produced by the same cause, compassing those different effects only by the difference of circumstances with which it is attended. Another proof of this being taken by our author from what he has discovered of the passage of light through thin transparent plates, viz. that any particular species of light, suppose, for instance, the red-making rays, will enter and pass out of such a plate, if that plate be of some certain thicknesses; but if it be of other thicknesses, it will not break through it, but be reflected back: in which is seen, that the thickness of the plate determines whether the power, by which that plate acts upon the light, shall reflect it, or suffer it to pass through.

13. BUT this last mentioned surprising property of the action between light and bodies affords the reason of all that has been said in the preceding chapter concerning the colours of natural bodies; and must therefore more particularly be illustrated and explained, as being what will principally unfold the nature of the action of bodies upon light.

14. TO begin: The object glass of a long telescope being laid upon a plane glass, as proposed in the foregoing chapter, in open day-light there will be exhibited rings of various colours, as was there related; but if in a darkened room the coloured spectrum be formed by the prism, as in the first experiment of the first chapter, and the glasses be illuminated by a reflection from the spectrum, the rings shall not in this case exhibit the diversity of colours before described, but appear all of the colour of the light which falls upon the glasses, having dark rings between. Which shews that the thin plate of air between the glasses at some thicknesses reflects the incident light, at other places does not reflect it, but is found in those places to give the light passage; for by holding the glasses in the light as it passes from the prism to the spectrum, suppose at such a distance from the prism that the several sorts of light must be sufficiently separated from each other, when any particular sort of light falls on the glasses, you will find by holding a piece of white paper at a small distance beyond the glasses, that at those intervals, where the dark lines appeared upon the glasses, the light is so transmitted, as to paint upon the paper rings of light having that colour which falls upon the glasses. This experiment therefore opens to us this very strange property of reflection, that in these thin plates it should bear such a relation to the thickness of the plate, as is here shewn. Farther, by carefully measuring the diameters of each ring it is found, that whereas the glasses touch where the dark spot appears in the center of the rings made by reflexion, where the air is of twice the thickness at which the light of the first ring is reflected, there the light by being again transmitted makes the first dark ring; where the plate has three times that thickness which exhibits the first lucid ring, it again reflects the light forming the second lucid ring; when the thickness is four times the first, the light is again transmitted so as to make the second dark ring; where the air is five times the first thickness, the third lucid ring is made; where it has six times the thickness, the third dark ring appears, and so on: in so much that the thicknesses, at which the light is reflected, are in proportion to the numbers 1, 3, 5, 7, 9, &c. and the thicknesses, where the light is transmitted, are in the proportion of the numbers 0, 2, 4, 6, 8, &c. And these proportions between the thicknesses which reflect and transmit the light remain the same in all situations of the eye, as well when the rings are viewed obliquely, as when looked on perpendicularly. We must farther here observe, that the light, when it is reflected, as well as when it is transmitted, enters the thin plate, and is reflected from its farther surface; because, as was before remarked, the altering the transparent body behind the farther surface alters the degree of reflection as when a thin piece of Muscovy glass has its farther surface wet with water, and the colour of the glass made dimmer by being so wet; which shews that the light reaches to the water, otherwise its reflection could not be influenced by it. But yet this reflection depends upon some power propagated from the first surface to the second; for though made at the second surface it depends also upon the first, because it depends upon the distance between the surfaces; and besides, the body through which the light passes to the first surface influences the reflection: for in a plate of Muscovy glass, wetting the surface, which first receives the light, diminishes the reflection, though not quite so much as wetting the farther surface will do. Since therefore the light in passing through these thin plates at some thicknesses is reflected, but at others transmitted without reflection, it is evident, that this reflection is caused by some power propagated from the first surface, which intermits and returns successively. Thus is every ray apart disposed to alternate reflections and transmissions at equal intervals; the successive returns of which disposition our author calls the fits of easy reflection, and of easy transmission. But these fits, which observe the same law of returning at equal intervals, whether the plates are viewed perpendicularly or obliquely, in different situations of the eye change their magnitude. For what was observed before in respect of those rings, which appear in open day-light, holds likewise in these rings exhibited by simple lights; namely, that these two alter in bigness according to the different angle under which they are seen: and our author lays down a rule whereby to determine the thicknesses of the plate of air, which shall exhibit the same colour under different oblique views[317]. And the thickness of the aereal plate, which in different inclinations of the rays will exhibit to the eye in open day-light the same colour, is also varied by the same rule[318]. He contrived farther a method of comparing in the bubble of water the proportion between the thickness of its coat, which exhibited any colour when seen perpendicularly, to the thickness of it, where the same colour appeared by an oblique view; and he found the same rule to obtain here likewise[319]. But farther, if the glasses be enlightened successively by all the several species of light, the rings will appear of different magnitudes; in the red light they will be larger than in the orange colour, in that larger than in the yellow, in the yellow larger than in the green, less in the blue, less yet in the indigo, and least of all in the violet: which shew that the same thickness of the aereal plate is not fitted to reflect all colours, but that one colour is reflected where another would have been transmitted; and as the rays which are most strongly refracted form the least rings, a rule is laid down by our author for determining the relation, which the degree of refraction of each species of colour has to the thicknesses of the plate where it is reflected.

15. FROM these observations our author shews the reason of that great variety of colours, which appears in these thin plates in the open white light of the day. For when this white light falls on the plate, each part of the light forms rings of its own colour; and the rings of the different colours not being of the same bigness are variously intermixed, and form a great variety of tints[320].

16. IN certain experiments, which our author made with thick glasses, he found, that these fits of easy reflection and transmission returned for some thousands of times, and thereby farther confirmed his reasoning concerning them[321].

17. UPON the whole, our great author concludes from some of the experiments made by him, that the reason why all transparent bodies refract part of the light incident upon them, and reflect another part, is, because some of the light, when it comes to the surface of the body, is in a fit of easy transmission, and some part of it in a fit of easy reflection; and from the durableness of these fits he thinks it probable, that the light is put into these fits from their first emission out of the luminous body; and that these fits continue to return at equal intervals without end, unless those intervals be changed by the light’s entring into some refracting substance[322]. He likewise has taught how to determine the change which is made of the intervals of the fits of easy transmission and reflection, when the light passes out of one transparent space or substance into another. His rule is, that when the light passes perpendicularly to the surface, which parts any two transparent substances, these intervals in the substance, out of which the light passes, bear to the intervals in the substance, whereinto the light enters, the same proportion, as the sine of incidence bears to the sine of refraction[323]. It is farther to be observed, that though the fits of easy reflection return at constant intervals, yet the reflecting power never operates, but at or near a surface where the light would suffer refraction; and if the thickness of any transparent body shall be less than the intervals of the fits, those intervals shall scarce be disturbed by such a body, but the light shall pass through without any reflection[324].

18. WHAT the power in nature is, whereby this action between light and bodies is caused, our author has not discovered. But the effects, which he has discovered, of this power are very surprising, and altogether wide from any conjectures that had ever been framed concerning it; and from these discoveries of his no doubt this power is to be deduced, if we ever can come to the knowledge of it. Sir ISAAC NEWTON has in general hinted at his opinion concerning it; that probably it is owing to some very subtle and elastic substance diffused through the universe, in which such vibrations may be excited by the rays of light, as they pass through it, that shall occasion it to operate so differently upon the light in different places as to give rise to these alternate fits of reflection and transmission, of which we have now been speaking[325]. He is of opinion, that such a substance may produce this and other effects also in nature, though it be so rare as not to give any sensible resistance to bodies in motion[326]; and therefore not inconsistent with what has been said above, that the planets move in spaces free from resistance[327].

19. IN order for the more full discovery of this action between light and bodies, our author began another set of experiments, wherein he found the light to be acted on as it passes near the edges of solid bodies; in particular all small bodies, such as the hairs of a man’s head or the like, held in a very small beam of the sun’s light, cast extremely broad shadows. And in one of these experiments the shadow was 35 times the breadth of the body[328]. These shadows are also observed to be bordered with colours[329]. This our author calls the inflection of light; but as he informs us, that he was interrupted from prosecuting these experiments to any length, I need not detain my readers with a more particular account of them.

~CHAP. IV.~

Of OPTIC GLASSES.

SIR ~ISAAC NEWTON~ having deduced from his doctrine of light and colours a surprising improvement of telescopes, of which I intend here to give an account, I shall first premise something in general concerning those instruments.

2. IT will be understood from what has been said above, that when light falls upon the surface of glass obliquely, after its entrance into the glass it is more inclined to the line drawn through the point of incidence perpendicular to that surface, than before. Suppose a ray of light issuing from the point A (in fig. 136) falls on a piece of glass B C D E, whose surface B C, whereon the ray falls, is of a spherical or globular figure, the center whereof is F. Let the ray proceed in the line A G falling on the surface B C in the point G, and draw F G H. Here the ray after its entrance into the glass will pass on in some line, as G I, more inclined toward the line F G H that the line A G is inclined thereto; for the line F G H is perpendicular to the surface B C in the point G. By this means, if a number of rays proceeding from any one point fall on a convex spherical surface of glass, they shall be inflected (as is represented in fig. 137,) so as to be gathered pretty close together about the line drawn through the center of the glass from the point, whence the rays proceed; which line henceforward we shall call the axis of the glass: or the point from whence the rays proceed may be so near the glass, that the rays shall after entring the glass still go on to spread themselves, but not so much as before; so that if the rays were to be continued backward (as in fig. 138,) they should gather together about the axis at a place more remote from the glass, than the point is, whence they actually proceed. In these and the following figures A denotes the point to which the rays are related before refraction, B the point to which they are directed afterwards, and C the center of the refracting surface. Here we may observe, that it is possible to form the glass of such a figure, that all the rays which proceed from one point shall after refraction be reduced again exactly into one point on the axis of the glass. But in glasses of a spherical form though this does not happen; yet the rays, which fall within a moderate distance from the axis, will unite extremely near together. If the light fall on a concave spherical surface, after refraction it shall spread quicker than before (as in fig. 139,) unless the rays proceed from a point between the center and the surface of the glass. If we suppose the rays of light, which fall upon the glass, not to proceed from any point, but to move so as to tend all to some point in the axis of the glass beyond the surface; if the glass have a convex surface, the rays shall unite about the axis sooner, than otherwise they would do (as in fig. 140,) unless the point to which they tended was between the surface and the center of that surface. But if the surface be concave, they shall not meet so soon: nay perhaps converge. (See fig. 141 and 142.)

5. FARTHER, because the light in passing out of glass into the air is turned by the refraction farther off from the line drawn through the point of incidence perpendicular to the refracting surface, than it was before; the light which spreads from a point shall by parting through a convex surface of glass into the air be made either to spread less than before (as in fig. 143,) or to gather about the axis beyond the glass (as in fig. 144.) But if the rays of light were proceeding to a point in the axis of the glass, they should by the refraction be made to unite sooner about that axis (as in fig. 145.) If the surface of the glass be concave, rays which proceed from a point shall be made to spread faster (as in fig 146,) but rays which are tending to a point in the axis of the glass, shall be made to gather about the axis farther from the glass (as in fig. 147) or even to diverge (as in fig. 148,) unless the point, to which the rays are directed, lies between the surface of the glass and its center.

4. THE rays, which spread themselves from a point, are called diverging; and such as move toward a point, are called converging rays. And the point in the axis of the glass, about which the rays gather after refraction, is called the focus of those rays.

5. IF a glass be formed of two convex spherical surfaces (as in fig. 149,) where the glass AB is formed of the surfaces A C B and A D B, the line drawn through the centers of the two surfaces, as the line E F, is called the axis of the glass; and rays, which diverge from any point of this axis, by the refraction of the glass will be caused to converge toward some part of the axis, or at least to diverge as from a point more remote from the glass, than that from whence they proceeded; for the two surfaces both conspire to produce this effect upon the rays. But converging rays will be caused by such a glass as this to converge sooner. If a glass be formed of two concave surfaces, as the glass A B (in fig. 150,) the line C D drawn through the centers, to which the two surfaces are formed, is called the axis of the glass. Such a glass shall cause diverging rays, which proceed from any point in the axis of the glass, to diverge much more, as if they came from some place in the axis of the glass nearer to it than the point, whence the rays actually proceed. But converging rays will be made either to converge less, or even to diverge.

6. IN these glasses rays, which proceed from any point near the axis, will be affected as it were in the same manner, as if they proceeded from the very axis it self, and such as converge toward a point at a small distance from the axis will suffer much the same effects from the glass, as if they converged to some point in the very axis. By this means any luminous body exposed to a convex glass may have an image formed upon any white body held beyond the glass. This may be easily tried with a common spectacle-glass. For if such a glass be held between a candle and a piece of white paper, if the distances of the candle, glass, and paper be properly adjusted, the image of the candle will appear very distinctly upon the paper, but be seen inverted; the reason whereof is this. Let A B (in fig. 151) be the glass, C D an object placed cross the axis of the glass. Let the rays of light, which issue from the point E, where the axis of the glass crosses the object, be so refracted by the glass, as to meet again about the point F. The rays, which diverge from the point C of the object, shall meet again almost at the same distance from the glass, but on the other side of the axis, as at G; for the rays at the glass cross the axis. In like manner the rays, which proceed from the point D, will meet about H on the other side of the axis. None of these rays, neither those which proceed from the point E in the axis, nor those which issue from C or D, will meet again exactly in one point; but yet in one place, as is here supposed at F, G, and H, they will be crouded so close together, as to make a distinct image of the object upon any body proper to reflect it, which shall be held there.

7. IF the object be too near the glass for the rays to converge after the refraction, the rays shall issue out of the glass, as if they diverged from a point more distant from the glass, than that from whence they really proceed (as in fig. 152,) where the rays coming from the point E of the object, which lies on the axis of the glass A B, issue out of the glass, as if they came from the point F more remote from the glass than E; and the rays proceeding from the point C issue out of the glass, as if they proceeded from the point G; likewise the rays which issue from the point D emerge out of the glass, as if they came from the point H. Here the point G is on the same side of the axis, as the point C; and the point H on the same side, as the point D. In this case to an eye placed beyond the glass the object should appear, as if it were in the situation G F H.

8. IF the glass A B had been concave (as in, fig. 153,) to an eye beyond the glass the object C D would appear in the situation G H, nearer to the glass than really it is. Here also the object will not be inverted; but the point G is on the same side the axe with the point C, and H on the same side as D.

9. HENCE may be understood, why spectacles made with convex glasses help the sight in old age: for the eye in that age becomes unfit to see objects distinctly, except such as are remov’d to a very great distance; whence all men, when they first stand in need of spectacles, are observed to read at arm’s length, and to hold the object at a greater distance, than they used to do before. But when an object is removed at too great a distance from the sight, it cannot be seen clearly, by reason that a less quantity of light from the object will enter the eye, and the whole object will also appear smaller. Now by help of a convex glass an object may be held near, and yet the rays of light issuing from it will enter the eye, as if the object were farther removed.

10. AFTER the same manner concave glasses assist such, as are short sighted. For these require the object to be brought inconveniently near to the eye, in order to their seeing it distinctly; but by such a glass the object may be removed to a proper distance, and yet the rays of light enter the eye, as if they came from a place much nearer.

11. WHENCE these defects of the sight arise, that in old age objects cannot be seen distinct within a moderate distance, and in short-sightedness not without being brought too near, will be easily understood, when the manner of vision in general shall be explain’d; which I shall now endeavour to do, in order to be better understood in what follows. The eye is form’d, as is represented in fig. 154. It is of a globular figure, the fore part whereof scarce more protuberant than the rest is transparent. Underneath this transparent part is a small collection of an humour in appearance like water, and it has also the same refractive power as common water; this is called the aqueous humour, and fills the space A B C D in the figure. Next beyond lies the body D E F G; this is solid but transparent, it is composed with two convex surfaces, the hinder surface E F G being more convex, than the anterior E D G. Between the outer membrane A B C, and this body E D G F is placed that membrane, which exhibits the colours, that are seen round the sight of the eye; and the black spot, which is called the sight or pupil, is a hole in this membrane, through which the light enters, whereby we see. This membrane is fixed only by its outward circuit, and has a muscular power, whereby it dilates the pupil in a weak light, and contracts it in a strong one. The body D E F G is called the crystalline humour, and has a greater refracting power than water. Behind this the bulk of the eye is filled up with what is called the vitreous humor, this has much the same refractive power with water. At the bottom of the eye toward the inner side next the nose the optic glass enters, as at H, and spreads it self all over the inside of the eye, till within a small diftance from A and C. Now any object, as I K, being placed before the eye, the rays of light issuing from each point of this object are so refracted by the convex surface of the aqueous humour, as to be caused to converge; after this being received by the convex surface E D G of the crystalline humour, which has a greater refractive power than the aqueous, the rays, when they are entered into this surface, still more converge, and at going out of the surface E F G into a humour of a less refractive power than the crystalline they are made to converge yet farther. By all these successive refractions they are brought to converge at the bottom of the eye, so that a distinct image of the object as L M is impress’d on the nerve. And by this means the object is seen.

11. IT has been made a difficulty, that the image of the object impressed on the nerve is inverted, so that the upper part of the image is impressed on the lower part of the eye. But this difficulty, I think, can no longer remain, if we only consider, that upper and lower are terms merely relative to the ordinary position of our bodies: and our bodies, when view’d by the eye, have their image as much inverted as other objects; so that the image of our own bodies, and of other objects, are impressed on the eye in the same relation to one another, as they really have.

12. THE eye can see objects equally distinct at very different distances, but in one distance only at the same time. That the eye may accomodate itself to different distances, some change in its humours is requir’d. It is my opinion, that this change is made in the figure of the crystalline humour, as I have indeavoured to prove in another place.

13. IF any of the humours of the eye are too flat, they will refract the light too little; which is the case in old age. If they are too convex, they refract too much; as in those who are short-sighted.

14. THE manner of direct vision being thus explained, I proceed to give some account of telescopes, by which we view more distinctly remote objects; and also of microscopes, whereby we magnify the appearance of small objects. In the first place, the most simple sort of telescope is composed of two glasses, either both convex, or one convex, and the other concave. (The first sort of these is represented in fig. 155, the latter in fig. 156.)

15. IN fig. 155 let A B represent the convex glass next the object, C D the other glass more convex near the eye. Suppose the object-glass A B to form the image of the object at E F; so that if a sheet of white paper were to be held in this place, the object would appear. Now suppose the rays, which pass the glass A B, and are united about F, to proceed to the eye glass C D, and be there refracted. Three only of these rays are drawn in the figure, those which pass by the extremities of the glass A B, and that which passes its middle. If the glass C D be placed at such a distance from the image E F, that the rays, which pass by the point F, after having proceeded through the glass diverge so much, as the rays do that come from an object, which is at such a distance from the eye as to be seen distinctly, these being received by the eye will make on the bottom of the eye a distinct representation of the point F. In like manner the rays, which pass through the object glass A B to the point E after proceeding through the eye-glass C D will on the bottom of the eye make a distinct representation of the point E. But if the eye be placed where these rays, which proceed from E, cross those, which proceed from F, the eye will receive the distinct impression of both these points at the same time; and consequently will also receive a distinct impression from all the intermediate parts of the image E F, that is, the eye will see the object, to which the telescope is directed, distinctly. The place of the eye is about the point G, where the rays H E, H F cross, which pass through the middle of the object-glass A B to the points E and F; or at the place where the focus would be formed by rays coming from the point H, and refracted by the glass C D. To judge how much this instrument magnifies any object, we must first observe, that the angle under E H F, in which the eye at the point H would see the image E F, is nearly the same as the angle, under which the object appears by direct vision; but when the eye is in G, and views the object through the telescope, it sees the same under a greater angle; for the rays, which coming from E and F cross in G, make a greater angle than the rays, which proceed from the point H to these points E and F. The angle at G is greater than that at H in the proportion, as the distance between the glasses A B and C D is greater than the distance of the point G from the glass C D.

16. THIS telescope inverts the object; for the rays, which came from the right-hand side of the object, go to the point E the left side of the image; and the rays, which come from the left side of the object, go to F the right side of the image. These rays cross again in G, so that the rays, which come from the right side of the object, go to the right side of the eye; and the rays from the left side of the object go to the left side of the eye. Therefore in this telescope the image in the eye has the same situation as the object; and seeing that in direct vision the image in the eye has an inverted situation, here, where the situation is not inverted, the object must appear so. This is no inconvenience to astronomers in celestial observations; but for objects here on the earth it is usual to add two other convex glasses, which may turn the object again (as is represented in fig. 157,) or else to use the other kind of telescope with a concave eye-glass.

17. IN this other kind of telescope the effect is founded on the same principles, as in the former. The distinctness of the appearance is procured in the same manner. But here the eye-glass C D (in fig. 156) is placed between the image E F, and the object glass A B. By this means the rays, which come from the right-hand side of the object, and proceed toward E the left side of the image, being intercepted by the eye-glass are carried to the left side of the eye; and the rays, which come from the left side of the object, go to the right side of the eye; so that the impression in the eye being inverted the object appears in the same situation, as when view’d by the naked eye. The eye must here be placed close to the glass. The degree of magnifying in this instrument is thus to be found. Let the rays, which pass through the glass A B at H, after the refraction of the eye-glass C D diverge, as if they came from the point G; then the rays, which come from the extremities of the object, enter the eye under the angle at G; so that here also the object will be magnified in the proportion of the distance between the glasses, to the distance of G from the eye-glass.

18. THE space, that can be taken in at one view in this telescope, depends on the breadth of the pupil of the eye; for as the rays, which go to the points E, F of the image, are something distant from each other, when they come out of the glass C D, if they are wider asunder than the pupil, it is evident, that they cannot both enter the eye at once. In the other telescope the eye is placed in the point G, where the rays that come from the points E or F cross each other, and therefore must enter the eye together. On this account the telescope with convex glasses takes in a larger view, than those with concave. But in these also the extent of the view is limited, because the eye-glass does not by the refraction towards its edges form so distinct a representation of the object, as near the middle.

18. MICROSCOPES are of two sorts. One kind is only a very convex glass, by the means of which the object may be brought very near the eye, and yet be seen distinctly. This microscope magnifies in proportion, as the object by being brought near the eye will form a broader impression on the optic nerve. The other kind made with convex glasses produces its effects in the same manner as the telescope. Let the object A B (in fig. 158) be placed under the glass C D, and by this glass let an image be formed of this object. Above this image let the glass G H be placed. By this glass let the rays, which proceed from the points A and B, be refracted, as is expressed in the figure. In particular, let the rays, which from each of these points pass through the middle of the glass C D, cross in I, and there let the eye be placed. Here the object will appear larger, when seen through the microscope, than if that instrument were removed, in proportion as the angle, in which these rays cross in I, is greater than the angle, which the lines would make, that should be drawn from I to A and B; that is, in the proportion made up of the proportion of the distance of the object A B from I, to the distance of I from the glass G H; and of the proportion of the distance between the glasses, to the distance of the object A B from the glass C D.

19. I SHALL now proceed to explain the imperfection in these instruments, occasioned by the different refrangibility of the light which comes from every object. This prevents the image of the object from being formed in the focus of the object glass with perfect distinctness; so that if the eye-glass magnify the image overmuch, the imperfections of it must be visible, and make the whole appear confused. Our author more fully to satisfy himself, that the different refrangibility of the several sorts of rays is sufficient to produce this irregularity, underwent the labour of a very nice and difficult experiment, whose process he has at large set down, to prove, that the rays of light are refracted as differently in the small refraction of telescope glasses as in the larger of the prism; so exceeding careful has he been in searching out the true cause of this effect. And he used, I suppose, the greater caution, because another reason had before been generally assigned for it. It was the opinion of all mathematicians, that this defect in telescopes arose from the figure, in which the glasses were formed; a spherical refracting surface not collecting into an exact point all the rays which come from any one point of an object, as has before been said[330]. But after our author has proved, that in these small refractions, as well as in greater, the sine of incidence into air out of glass, to the sine of refraction in the red-making rays, is as 50 to 77, and in the blue-making rays 50 to 78; he proceeds to compare the inequalities of refraction arising from this different refrangibility of the rays, with the inequalities, which would follow from the figure of the glass, were light uniformly refracted. For this purpose he observes, that if rays issuing from a point so remote from the object glass of a telescope, as to be esteemed parallel, which is the case of the rays, which come from the heavenly bodies; then the distance from the glass of the point, in which the least refrangible rays are united, will be to the distance, at which the most refrangible rays unite, as 28 to 27; and therefore that the least space, into which all the rays can be collected, will not be less than the 55th part of the breadth of the glass. For if A B (in fig. 159) be the glass, C D its axis, E A, F B two rays of the light parallel to that axis entring the glass near its edges; after refraction let the least refrangible part of these rays meet in G, the most refrangible in H; then, as has been said, G I will be to I H, as 28 to 27; that is, G H will be the 28th part of G I, and the 27th part of H I; whence if K L be drawn through G, and M N through H, perpendicular to C D, M N will be the a 28th part of A B, the breadth of the glass, and K L the 27th part of the same; so that O P the least space, into which the rays are gathered, will be about half the mean between these two, that is the 55th part of A B.

20. THIS is the error arising from the different refrangibility of the rays of light, which our author finds vastly to exceed the other, consequent upon the figure of the glass. In particular, if the telescope glass be flat on one side, and convex on the other; when the flat side is turned towards the object, by a theorem, which he has laid down, the error from the figure comes out above 5000 times less than the other. This other inequality is so great, that telescopes could not perform so well as they do, were it not that the light does not equally fill all the space O P, over which it is scattered, but is much more dense toward the middle of that space than at the extremities. And besides, all the kinds of rays affect not the sense equally strong, the yellow and orange being the strongest, the red and green next to them, the blue indigo and violet being much darker and fainter colours; and it is shewn that all the yellow and orange, and three fifths of the brighter half of the red next the orange, and as great a share of the brighter half of the green next the yellow, will be collected into a space whose breadth is not above the 250th part of the breadth of the glass.

And the remaining colours, which fall without this space, as they are much more dull and obscure than these, so will they be likewise much more diffused; and therefore call hardly affect the sense in comparison of the other. And agreeable to this is the observation of astronomers, that telescopes between twenty and sixty feet in length represent the fixed stars, as being about 5 or 6, at most about 8 or 10 seconds in diameter. Whereas other arguments shew us, that they do not really appear to us of any sensible magnitude any otherwise than as their light is dilated by refraction. One proof that the fixed stars do not appear to us under any sensible angle is, that when the moon passes over any of them, their light does not, like the planets on the same occasion, disappear by degrees, but vanishes at once.