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tion; for, if the glasses exceed a certain length, the colors may be spread too wide to be admitted through the pupil of the eye; which is the cause that in long telescopes, with three eye-glasses, the field is always greatly contracted.

380. These considerations first set Mr. Dollond on contriving how to enlarge the field by increasing the number of eye-glasses without any hindrance to the distinctness or brightness of the image; and though others had been about the same work before, yet, observing that some fiveglass telescopes then made would admit of farther improvement, he endeavoured to construct one with the same number of glasses in a better manner; which was allowed by the best judges to be a considerable improvement on the former. Thus encouraged he resolved to try if he could make some farther enlargement on the field by the addition of another glass, and by placing and proportioning the glasses in such a manner as to correct the aberrations, without detriment to the distinctness. At last he obtained as large a field as is necessary, even in the longest telescopes that can be made. These telescopes with six glasses having been well received, and some of them purchased abroad, the author fixed the date of his invention, in a letter, addressed to Mr. Short, which was read to the Royal Society, March 1st, 1753.

381. Various attempts were made about this time to shorten and otherwise improve telescopes. Among these we must mention that of Mr. Caleb Smith, who thought he had found it possible to rectify the errors which arise from the different degrees of refrangibility, on the principle that the sines of refraction, or rays differently refrangible, are to one another in a given proportion, when their sines of incidence are equal; and he proposed for this purpose to make the speculums of glass instead of metal, the two surfaces having different degrees of concavity. But his scheme was never executed; nor is it probable, for reasons which have been mentioned, that any advantage could be made of it.

382. To Mr. Short we are indebted for the excellent contrivance of an equatorial telescope, or portable observatory; whereby pretty accurate observations may be made with little trouble by those who have no building adapted to the purpose. This instrument consists of an ingenious piece of machinery, by the help of which a telescope mounted upon it may be directed to any degree of right ascension or declination, so that, the place of any of the heavenly bodies being known, they may be found without any trouble, even in the day-time. Being made to turn parallel to the equator, any object is easily kept in view, or recovered, without moving the eye from its situation. By this instrument, Mr. Short informs us, that most of the stars of the first and second magnitude have been seen even at midday, and the sun shining bright; as also Mercury, Venus, and Jupiter. Saturn and Mars are not so easy to be seen, on account of the faintness of their light, except when the sun is but a few hours above the horizon. This particular effect depends upon the telescope excluding almost all the light, except what comes from the object itself, and which might otherwise efface the impression made by its weaker light upon the eve.

For the same reason stars are visible in the daytime from the bottom of a deep pit. Mr. Ramsden has also invented a portable observatory or equatorial telescope. This, however, as well as the improved telescopes by Herschel and Ramsden, will be fully described under the article exclusively devoted to the subject.

383. The most important part of every compound optical instrument is the lens; it may therefore be advisable to illustrate their general form by a series of diagrams, and then furnish the mathematical data for their construction.

384. A lens is any transparent substance, as glass, crystal, water, or diamond, having one or both of its surfaces curved to collect or disperse the light transmitted by it. The lenses in general use are made of glass, and are usually called magnifying glasses. Glass, however, does not possess a greater share of the magnifying property than other transparent substances. In fig.

there are six differently shaped lenses, shown in section. A is called a plano-convex, from having one side flat, and the other spherically rounded. B is a double convex, and has both sides spherically rounded. When these sides are unequally curved, as at C, it is termed a crossed lens. D is a plano-concave, having one side spherically hollow. E is a double concave with both sides hollow. F is a meniscus (so called from its moon shape), and has one side convex and the other concave.

385. The passage of light when transmitted by a plano-convex lens, is shown in the accompanying diagram. The parallel rays a, b, c, &c., fall

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ing upon the plano-convex lens A D B, and passing through it, are but half as much refracted as they would be in passing through the double convex lines A D B E, and therefore their focus or point of meeting is not at C but at F, which is at twice the distance, or double the radius of the convexity of the lens. After intersecting at F they diverge.

386. When an object is placed in the focus of a lens, the rays diverging from it will, by the action of the lens, be rendered parallel. Thus, in the annexed diagram, the radiant point A,

B

C

D

from which the rays d, e, f, &c., diverge, is in the centre of convexity of the double convex lens a, b, c. After passing through the lens, the rays go on parallel to each other in the space C D. If the lens had been plano-convex, the radiant point for this purpose must have been at B, or at twice the distance of A from B.

387. Rays diverging from a radiant point beyond the focal distance of a convex lens, will, after passing through the lens, converge to a point or focus on the other side of the lens. Thus in the following diagram F is the focus of the lens

meet in a focus or point at C, which is the centre of the lens's convexity, beyond which they diverge to the contrary sides as a, b, c, d, &c. The middle ray d, falling perpendicularly on the surface of the lens at D, suffers no refraction in passing through it.

390. A convex glass magnifies the angle of vision; the reason is this. Without a lens, F G,

A

B

G

E

B, and A is the radiant point from which the rays a, b, c, &c., diverge. After passing through the lens they will converge and meet in a focal point, as at C. The farther A is from B the nearer will C be to it.

388. Rays diverging from a radiant point between a convex lens and its focus will continue to diverge, though in a less degree, after passing through the lens, as in the accompanying figure,

the eye would see the arrow BC under the angle bAc. But the rays BF and CG, from the extremities of the arrow, in passing through the lens are refracted to the eye in the directions fA, gA, which makes the arrow to be seen under the much larger angle D A E, the same as the angle fA g. Therefore the arrow will appear so much magnified as to extend in length from D to E.

391. Parallel rays become parallel again by passing through two convex lenses placed parallel to each other and at double their focal distance. Thus, in the accompanying diagram, C is the fo

F

B

D

e

B

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cus of both the lenses A and B. The parallel rays a, b, c, d, e, f, having passed through the lens A, go on converging to its focus C, where to the lens B, and after passing through it they they unite and thence diverge in a contrary order go on parallel to each other, but in an inverted order as a, b, c, d, e, f, g. The middle ray d goes on straight, because it falls perpendicularly on the surface of both the lenses.

392. Concave lenses obey the same laws of refraction as convex, but, as the curvature is reversed, the rays are bent outwards; hence a concave lens will render parallel rays diverging, as may be seen in the following diagram. The rays a, b, c, &c., after passing through a plano-concave lens A, will go on in a diverging state, the same as if the lens were taken away, and the rays had issued from a radiant point F in the virtual focus of the lens, which is at double the distance CA or radius of concavity of the lens.

393. Parallel rays passing through a double concave lens may also be made to diverge. Thus

a

b

C

the rays a, b, c, &c.,after passing through the double concave lens A, will go on in a diverging state, the same as if the lens were taken away and the rays had proceeded from a radiant point F in the virtual focus or centre of concavity of the lens.

394. The manner in which the foci of lenses of different curves are calculated, and how the foci of combined lenses may be obtained, are as follows:-When the lenses are made of plateglass, the focal distance is nearly the diameter of the sphere from which we may suppose a planoconvex lens to be cut, or it is equal to twice the

radius of the circle that forms the convex surface of the lens. For example, if the globe of glass is one inch in diameter, and a portion is cut off to form a plano-convex lens, the focus will be one inch, or twice the radius of the circle. If the lens is double convex, the focus will be equal to the radius, or half the diameter. When the lens is crossed, or unequally convex, the focal length will be twice the product of the two radii, divided by the sum of the radii. For example, let the radius on one side be two inches, and on the other side six inches; the focus of this will be 2 × 2 × 6 = 24, divided by 2 + 6 8 or

three inches. The focus of the miniscus lens is

found by dividing twice the product of the two radii by their difference. Example; let the radius on the convex side be two inches, and on the concave side four, the focus is 2 x 2 x 4 16 divided by 4 - 2 = 2, or eight inches, the focus of the lens.*

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395. If two lenses are placed in contact, the compound focus, when each lens has the same power, will be half the focus of the single lens. When two convex lenses are in contact, having different focal lengths, then, as the sum of the two foci is to one of them, so is the other to the compound focus required. For example, let the foci of the lenses be 2 and 6; then, as 2+6=8 : 2. 61, the compound focus. Lastly, if two lenses are not in contact, the compound focus is found by dividing the product of the two lenses by the sum lessened by their distance. Example: let the foci of the lenses be 2 and 4, their distance 2; then 2 x 4 8 divided by (2 + 4)—2 = 4 gives 2 as the compound focus.

396. If lenses be made of different substances, although the curves may be the same, the focal lengths will vary; while, in like mediums, the action will always be equal. Let ab, fig. 6, be a ray of light, and let it enter the medium c d at the point b; instead of continuing in a right line to e it will pass on in the direction bf, should the medium c d be denser than the first a b; now if on the point b a circle be drawn, and a line si parallel to the surface of the medium, touching the incident ray a b, be produced to e, this line will be the sine of incidence; and, if another line pr be drawn in the same manner to the refracted ray, it will be the sine of refraction. if the angle abc be varied to any degree, the sine si will always be in the same proportion to the sine of refraction pr. If the dense medium is water, the sine pr will be three-fourths of si. When glass is used the sines are as 2 to 3 nearly, and in diamond as 2 to 5.

Now

397. When a ray is passing out of a dense medium into a rarer, the direction will be changed, and the ray bf will now be bent further from the perpendicular, so as to make the sines the reverse of the former case. Out of water they will be as 4 to 3; from glass as 3 to 2, and from diamond as 5 to 2. The theorems just described for finding the foci of lenses are called geometrical, and will be nearly the same as the refracted, when the lens is made of plate-glass. The refracted focus is onlyst part less than the geometrical, when ascertained by accurate experiment. The refracted focus of lenses of other media may be obtained by dividing the geometrical focus by the quotient obtained when the sine of incidence (i), minus the sine of refraction (r), is divided by half the sine of refraction. (")

398. Convex lenses, in their simple state, have been applied to collect the heat of the sun's rays for purposes similar to that of burning mirrors. One of the largest lenses that have been mounted for these purposes was that made of flint glass by Mr. Parker. This lens was three feet in diameter, and, when mounted, exposed a surface of 330 square inches to the sun's light; its focal distance was three feet nine inches, and the diabe effected by forming a reflected image by the pos- But, in order that the light might be condensed meter of the circular spot of light was one inch. as much as possible, he employed another lens

In many cases it is found advisable to ascertain the radii of the two surfaces of a convex lens, as well as its focus, by a more accurate method. This may

terior surface, which distance will be half of the ra dius of curvature (or one quarter the focus of a plano-convex lens); then, by exposing the other side, we obtain the radii of the opposite surface. This sure the different radii of double and triple achromatic method was adopted by professor Robison to mea- object-glasses.

thirteen inches diameter, and of twenty-nine inches focus, so as to decrease the diameter of the focal point to three-eighths of an inch. The apparatus on which it was mounted is shown in fig. 7a is the large convex lens mounted in a ring, and connected to the smaller lens b by wooden ribs c, c; the lower rib has a piece e at tached to it, capable of adjustment to or from the smaller lens: to this bar is fixed the holder d, having a universal joint. On this holder the substance to be experimented on is placed. The following are some of its effects on bodies placed in its focus; twenty grains of pure gold were fused in four seconds; ten grains of platina fused in three seconds; and a diamond, weighing ten grains, exposed for thirty minutes, lost four grains. This lens, which is now in the possession of the emperor of China, cost £700.

399. In large burning lenses the weight of the glass employed becomes of considerable importance; and, to effect as great a saving as possible, count Buffon has proposed to construct them of circular rings, as shown in fig. 8, where the lens is composed of three pieces, two rings, a and b, and a lens c. When, however, the size is very great, the rings may be composed of several pieces, as shown by the front view E, where the lens is built of ten pieces. These instruments have been denominated by Dr. Brewster, who suggested this division, polyzonal lenses.

400 The following advantages of these lenses have been laid down by Dr. Brewster :

1. The difficulty of procuring a mass of flintglass proper for a solid lens of great dimensions is in this construction completely removed.

2. If impurities exist in the glass of any of the spherical segments, or if an accident happen to any of them, it can be easily replaced at a very trifling expense. Hence the spherical segments may be made of glass much more pure and free from flaws and veins than the corresponding portions of a solid lens.

3. From the spherical aberration of a convex lens, the focus of the outer portion is nearer the lens than the focus of the central parts, and therefore the solar light is not concentrated in the same point of the axis. This evil may, in a great measure, be removed in the present construction, by placing the different zones in such a manner that their foci may coincide.

4. A lens of this construction may be formed by degrees, according to the convenience and means of the artist. One zone, or even one segment, may be added after another, and at every step the instrument may be used as if it were complete, without the rest of the zone to which it belongs; and it will contribute, in the proportion of its area, to increase the general effect.

5. If it should be thought advisable to grind the segments separately, or two by two, a much smaller tool will be necessary than if they formed one continuous lens. But, if it should be reckoned more accurate to grind each zone by itself, then the various segments may be easily held together by a firm cement.

6. Each zone may have a different focal length, and may, therefore, be placed at different distances from the focal point, if it is thought

proper.

401. When two lenses are mounted in a frame to fix before the eyes, they are denominated spectacles: the lenses are employed to render the objects before the wearer more distinct. The eye, which consists of a convex lens, called the crystalline lens, refracts the light proceeding from the object placed before it in the same manner as a convex glass: the image of the object is formed at the focus of the lens, where it is received on a screen at the back of the eye; this screen, called the retina, is an expansion of the optic nerve, which conveys the sensation of vision to the mind. As the crystalline lens of the eye will only produce distinct vision when the focus is thrown on the retina, it is obvious that, should any defect occur with respect to that organ, indistinct and imperfect vision will arise. Thus, if the lens of the eye is not of a proper convexity to bring the image on the screen, an indistinctness must ensue. This is the case when the lens through age has become flattened; the image will then be thrown beyond the retina, and thus convey an imperfect representation of the object to the mind. To obviate this defect, we must make the rays pass through a glass of sufficient convexity to assist the eye, and enable it to form the image at the required place, which is in this instance done by shortening the focal distance of the crystalline lens of the eye. If, on the contrary, the eye should be too convex, or shortsighted, as is often the case with young persons, then the image will not be formed at a sufficient distance from the lens of the eye to reach the retina, and thus imperfect vision of distant objects is produced. To remedy this defect concave lenses must be resorted to, in order to diverge the rays before they enter the eye, and thus lengthen the focus of the crystalline lens to form an image on the retina. When the eyes are not directed near the centre of the spectacle-glasses, the obliquity of their surface to the rays will be increased, so as to occasion a confused appearance of the object. A great portion of this confusion is removed in the spectacles now usually made, when compared with those formerly employed, whose size, being very large, augmented the imperfection; for it may be observed that, when objects are seen through spectacle-glasses, no more of the glass is employed at one view than a portion equal to the size of the pupil of the eye this on an average may be reckoned at the eighth of an inch in diameter. Thus we see how small a portion is used for the purposes of vision; but as it would be tedious to require the eye always to look through a small aperture, the glasses are left of a sufficient size to admit of a moderate degree of motion; and, as we require a greater latitude horizontally than vertically, their figure is made of an oval form.

402. In the selection of spectacle glasses great care should be used in examining them, and the first point of importance is the goodness of the material of which they are formed; this should be free from all veins or small bubbles, for if one of these occur in the portion through which we look it will greatly impair the eyes. The next circumstance is the color of the glasses; the best adapted for general purposes is a pale blue. The figure of their surfaces should be perfectly spho-.

rical; for if they are curved more in one direction than in another they will injure the sight, unless they are cylindrically formed, as for some particular disease. The polish should be clean, and free from flare, which too often arises from the manner in which they are usually polished on heterogeneous surfaces, producing what is technically termed a curdled glass.

403. Dr. Wollaston, in order to allow the eyes a considerable latitude without fatigue, invented a peculiar form of glasses, called by him periscopic, from two Greek words signifying seeing about; their form is that of a meniscus with the concave side always turned towards the eye. When they are intended for long-sighted persons, or old age, the anterior surface, or that next the object, is formed spherically convex, with a curve deeper than the concave, so as both to gain the required power, and compensate for the divergency occasioned by the concave side; this form is shown at A, fig. 9. The periscopic form employed for correcting the defect of a short or near sight is shown in section at B, having its anterior surface convex, as in the former case; but here the concavity on its posterior side is increased to procure the required divergency, and compensate for the convex side.

404. The calculation of an achromatic objectglass, and in general that of every achromatic telescope, requires a precise knowledge of the ratio of the sines of incidence and refraction, and of the ratio of dispersion of the different kinds of glass which are used in the composition of telescopes. The methods hitherto employed for measuring these ratios have given results differing considerably from each other, in spite of the care and accuracy employed in the computation. We ought, therefore, to expect inaccuracies, which render the perfection of the object-glass doubtful. Experiments, repeated during many years, have led M. Frauenhofer, of Munich, to discover new methods of obtaining these ratios. The following is the order in which he made those experiments :

405. He began by determining the dispersion of the single kind of glass, from the size of the prismatic spectrum, formed by a prism of a given angle in a dark chamber, and at a given distance, and from this he deduced the dispersion. The ends of the spectrum, however, were ill terminated, and a considerable uncertainty was attached to the results.

406. In order to determine the ratio of the refraction and dispersion of flint and crown glass, M. Frauenhefer made use of prisms of these two kinds of glass, having their respective angles small, and placed in opposite directions. These last were then successively changed, till, on the one hand, the refrangibility, and on the other the refraction, was nothing. The ratio of the angles was then the inverse ratio of that of the refrangibility or the refraction. Several prisms, however, thus put together in pairs, gave different results, particularly for the dispersion. Hence, in order to determine the relative dispersion, he selects larger prisms, having their refracting angles also greater, and placed in opposite directions. The prism of crown-glass had an angle of from 60° to 70°. The angle of one of the prisms was changed till the dis

persion was almost destroyed; and the little that remained was then corrected, by changing the angle of incidence of the ray. Since, in prisms with great angles, the light is totally reflected at the second surface, even by a small variation of the angle of incidence, he covered the two touching faces of the prisms with a strong refracting fluid, such as oil, and by this means the light was transmitted at almost all angles of incidence. He applied the two prisms before the object-glass of the telescope, and a repeating theodolite, having placed them upon a horizontal plane, with a steel axis, round which it moved. The box in which the axis turned was firmly united with the telescope, as shown in fig. 10. By this procedure he was enabled to measure exactly the angle of incidence at which the dispersion was destroyed. He first looked through the telescope across the prism, at a distant object, having its edges vertical and very distinct; he then changed the angle of incidence, by turning the plane upon which the prism rested, and the alidade of the theodolite, till the dispersion appeared to be very small, or rather till the vertical edges of the object were most distinct. In order to measure the angle of incidence, he had put upon the turning-plane a ruler, which carried two steel points that exactly touched the first surface of the prisms. On this ruler was fixed a telescope, a little elevated, whose axis was perfectly parallel to the two points of steel. See fig. 11. This telescope was fixed upon the ruler only by its two ends, so that, through the interstice between the telescope and the ruler, the light could freely fall upon the prisms. Hence it was easy to measure in this manner by the theodolite the angle of incidence. Knowing, therefore, this angle, and also the index of refraction, and the angles of the prisms, which can be obtained exactly by the same ruler of the theodolite, the ratio of dispersion could then be deduced by a very exact expression.

407. The observation made with two similar prisms agreed so well that, in an object-glass calculated after these data, there was no injurious aberration of color. But if, in determining the relative dispersion, we employ different pairs of prisms, formed of the same kind of glass, and having their angles different, the results present differences which might leave an uncorrected aberration injurious to object-glasses of considerable dimensions. This result conducted him to the following experiments :

408. If we look at an object across two prisms of flint and crown-glass, with their refracting angles in opposite directions, particularly with a telescope, it will never appear without color. At a certain angle of the incident rays the dispersion is a minimum, and, either by increasing or diminishing this angle, the dispersion increases. The remaining dispersion arises, as i3 well known, from the different prismatic colors having a different ratio of dispersion in the two kinds of glass. If, in crown-glass, for example, the dispersion of the red rays is to that of the same rays in flint-glass as ten to nineteen, then the violet rays may be dispersed in the ratio of ten to twenty-one. Hence, the two dispersions can never entirely compensate one another.

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