lenfes being the fight of a larger field or portion of an object magnified in the fame degree. IV. Of TELESCOPES. 578. I. The REFRACTING TELESCOPE. After what has been faid concerning the structure of the compound microscope, and the manner in which the rays pafs through it to the eye, the nature of the common aftronomical telescope will eafily be understood: for it differs from the microfcope only in that the object is placed at so great a diftance from it, that the rays of the fame pencil, flowing from thence, may be confidered as falling parallel to one another upon the object-glafs; and therefore the image made by that glafs is looked upon as coincident with its focus of parallel rays. 579. This will appear very plain from fig. 3. pl. CCLX, in which AB is the object emitting the feveral pencils of rays A c d, Bcd, &c. but fuppofed to be at fo great a distance from the object-glass ed, that the rays of the fame pencil may be confi: dered as parallel to each other; they are therefore fuppofed to be collected into their respective foci at the points m and p, fituated at the focal diftance of the object-glafs cd. Here they form an image E, and croffing each other proceed diver ging to the eye-glafs hg; which being placed at its own focal diftance from the points m and p, the rays of each pencil, after paffing through that glafs, will become parallel among themselves; but the pencils themselves will converge confiderably with respect to one another, even so as to crofs at e, very little farther from the glass gh than its focus; becaufe, when they entered the glafs, their axes were almoft parallel, as coming through the object-glafs at the point k, to whofe diftance the breadth of the eye-glafs in a long telescope bears very fmall proportion. So that the place of the eye will be nearly at the focal diftance of the eyeglafs, and the rays of each refpective pencil being parallel among themselves, and their axes croffing each other in a larger angle than they would do if the object were to be feen by the naked eye, vifion will be diftinct, and the object will appear magnified. The power of magnifying in this telescope is as the focal length of the object-glass to the focal length of the eye-glafs. 580. DEM. To prove this, we may confider the angle AB as that under which the object would be feen by the naked eye; for in confider ing the distance of the object, the length of the telescope may be omitted, as bearing no proportion to it. Now the angle under which the object is feen by means of the telescope is geb, which is to the other AkB, or its equal gk b, as the diftance from the centre of the object-glafs to that of the eye-glafs. The angle, therefore, under which an object appears to an eye affifted by a telescope of this kind, is to that under which it would be feen without it, as the focal length of the object glafs to the focal length of the eye-glafs. It is evident from the figure, that the vifible area, or space which can be feen at one view when we look through this telescope, depends on the breadth of the eye-glafs, and not of the object-glafs; for if the eye-glafs be too fmall to receive the rays gm, pb, the extremities of the object could not have been feen at all: a larger breadth of the object glafs conduces only to the rendering each point of the image more luminous, by receiving a larger pencil of rays from each point of the object. 581. It is in this telescope as in the compound microfcope, where we fee, when we look through it, not the object itself, but only an image of it at CED: now that image being inverted with refpect to the object, as it is, because the axis of the pencils that flow from the object cross each other at k, objects feen through a telescope of this kind neceffarily appear inverted. This is a circumftance not at all regarded by aftronomers; but for viewing objects upon the earth, it is convenient that the telescope fhould reprefent them in their natural pofture; to which use the telescope with three eye-glaffes, as reprefented fig. 4. pl. CCLX. is peculiarly adapted, and the progrefs of the rays through it from the object to the eye is as follows: AB is the object fending out the feveral pencils A cd, Bed, &c. which paffing through the object-glafs cd, are collected into their respective foci in CD, where they form an inverted image. From hence they proceed to the first eye-glafs ef, whofe focus being at 1, the rays of each pencil are rendered parallel among themfelves, and their axes, which were nearly parallel before, are made to converge and crofs each other: the fecond eyeglass gh, being fo placed that its focus fhall fall upon m, renders the axes of the pencils which diverge from thence parallel, and causes the rays of each, which were parallel among themselves, to meet again at its focus EF on the other fide, where they form a fecond image inverted with refpect to the former, but erect with refpect to the object. Now this image being feen by the eye at ab through the eye-glafs ik, affords a direct representation of the object, and under the fame angle that the first image CD would have appeared, had the eye been placed at 1, fuppofing the eye-glaffes to be of equal convexity; and therefore the object is feen equally magnified in this as in the former telescope, that is, as the focal distance of the object-glafs to that of any one of the eye-glaffes, and appears erect. 582. If a telefcope exceeds 20 feet, it is of no ufe in viewing objects upon the furface of the earth; for if it magnifies above 90 or 100 times, as thofe of that length ufually do, the vapours which continually float near the earth in great plenty, will be fo magnified as to render vifion obfcure. 583. The GALILEAN TELESCOPE with the concave eye-glafs is conftructed as follows: AB (fig. 5. pl. CCLX.) is an object fending forth the pencils of raysg bi, klm, &c. which, after paffing through the object-glafs cd, tend towards eEf(where we will fuppofe the focus of it to be), in order to form an inverted image there as before; but in their way to it are made to pafs through the concave glafs no, fo placed that its focus may fall upon E, and confequently the rays of the feveral pencils which were converging towards thofe refpective focal points e, E, f, will be rendered parallel among themselves: but the axes of thofe pencils croffing each other at F, and diverging from thence, will be rendered more diverging, as reprefented in the figure. Now thefe rays entering the pupil of an eye, will form a large and diftinct image ab upon the retina, which will be inverted with refpect to the object, because the axis of the pencils cross in F. The object of courfe will be Leen erect, and the angle under which it will appear will be equal to that which the lines aF, bF, produced back through the eye-glafs, form at F. 584. It is evident, that the lefs the pupil of the eye is, the lefs is the visible area feen through a telescope of this kind; for a lefs pupil would exclude fuch pencils as proceed from the extremities of the object AB, as is evident from the figure. This is an inconvenience that renders this telescope unfit for many uses; and is only to be remedied by the telescope with the convex eye-glafses, where the rays which form the extreme parts of the image are brought together in order to enter the pupil of the eye, as explained above. It is apparent also, that the nearer the eye is placed to the eye-glafs of this telescope, the larger is the area feen through it; for, being placed clofe to the glafs, as in the figure, it admits rays that come from A and B, the extremities of the object, which it could not if it was placed farther off. The degree of magnifying in this telescope is in the fame proportion with that in the other, viz. as the focal diftance of the object-glafs is to the focal diftance of the eye-glafs. For there is no other difference but this, viz. that as the extreme pencils in that telescope were made to converge and form the angle geh (fig. 3. Pl. CCLX.) or ink (fig. 4.), thefe are now made to diverge and form the angle a Fb (fig. 5.) which angles, if the concave glafs in one has an equal refractive power with the convex one in the other, will be equal, and therefore each kind will exhibit the object magnified in the fame degree. 585. There is a defect in all these kinds of telescopes, not to be remedied in a fingle lens by any means whatever, which was thought only to arife from hence, viz. that spherical glaffes do not collect rays to one and the fame point. But it was happily discovered by Sir Ifaac Newton, that the imperfection of this fort of telescope, fo far as it arifes from the spherical form of the glaffes, bears almost no proportion to that which is owing to the different refrangibility of light. This diverfity in the refraction of rays is about a 28th part of the whole; fo that the object-glafs of a telescope cannot collect the rays, which flow from any one point in the object into a less room than the circular space, whose diameter is about the 56th part of the breadth of the glafs. To fhow this, let AB (fig. 15. pl. CCLVIII.) reprefent a convex lens, and let CDF be a pencil of rays flowing from the point D; let H be the point at which the leaft refrangible rays are collected to a focus; and I, that where the most refrangible concur. Then, if IH be the 28th part of EH, IK will be a proportionable part of EC (the triangles HIK and HEC being fimilar): confequently LK will be the 28th part of FC. But MN will be the leaft space into which the rays will be collected, as appears by their progrefs reprefented in the figure. Now MN is but about half of KL; and therefore it is about the 56th part of CF: fo that the diameter of the space into which the rays are collected will be about the 56th part of the breadth of that part of the glafs through which the rays pafs; which was to be shown. Since therefore each point of the object will be reprefented in fo large a space, and the centres of thofe fpaces will be contiguous, because the points in the object the rays flow from are fo; it is evident, that the image of an object made by fuch a glafs must be a moft confufed reprefentation, though it does not appear fo when viewed through an eye-glafs that magnifies in a moderate degree; confequently the degree of magnifying in the eye-glafs muft not be too great with refpect to that of the object-glafs, left the confufion become fenfible. 586. Notwithstanding this imperfection, a dioptrical telescope may be made to magnify in any given degree, provided it be of fufficient length; for the greater the focal diftance of the objectglafs is, the lefs may be the proportion which the focal diftance of the eye-glafs may bear to that of the object-glafs, without rendering the image obfcure. Thus, an object-glass, whofe focal distance is about 4 feet, will admit of an eye-glafs whofe focal diftance fhall be little more than an inch, and confequently will magnify almoft 48 times; but an object-glafs of 40 feet focus, will admit of an eye-glafs of only 4 inches focus, and will therefore magnify 120 times; and an object-glafs of 100 feet focus will admit of an eye-glafs of little more than fix inches focus, and will therefore magnify almoft 200 times. 587. The reafon of this difproportion in their feveral degrees of magnifying is thus explained: Since the diameter of the fpaces, into which rays flowing from the feveral points of an object are collected, are as the breadth of the object-glass, it is evident that the degree of confufedness in the image is as the breadth of that glafs; for the degree of confufedne's will only be as the diameters or breadths of thofe fpaces, and not as the spaces themfelves. Now the focal length of the eyeglafs, that is, its power of magnifying, must be as that degree; for, if it exceeds it, it will render the confusedness fenfible; and therefore it must be as the breadth of diameter of the object-glass. The diameter of the object-glass, which is as the square root of its aperture or magnitude, must be as the fquare root of the power of magnifying in the telefcope; for unless the aperture itself be as the power of magnifying, the image will want light: the fquare root of the power of magnifying will be as the fquare root of the focal distance of the object-glass; and therefore the focal distance of the eye-glafs must be only as the fquare root of that of the object-glafs. So that in making ufe of an object-glafs of a longer focus, fuppofe, than one that is given, you are not obliged to apply an eye-glafs of a proportionably longer focus than what would fuit the given object-glass, but fuch an one only whose focal distance fhall be to the focal diftance of that which will fuit the given object-glafs, as the fquare root of the focal length of the object-glafs, you make ufe of, is to the fquare root of the focal length of the given one. And this is the reafon, that longer telescopes are capable of magnifying in a greater degree than shorter ones, without rendering the object confused or coloured. 588. But the inconveniency of very long telescopes is fo great, that different attempts have been made to remove it. Of thefe, the most fuc cefsful fo. 589. But, though we have hitherto fuppofed the refraction of the concave lens to be greater than that of the convex one, it is easy to see how the errors occafioned by the firft lens may be cor. rected by it, though it should have even a lefs power of refraction than the convex one. Thus, let a b, a b, (fig. 6. pl. CCLX.) be two rays of red light falling upon the convex lens c, and refracted into the focusq; let also gb, gh, be two violet rays converging into a focus at r; it is not neceffary, in order to their convergence into a common focus at x, that the concave lens fhould make them diverge: it is fufficient if the glass has a power of difperfing the violet rays fomewhat more than the red ones; and many kinds of glass have this power of difperfing fome kinds of rays, without a very great power of refraction. It is better, however, to have the object-glafs compofed of 3 lenfes; because there is then another correction of the abberration by means of the 3d lens; and it might be impoffible to find two lenfes, the errors of which would exactly correct each other. The effect may be the fame, whether the concave glafs is a portion of the fame fphere with the others or not; the effect depending upon a combination of certain circumstances, of which there is an infinite variety. cessful have been by DOLLOND and BLAIR; and all meet together at the point x, or very nearly the general principles upon which thefe eminent opticians proceeded have been mentioned above. (See 31, 35-40, 55, 56, 196.) The objectglaffes of M. Dollond's telescopes are compofed of 3 diftinct lenfes, two convex, and one concave; of which the concave one is placed in the middle, as is reprefented in fig. 16. pl. CCLVIII. where a and c show the two convex lenfes, and bb the concave one, which is by the British artists placed in the middle. The two convex ones are made of London crown glafs, and the middle one of white flint glafs; and they are all ground to fpheres of different radii, according to the refractive powers of the different kinds of glaís and the intended focal diftance of the object-glafs of the telescope. According to Bofcovich, the focal diftance of the parallel rays for the concave lens is one half, and for the convex glass one third of the combined fo. cus. When put together, they refract the rays in the following manner. Let ab, ab (fig. 1. pl. CCLXI.) be two red rays of the fun's light falling parallel on the first convex lens c. Suppofing there was no other lens prefent but that one, they would then be converged into the lines be, be, and at laft meet in the focus q. Let the lines gb, gb, represent two violet rays falling on the fur. face of the lens. Thefe are alfo refracted, and will meet in a focus ; but as they have a greater degree of refrangibility than the red rays, they muft of confequence converge more by the fame power of refraction in the glafs, and meet fooner in a focus, fuppofe at r-Let now the concave lens dd be placed in fuch a manner as to intercept all the rays before they come to their focus. Were this lens made of the fame materials, and ground to the fame radius with the convex one, it would have the fame power to caufe the rays diverge, that the former had to make them converge. In this cafe, the red rays would become parallel, and move on in the line 00, 00: But the concave lens, being made of flint glafs, and upon a fhorter radius, has a greater refractive power, and therefore they diverge a little after they come out of it; and if no 3d lens was interpofed, they would proceed diverging in the lines opt, opt; but, by the interpofition of the 3d lens ovo, they are again made to converge, and meet in a focus fomewhat more diftant than the for mer, as at x. By the concave lens, the violet rays are also refracted, and made to diverge: but having a greater degree of refrangibility, the fame power of refraction makes them diverge fomewhat more than the red ones; and thus, if no 3d lens was interpofed, they would proceed in fuch lines as Imn, Imn. Now, as the differently coloured rays fall upon the 3d lens with different degrees of divergence, it is plain, that the fame power of refraction in that lens will operate upon them, in fuch a manner as to bring them all together to a focus very nearly at the fame point. The red rays, it is true, require the greatest power of refraction to bring them to a focus; but they fall upon the lens with the leaft degree of divergence. The violet rays, though they require the leaft power of refraction, yet have the greateft degree of divergence; and thus 590. By this correction of the errors arifing from the different refrangibility of the rays of light, it is poffible to fhorten dioptric telescopes confiderably, and yet leave them equal magnifying powers. The reafon is, that the errors arifing from the object-glafs being removed, those which are occafioned by the eye-glafs are inconfiderable: for the error is always in proportion to the length of the focus in any glafs; and in very long telefcopes it becomes exceedingly great, being no less than 1th of the whole; but in glaffes of a few inches focus, it becomes trifling. Dollond's refracting telescopes are therefore now constructed in the following manner. Let AB (fig. 7. pl. CCLX.) represent an object-glafs composed of three lenfes, as above defcribed, and converging the rays 1, 2, 3, 4, &c. to a very diftant focus as at x. By means of the interpofed lens CD, however, they are converged to one much nearer, as at y, where an image of the object is formed. The rays diverging thence fall upon another lens EF, where the pencils are rendered parallel, and an eye placed near that lens would fee that object magnified and very diftin&t. To enlarge the magnifying power fill more, however, the pencils thus be come parallel are made to fall upon another at GH; by which they are again made to converge to a diftant focus: but, being intercepted by the lens IK, they are made to meet at the nearer one ; whence diverging to LM, they are again rendered parallel, and the eye at N fees the object very distinctly. 591. From an infpection of the figure it is evident, that Dollond's telescope thus conftructed is in fact two telescopes combined together; the first ending with the lens EF, and the ad with LM. In the first we do not perceive the object itself, but the image of it formed at y; and in the ad |