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THE PRINCIPLES INVOLVED IN THE CONSTRUCTION

OF THE TELESCOPE.

By THOMAS NOLAN, B. S.

Written for VAN NOSTRAND'S ENGINEERING MAGAZINE.

THE

INVOLVED IN

I The Telescope is certainly one of the my purpose in this dissertation to enter noblest monuments of human genius, into the discussion of the question as to and its invention will always be con- who was the inventor of the first “opticksidered as among the most remarkable tube," or to describe minutely and hisin the whole circle of human knowledge. torically all the several successive It is a work, in which, by following un- changes and improvements which it has consciously the plan of nature in the undergone in the hands of different formation of the eye, we have come the philosophers ; but rather, to examine the nearest to the construction of a new theory of those forms of refracting and organ of sense, and by means of which, reflecting telescopes which have been of we have extended our views and re- more general application. searches far beyond the limits of our own globe-that sphere which nature

OPTICAL PRINCIPLES seemed to have designed for our in

THE CONSTRUCTION OF THE TELESCOPE. quiries. Enabling us to penetrate into A telescope, in general, consists of a the immensity of space, and to become, tube containing a system of glass lenses, as it were, familiar with other worlds or a speculum in combination with such placed at almost immeasurable distances lenses; and is used to render distant obfrom us, the telescope has revealed an jects more clearly visible; (1) by enlarginfinitude of celestial bodies, whose ex- ing their apparent angular dimensions, istence must forever have remained un- and (2) by introducing into the eye a known to us, but for its invention. Its superior quantity of their light. history, like that of every complicated Those constructed with glass lenses instrument, has been a history of im- only, are called dioptric or refracting, provements. The question of the origin and the others catoptric or reflecting telof the invention, although abundantly escopes. In the efracting telescope, inquired into, has never met with a satis- rays of light coming from the object are factory answer; and the question-who made to converge by a convex lens, and, made the first telescope ? will probably if not intercepted, form an image at its never be conclusively settled. For the focus. In the reflecting telescope, the invention, in its original form, we are image is formed by the reflection of the indebted to accident, or to the trials of rays which impinge upon upon the conmen who had little knowledge of the cave surface of a speculum. principles of the science upon which We will first consider, they were conferring so great a favor.

I. THE SIMPLE REFRACTING TELESCOPE. Not a single thing, but a combination of things, the telescope in its earliest forms In exhibiting the principles on which was a simple combination of certain the refracting telescope is constructed, kinds of convex and concave lenses, we must first explain the formation of known and used as spectacles many the image of an object at the focus of a years before; and whether the credit of lens. the invention should be given to Metius, When a convex lens is placed before Lipperhey, Jansen, Baptista Porta, Gali- an object, an image of the latter is leo, or to others whose names are un- formed at a certain distance behind or known, it is a most difficult and invidi- before the refracting surface, whose mag.

to decide. But interesting nitude is greater or less, according as it though these inquiries may he, it is not is formed farther from, or nearer to the

ous task

surface. The one particular distance at came from some point F, called the virwhich the image is distinct, is called the tual focus. focus. At every other distance it is The first condition which a telescope hazy and confused. By the use of the must fulfill is, that it shall so dispose all telescope the image is produced on the rays emanating from any point in an obretina of the eye itself, and its office is ject, that they may emerge from the instruto prepare the rays of light for forming ment parallel to each other, in the usual on the retina an image larger and clearer or medium situation of the mechanthan would be formed without its help. ism.

In (Fig. 1) two rays proceeding from The second condition is, that the me

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the top and bottom of the object AB chanism itself shall be adjustable, so as, are represented separately. The ray Aa, by a movement of the parts inter se, to passing through the center of the lens convert this parallelism into a slight O, is unaffected, because the surfaces divergence or convergence, to suit the through which it passes are parallel to eyes of near or long-sighted persons. each other, and from the property of the The third condition is, that the pencils lens, all other rays from A, on passing of parallel rays coming into the eye through it, are brought to a focus some from different points of the object, shall where on Aa, depending upon the curva- be inclined to each other at greater anture of the lens. In like manner, all gles than those actually subtended at the rays from B are brought to a focus at b, eye, by the respective intervals between each point of AB having its correspond- the points themselves. The number ex

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ing focus in ab. The latter is smaller pressing this ratio is the measure of the than AB in proportion as co is less than magnifying power of the telescope, and CO; and if we increase the focal length the apparent linear dimensions of an obof O till ab is twice the distance away, ject being in proportion to its magnifyit becomes double its present size. The ing power, the apparent enlargement of place of an image depends upon the dis- its superficial area is as the square of the tance of an object, and when the latter magnifying power. is considered at an infinite distance, as is The simplest construction of the rethe case with the heavenly bodies, the fracting telescope is that in which the image is formed at the principal focus of image formed in the focus of a convex the lens, or the focus of parallel ray. lens, or object-glass, is viewed through a

If rays ABC &c., pass through a con- second lens, or eye-glass, so placed as to cave lens, as in (Fig. 2), they are not have the image in its focus for parallel brought to a focus, but diverge as if they rays incident in the contrary direction,

and its axis coincident with that of the pupil is small, and since it involuntarily first lens.

contracts in proportion to the quantity Three cases arise by applying this of light impinging upon the eye, the principle, which afford telescopes of dif- field of view is so much the less as the ferent characters:

focus of PQ is greater. 1. The Galilean telescope, with double (3.) Since the nature of light will not concave eye-glass, showing objects erect. admit of an eye-glass whose focus is

2. The Astronomical telescope, first diminished beyond a certain limit, and suggested by Kepler, with double con- since the focus ought to be longer in vex eye-glass, showing objects inverted. proportion to the length of the focus of

3. The Terrestrial telescope, suggested the object-glass, the field of view will be by Rheita, with three double convex eye-less the greater the length of the instruglasses, showing objects erect.

ment, which inconvenience, together

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1. THE GALILEAN TELESCOPE. with those above described, render this In this instrument, the eye.glass PQ instrument almost useless for purposes (Fig. 3) is placed between the object-glass of astronomical observation. MN and its focus O', so that the axes of (4.) The pencil of rays C, from B, both glasses are in the same line AO', under the axis, meets the eye in the and their foci in the same point O'. direction cF, answering to a point also

(1.) The object OB being supposed below the axis; and in the same manner, infinitely distant, incident parallel rays, a ray issuing from any point of the as AD, A'D', A'D', are first rendered object, above the axis, has a similar converging towards O' by MN, and af direction on emerging from the eyeterwards parallel by PQ. They are also glass. Consequently, objects and their much denser than before their first refrac- images have like positions with respect tion, and, when received by the eye, paint to direction, when viewed through a an image of the object, so much the more telescope of this construction.

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vivid, as the density of the pencil of rays (5.) To determine the field of view, is then greater than before it fell upon we let MN (Fig. 4) be the diameter of MN.

the object-glass, AB that of the pupil of (2.) The point B sends forth parallel the eye whose center is in the axis of the rays as CD and its two parallels, which telescope, and join M and B, the oppo. are refracted towards some point b, and site extremities of these diameters, and then rendered parallel by PQ. Since let MB meet the axis in x, and the this pencil, in emerging from PQ, diver- image in p. We draw also LB and Lp, ges from that formed by the point O, a and suppose pL and qL to be produced greater number of the parts of the ob- till they meet the object in P and Q. ject will be seen as the eye is placed PM is refracted to the pupil in the direcnearer to PQ, and as the pupil is more tion MB, but every other ray in the dilated. But since the dilation of the pencil, as PL, and every ray which

comes from a point more distant_from diverging from 0, and falling on PQ the axis, falls below the pupil. There emerge parallel to each other, and are so fore, PQ is half the linear magnitude of much the more dense as the focal length the greatest visible area. QP is meas- of PQ is less than that of MN. They ured by the angle QLP, or by its equal therefore paint on the retina a new qLp.

image of 0, which is so much the more Lp=ELB + BLp, and

vivid, as the surface of MN is greaterBLP=LBM-LpM. that is, as it admits a greater quantity of

light. .. qLp=ELB + LBM–LpM.

(3.) Rays from B form in b, an image And 2QP is measured by

of this point, and falling afterwards on 2ELB+2LBM-2 LpM. PQ, emerge parallel and more inclined to

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That is, the linear magnitude of the field | AF as the curvature of PQ is greater; so of view is measured by the angle which that the axis of the pencil which they the diameter of the pupil subtends at form, cuts the common axis of the two the center of the object-glass, increased lenses in F, the focus of PQ. Conseby the difference between the angles quently, to see all of ob at the same which the diameter of the object-glass time, the eye must be placed at F, the subtends at the pupil and at the image. common intersection of all rays emitted

from each point of ob, or of OB. ASTRONOMICAL TELESCOPE.

(4.) b, the image of B, is refracted to This instrument, represented in (Fig. 5) the eye in the direction PF, and has a differs from the Galilean, in having a different direction from that in which it convex instead of a

concave eye-lens, is emitted from B; and the ray which which is so placed with regard to the renders visible a point above the axis

2. THE

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object-glass that their foci coincide in reaches the eye as if it proceeded from the axis of the telescope between the below the axis; and thus the entire two glasses, instead of being beyond the image is reversed. eye-glass as in the Galilean telescope. (5.) To find the field of view, we let PQ is the eye-glass, MN the object- MN (Fig. 6) be the diameter of the obglass, KD the axis, and o the common ject-glass, AB that of the eye-glass, and focus.

draw NB, letting it cut the image par in (1.) The rays AD, A'D', A'D' from p. We draw also pl, and conceive pL O in the object OB, infinitely distant, and EL to be produced until they meet are refracted to the focus o where they the object in P and Q; and draw pE and form an image of 0.

NP, and also BO parallel to pE. Then (2.) This image o is considered as an the eye at receives the ray NBO, object placed in the focus PQ, and rays which comes from a point in the object at

the greatest visible distance from the an infinitely distant object, the parallel axis of the telescope. For rays from rays from ó, in the axis produced, from any point above P, converge to a point an image in the focus o, whence, falling below p, and fall below AB; consequent- on, Pe they emerge parallel to each ly P is the exteme visible point in the other and to the axis. Falling upon KS, object, and QP is half the linear magni- they are refracted to the focus o', where tude of the visible area.

a second image is formed, and then di(6.) To find the brightest area, we verging, and falling on TV, they are redraw MB cutting par in s, and the axis fracted to the eye in directions parallel LE in x', and draw Ls, and conceive it to the axis. In like manner, rays

from produced till it meet the object in S. B form in b an image of that point, Then, (a) if x'E be greater than 9E, all whence, falling in PQ they are rendered rays from S falling upon MN, are refract- parallel to each other, but oblique to the ed to AB; for, SM is refracted in the axis till they meet RS, by which they redirection M&B, and any other ray of the fracted to the second focus b'; whence, pencil, as SL, crosses MB at s, and falls falling on TV, they are again rendered

Fig. 7.

M

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somewhere between A and B. In like parallel to each other, but so inclined to manner, rays from any point between S the axis as to meet it again with all the and Q, are refracted to AB. (6) If ac other

rays

in the focus f, where the eye and q coincide, the brightness of the is placed to receive the final impression, field increases to the center. (c) If q which is that of an image corresponding, fall between L and x', all the rays belong as to its direction, with the object itself. ing to any one pencil incident upon MN, For the ray b'Vf, which carries the image are not received by AB.

of the point B, has a similar direction

with respect to the axis, as the ray pro3. THE TERRESTRIAL TELESCOPE.

ceeding immediately from B. The nature of this construction is easi. As the properties of this instrument ly comprehended by reference to (Fig. 7). are analogous to those of the astronomiThe four lenses have one common axis cal telescope, it is unnecessary to enter A f. and each contiguous two are so sit- into further discussion of the principles uated that their foci coincide. If OB bei of its construction.;

FILTRATION THROUGH SPONGY IRON.

From "Engineering."

It is now some years since Mr. Gustav Pollution, in thc reports of the RegisBischof demonstrated the remarkable trar General, in the Army Medical Reproperties of spongy iron as a filtering port for 1877, and elsewhere, the mamaterial for the purification of water for terial has not yet been employed on a drinking purposes, and spongy iron filt- large scale for the filtration of water at ers are already in extensive use for do- any of our water works, a fact which is mestic purposes. Notwithstanding this, to be regretted when the remarkable efhowever, and notwithstanding also the fect of the material on Thames water is testimony to the powers of spongy iron taken into consideration. which has been afforded in the sixth re Although, however, spongy iron has port of the Royal Commission on Rivers not yet been introduced at water works

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