103 



TK 1. 1 'SCOPE. 



101 



penetrating power, he obterres that the quantity of light received by 

 the natural eye varim directly with tlie a|>erture of the ;iyV, 

 the square of iu radiii*, and inversely with the square of the dutanoe 

 of the object : also that the quantity of light transmitted by a tele- 

 Hope, supposing none to be loot in the reflection! from the mirror*, or 

 in refraction through the lenses, will vary directly with the square of 

 the radiuH of the aperture and inversely with the nquare of the distance 

 of tha object. But, from experiment* on the measure ! 1L-M. it 

 appears that the whole quantity incident upon a plate of ghiM is to 

 the quantity transmitted through it as 1 is to -M81, or to the quantity 

 .out as 1 is to -0619; and from this, tlie whole quantity of incident 

 light being unity, an estimate may be made of the quantity of light 

 tranauitted through all the lenses of a telescope : with respect to the 

 quantity lost in reflection from mirmn Sir \V. Herachel found tli.it 

 out of 100,000 incident rays, only 4.VJ-TJ reached the eye after two 

 n (lections. 



Let the quantity of incident light be to that which Arrives at the 

 rye as 1 to my then r being the radius of the pupil, and R that of 



the aperture of a telescope, y will express the ratio between the 



quantity of light transmitted to the naked eye, and through a dioptric 

 telescope : therefore the space-penetrating power varying with the 



square root of the quantity of light, - \m expresses the penetrating 



power. With respect to reflecting telescopes, if R' be the radius of 

 the small speculum, the penetrating power will be expressed by 



x {W(R S R'-)}. It is necessary to observe that, in these expressions, 



it U supposed that the pencil of light transmitted by the telescope is 

 nut greater than the pupil of the eye. 



It has been said above that, in reflecting telescopes, a speculum at 

 one extremity of the tube serves the purpose of the object-glass in 

 refracting telescopes by forming an image at its focus ; and the manner 

 in which, in the former instruments, the image is transmitted to the 

 eye remains now to be explained. 



The following diagram represents a longitudinal section through the 



Pip. 9. 



axis X T of the instrument, which is supposed to be of tlie Gregorian 

 kind. A B is the tube which contains the specula, and is open at the 

 end c B ; and at the extremity nearest to the eye of the observer is a 

 tube V. r containing two lenses. M N is the anterior surface of the 

 great speculum, which has a circular perforation, mh, at its centre : < 

 is a small speculum, concave like the former, its surface being either 

 spherical or parabolical. It is connected with the side of the tube A B 

 by the arm H K, and is capable of being moved in the direction of the 

 axis x Y by means of the rod J-s : the latter passes through a knob <j 

 which is fixed to the side of the tube, and works in the kuob K, whicl 

 panes through an oblong perforation in the side of the tube, and is 

 attached to the part K of the arm H K. This movement is given to the 

 small mirror in order that its focus may be made to coincide with tin 

 place of the image formed by the great speculum ; that image being 

 at different distances from the hitter according to the distance of th 

 object from the observer. 



\A-\. o be the upper part of an object, and let o N be the direction o 

 thi> rays in n |>encil of light diverging from o ; the rays of this penci 

 will, after being reflected at i, converge to o, which will be the l"wr 

 part of the image ot. From o the rays in the pencil diverge, and havinj, 

 fallen upon the small mirror at n, they are reflected from thcnc 

 towards the eye-piece t r : having passed through the orifice mli, they 

 fall on the lens at r, by which they are made to unite at />, where an 

 image, pq, of the object is formed. From j> the rays in the sara 

 pencil again diverge, and, falling on the lens at it, they are made t 

 (merge in parallel directions, so that the eye is enabled to obtain dis 

 tinct vision of the object in the same position as if the latter wer 

 viewed by the naked eye. The rays, after being reflected at n, migh 

 with a due concavity of the smaller mirror have united, as at ;)', in 

 fnrnt of the great mirror, and the second image might have been 

 formed at ;//' ; in this case the rays in each pencil, after crossing on 

 another, would have fallen in a divergent state on the lens at r, anc 

 then, by the refractive powers of both lenses, they would have cntere 

 the eye in parallel directions as before. The positions of the lenses a 

 K and r, and the curvatures of their surfaces, are determined according 

 method of Huyxhens ; and the construction differs in no respec 

 fmm that which has been described in speaking of the eye-pieces o 

 dioptric telescopes. 



Tlie magnifying power of a reflecting telasoope of this kind is ex- 



reused by the formula 



Vt ' 



in which v: is the focal length of the 



real speculum, c,y is the distance of the small speculum from the 

 mage p<i, X y is the focal length of the second eye-glass, and 

 ocal length of tl> email speculum for parallel rays. 



In the Cassegrainian telescope the small mirror o is made convex, 

 and it is placed so as to intercept the rays from the great m-ciilu 

 tefore the image ot is formed; the rays of each pencil r.nmcqu. ntly 

 all in a convergent state on the small mirror, and, after reflection from 

 unite to form the image either at p'g' or after refraction in tin' 

 rat eye-glass F. It is obvious that these telescopes, with equal mag- 

 ifying power, will be shorter than the Gregorian telesco|x's 1>> 

 han twice the focal length of the small speculum ; and it may !>< 

 h.it, in some degree, the spherionl aberration is corrected 1>\ the <n- 

 rary curvatures of the two mirrors. 



The Newtonian reflecting telescojies have one concave speculum at 

 he bottom of the tube ; and, in each pencil of light, the rays reflected 

 rom it fall in a convergent state upon a small plane mirror placed so 

 as to make an angle of 45 with the axis x Y of the telescope : after 

 he second reflection the rays unite and form an image which is \ 

 through a Huyghenian eye-piece fixed in the side of the tube A B .oppo- 

 site the plane mirror ; that is near the open end of the tube. 



The great telescope constructed by Herachel differs from the New. 

 toiiian telescope only in having no small mirror. The surface of the 

 p-eat speculum, which is 4 feet iu diameter, has a small obliquity to 

 ,he axis x Y, so that the image formed by reflection from it falls near 

 the lower side of the tube at its open end : at this place there is a 

 sliding apparatus which carries a tube containing the eye-glassee. The 

 observer in viewing, is situated at the open end of the tube, with his 

 back to the object, and he looks directly towards tlie centre of the 

 speculum, the magnitude of which is such that the rays intercepted 

 by his head, in coming from the object, do not in any sensible degree 

 diminish the brightness of the image. 



Formerly the great speculum of a reflecting telescope was pressed 

 into its cell by means of springs attached to the interior side of the 

 brass plate at A ; but the vibrations of the springs were found to cause 

 tremulous motions iu the image at the focus of the mirror ; and this 

 effect was so great as to render reflecting telescopes inferior to those of 

 the dioptric kind. The Hev. Mr. Edwards, who detected the cause of 

 the tremors, at once removed it by taking away the springs (' Naut. 

 Aim.,' 1787); and the same gentleman further improved the distinct- 

 ness of the image by enlarging the aperture to which the eye is applied. 

 It has been observed also that when the great speculum is nearly in a 

 vertical position, and consequently rests on its lower extremity, its 

 weight bends it, and thus causes a change in the figure of ite polished 

 surface : on this account it is recommended that the speculum should 

 be made to rest on two small wedges, placed one on each side, at about 

 45 from the lowest point. 



Since specula have been enlarged in their proportions the difficulties 

 in the way of attaining distinct vision have increased. Sir \V. 

 Herschel's 48-inch reflector weighed 25 cwt., but the 6-feet speculum 

 of Lord Rosse weighs no less than 4 tons. This, as Sir .lolm Hcr,-chel 

 remarks, requires the use of very powerful and costly machinery in the 

 construction of such specula and also in their management when CM in- 

 structed. Speculum metal, though highly elastic and rigid is, as above 

 noticed, liable to bend, and thus lose its figure. Herschel notices the 

 case of a speculum of 18 inches aperture, 20 feet focus, and 2 inches in 

 thickness which was found to be totally spoilt, by being supported mi 

 three points at its circumference, and when reclined against a flat and 

 strong wooden back, with a single thin packthread interposed down tlie 

 middle, all trace of figure was destroyed, and the surf.-irr was divided 

 into two lobes, each producing an imperfect image of a star, com: 

 with an irregular burr of light. Lord Rosse found that a strong 

 pressure of the hand at the back of his 6-feet speculum, which in 

 nearly 6 inches in thickness, produced sufficient flexure to distort the 

 image of a star ; and in one of Foucault's silver-gloss mirrors the 

 excess of central pressure of a somewhat over-inflated air cushion 

 destroyed distinct vision. The speculum, therefore, requires to be. 

 uniformly supported over every part of the back. Where the weight 

 does not exceed 200 or 300 Ibs. a bed of several layers of even 

 textured woollen blanket is sufficient, provided, as Herschel remarks 

 " the whole be supported on a back so strong as not to yield under tlie 

 pressure in any part more than a small aliquot of the total compi 

 of the cushion." For small mirrors or for light gloss ones an air- 

 cushion U a good contrivance. For a very heavy one, such M- 

 Rosse 's six-feet speculum, on ingenious plan was adopted on the idea 

 of the common " splinter bar," by which the pull of two, four, 'or eight 

 horses drawing at once is equalised so as to distribute the work 

 equally among them. The bock of the mirror, supposed to be of 

 uniform thickness, is divided into three sectors of 120. Let the 

 'f gravity of each of these sectors be sustained by a projecting 

 knob, at one of the angular points of a slab of iron in the form of ,m 

 equilateral triangle, which is itself sustained by a point under its centre 

 of gravity. In this way each sector being separately supported would 

 produce no strain on the others, and the whole weight would be 

 equally distributed among the three points of support. But to prevent 



