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703
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screw) contains the scioptric ball EF, placed in a hole of the saidshutter adapted to its size. This ball is perforated w ith a holeabed through the middle ; on the side be is screwed into the saidhole a piece of wood, and in that is screwed the end of a commonrefracting telescope GH, IK, with its object-glass GH, and oneeye-glass at IK ; and the tube is drawn out to such a length, asthat the focus of each glass may fall near the same point. Thisbeing done, the telescope and ball are moved about in such a man-ner as to receive the sun beams perpendicularly on the lens Gil,through the cylindric hole of the ball ; by this glass they will beCollected all in one circular spot m, which is the image of the sun.The lens IK is to be moved nearer to or farther from the saidunage m, as the distance at which the secondary image of the sunis to be formed requires, which is done by sliding the tube IKLMbackwards and forwards in the tube LMNO. Then of the firstimage of the sun m will be formed a second image PQ, very large,luminous, and distinct. In this manner the sun’s face is viewed atany time, without offence to weak eyes; and whatever changeshappen therein, may be duly observed. The spots (which makeso rare an appearance to the naked eye, or through a small tele-scope in the common way) are here all of them conspicuous, andeasy to be observed under all their circumstances of beginning toappear, increase, division of one into many, the uniting of manyinto one, the magnitude, decrease, abolition, disappearance behindthe sun’s disk, &c. I5y the solar telescope, we also view aneclipse of the sun to the best advantage, as having it in our powerby this means to represent the sun’s face or disk as large as weplease, and consequently the eclipse proportionably conspicuous.Also the circle of the sun’s disk may be so divided by lines andcircles drawn thereon, that the quantity of the ec lipse estimated indigits, may this way be most exactly determined; also the mo-ments of the beginning, middle, and end thereof, for finding thelongitude of the place: with several other things relating thereto.The transits of Mercury and Venus over the face of the sun, areexhibited most delightfully by this instrument. They w ill hereappear truly round, well defined, and very black; their compara-tive diameters to that of the sun may this way be observed, the di-rection of their motion, the times of their ingress and egress, withother particulars for determining the parallax and distance of thesun, more nicely than has hitherto been done. By the solar tele-scope, you see the clouds most beautifully pass before the face ofthe sun, exhibiting a curious spectacle according to their variousdegrees of rarity and density. The general aim in the construc-tion of a telescope is, to form, by means of mirrors and lenses, anjmage of the distant object, as large, as bright, and as extensive, asis possible, consistently with distinctness; and then to view the•mage with a magnifying glass in any convenient manner. Theindistinctness to be avoided arises from two causes; the sphericalfigures of the refracting and reflecting surfaces, and the differentmfrangibility of the differently coloured rays of light. The firstthese may be thus shewn: I. In Reflection, let AVB, (fig.Plate CLXXII.) he a concave spherical mirror, of which C isjpe centre, V the vertex, CV the axis, and F the focus of an in-finitely slender pencil of parallel rays passing through the centre.~ e t the ray «A, parallel to the axis, be reflected in AG, crossinghe central ray CV in /. Let AP be the sine of the semi-apertureAV, AD its tangent, and CD its secant. 'Ilie aberration Vf from1 ’ e Principal focus of central rays is equal to \ of the excess VDof the secant above the radius, or very near equal to * ot VP, thev ersed sine of the semi aperture. For because AD is perpendicu-?. r to CA, the points C, A, D, are in a circle, of which CD is themanieter ; and because A/ is equal to Cf, by reason of the equality7' the angies/AC,/CA, and CAa,/isthecentreof the circle through'“■A, D, and /D is = l CD. But FC is = -j C V; therefore Vf is -f' VD. But because DV : VP : : DC : VC, and DC is very littlegreater than VC when the aperture AB is moderate, DV is very littlegreater than VP, and l'/is very nearly equal to \ of VP. Cor. 1 .
Ti AV S
he longitudinal aberration is = ; for PV is very nearly =
A V» AV 2
”2CV~' Cor. 2. The lateral aberration FG is = — ^ r For
: F/:: AP ; P/, : : AV : $ CV nearly, and therefore FG =
AV* , 2 _ AV 5
4CV X CV “ 2 CV 2 *
9,) be a spherical surface separating two refracting substances, C thecentre, V the vertex, AV the semi aperture, AP its sine, PV itsversed sine, and F the focus of parallel rays infinitely near to theaxis. Let the extreme ray aA, parallel to the axis,'be refractedinto AG, crossing CF in f, which is therefore the focus of extremeparallel rays. (The rectangle of the sine of incidence, by the dif-ference of the sines of incidence and refraction, is to the square ofthe sine of refraction, as the versed sine of the semi aperture is tothe longitudinal aberration of the extreme rays.) Call tire sine ofincidence i, the sine of refraction r, and their difference d. JoinCA, and about the centre / describe the arch AD. The angleACV is equal to the angle of incidence, and CA /is the angle cfrefraction. Then, since the sine of incidence is to the sine of re-fraction as VF to CF, or as A/ to Cf, that is, as D/to Cf, wehave
CF : FV :: Cf: f Dby conversion CF : CV :: Cf: CD
alternation conversion CF— Cf; CV—CD :: CF : CV
Or Vf : VD :: CF : CV,:: r ; d. Now PV
AP 2 AP 2 AP*
— nearly, and PD
~CP + CV’
AP 2
2/V
nearly, =
2 CV
AP 22 FV
/ P +/V ’ ~
nearly. Therefore PV : PD FV :
CV, and DV : PV CF : FV nearly.
We had aboveand nowtherefore
Vf: VD ::r:d,
VD ; PV :: CF : FV, = r : *;Vf: PV :: r 2 : di,
andF/=-^— x PV. 2. E. D. The aberration will be dif-di
ferent according as the refraction is made towards or from the per-pendicular; that is, according as r is less or greater than i. They
y? 2 2
are in the ratio of ^ to or of r 3 to i 3 . The aberration there-
fore is always much diminished when the refraction is made froma rare into a dense medium. The proportion of the sines for airand glass is nearly that of three to two. When the light is refract-ed into the glass, the aberration is nearly f of PV ; and when thelight passes out of glass into air, it is about f of PV. Cor. 1 . Vfr* AP 3 , , , r* AP 2
= 57 x Ycv near y * and 111S allsro = # x Tfv"’ because
PV = gjjy nearly, and i ; d :: FV : CV.
Cor. 2. Because/P : PA :: Vf; FG
or FV : AV :: I/: FG nearly,
we have FG, the lateral aberration, Vf X — r ~r x -~-
IV a 1 SI V 2
r 2 AV 3
= -X ■ Cor. 3. Because the angle F. A/ is proper-
FG
lional to very nearly, we have the angular aberration FA/=
r 2 Ays r 2 AV 3
gr X - 2 FW = fT X 2 CV 3 • In general, the longitudinal aber-rations from the focus of central parallel rays are as the squares ofthe apertures directly, and as the focal distances inversely ; andthe lateral aberrations are as the cubes of the apertures directlyand the squares of (he focal distances inversely; and the angularaberrations are as the cubes of the aperture directly, and the cubesof the focal distances inversely. It has been determined that theindistinctness arising from the refrangibility of light, called thechromatic indistinctness is much greater than that arising from thespherical figure of the lens, the effects of which it is therefore ofmore consequence to remove as much as possible. This defect
was