TELESCOPE. 



rcfpefti»ely 34. and 3, at a diftance of 4^ ; the fourth lens 

 being that next the primar)- image. The convex portion of 

 all the four Itnfes is turned to the centre of the tube in 

 all the terreftrial eye-pieces, except when Ramfden's, or the 

 poCtivc tye-piece, is fubftituted for the common or negative 

 one. Another good day eye-tube, of 9^ inches length, has the 

 firll, or eve-lens, i| ; tlie fecond, or amplifier, 2, at a diftance 

 of 2i ; the third 3, revcrfed as ufual ; and the fourth 2i, at a 

 diftance of 3 J. .When d, great power is wanted, the cele/lial 

 eye-piece does very well for the eye-end of the terreftrial 

 tube ; and it would be an advantage to every good telcfcope, 

 if they were fitted for this purpsfe by an adapter, fuch as 

 we fhall have occafion to dcfcribe in our fifth feftion ; for 

 then each telefcope would have a great variety of powers ; 

 and if the celeftial eye-pieces were fcrewed into a feparate 

 tube, inftead of a iirnplc adapter, the power might be 

 varied at pleafure, in any proportion, by altering the dif- 

 tance between the two feparate pairs of lenfes, as we fhall 

 hereafter Ihew has been done by the writer hereof, in his 

 micrometrical meafurement of diftances in the laft feftion 

 of this article. 



But to refume the confideration of our compound mi- 

 crofcope [P/iile XXIV. Jig. II.), we now fee that the 

 lenfes C D and tif combine in fuch a way, that the objeft 

 a b, inftead of being a little out of the focus of the fingle 

 lens df, is a little way out of the compound focus of the 

 two ; and a circular piece of metal, perforated in the centre, 

 culled a diaphragm, is fixed in the tube, at the feparate 

 focus of the lens df, to exclude the coloured rays arifing 

 from the prifmatic difpcrfion of this lens ; and then the rays 

 of leaft difpcrfion, that pafs through this hole, enter the 

 lens C D near its centre, and, therefore, have afterwards 

 but little fpherical aberration ; on which account it is ob- 

 vious, that the image in the microfcope, or fecondary image 

 in the telefcope, will be diflinH and colourlefs ; and it is 

 Tery extraordinary, that while improvements are daily medi- 

 tated in every mechanic art, the addition of a fecond lens, 

 to diminifh the aberrations, is not yet made to the objeft- 

 end of the compound microfcope, though the fame thing 

 has been done in the terreftrial eye-tube of an achromatic 

 telefcope, which not only anfwers precifely the fame pur- 

 pofe, but is in faft itfelf an achromatic compound microfcope. 



After having gone through our explanation of the prac- 

 tical forms of both the double and triple achromatic objeft- 

 glalTes, and alfo of the various achromatic eye-tubes, which 

 we have endeavoured to render intelligible to young opti- 

 cians, we fhall finifh this long feftion by giving a ftiort ac- 

 count t)f the different arrangements of the glaffes of an achro- 

 matic telefcope depending on thefe various forms, as we 

 have already done with refpeft to the old telefcopes, repre- 

 fented hyjigs. 1, 2, and 3. Plate XXV. Fig. 4. fhews the 

 arrangement of a double objeft-glafs in conjunction with a 

 ■egative eye-piece of two lenfes, with the image between 

 them, the power of which is fimply the compound focal 

 length of the objeft-glafs A, divided by the compound focal 

 length of the eye-lenfes B and C. This arrangement is 

 that of the beft achromatic telefcope with a celeftial eye- 

 piece, and, being ihorter than the terreftrial telefcope, is 

 more conveniently managed. When the eye -piece has a flip 

 of graduated motber-ot-pearl, contrived by Cavallo, and 

 divided by Mr. Barton, at its diaphragm, it makes an ufeful 

 micrometer for meafuring fmall angles : and when this eye- 

 piece is taken out, the wire or cobweb micrometer may be 

 fcrewed in, inftead thereof ; and then, if the telefcope is of 

 a good fize, an angle witliin its reach may be meafured 

 with great accuracy. With this celeftial telefcope the ob- 

 jeA it inverted, and the light will be direAly as the area 



of the aperture, and inverfely z& tlie magnifying power^ 

 Fig. 5. gives the arrangement of the lenfes in a terreftrial 

 achromatic telefcope with a triple objeft-glafs ; in which A 

 is the objedt-glafs, B the eye-lens, and C the amphfier, or 

 field-lens of the eye-piece B C ; D is the third lens, that 

 diminifties the aberration of the fourth lens E, wliich, in a 

 compound microfcope, is called the objcft-lens. This is 

 coniidered the beft conftruftion of a terreftrial telefcope. 

 The power is equal to the compound focus of the objeft- 

 glafs, divided by the compound focus of the eye-piece B C, 

 when the quotient is niultiphed by the firft part of the mi- 

 crofcopic power of the lenfes E, D, which part will vary 

 with the diftance between the two pairs of lenfes. The 

 arrangement injfj . 6. diff^ers from that in Jig. 4. only in the 

 eye-piece, which has here the image beyond it. Alfo tlie 

 arrangement in Jig. 7. differs in like manner from that in 

 Jig. 5 ; and what we faid refpcfting power and light of thofe 

 lenfes, is equally true of thefe. The eye-pieces of the tele- 

 fcopes in Jigs. 6. and 7. are thofe of the wire and cobweb 

 micrometers. 



3. Theory of cata-dioptric Telefcopes. — When the image of 

 a diftant objeft is formed in any telefcope entirely by re- 

 Jle8ed rays meeting at a focus, this image is properly 

 catoptric (from the Greek word xztottoov, fpeculum'); but 

 when it is formed partly by refleftion and partly by re- 

 fraftion of the rays, in coming to a focus, it is then cata- 

 dioptric, that is, both catoptric and dioptric ; and as the 

 image cannot be viewed without an eye-glais, all reflefting' 

 telefcopes are promifcuoufly called cata-dioptric. 



Before we defcribe any of the different conftruftions of 

 a telefcope where refleftion is concerned, we will explain 

 the principles on which the catoptric theorems are founded, 

 and give a fmall table of thofe theorems that determine the 

 focus tinder different circumftances, as we have already 

 done with refpeft to the dioptric theorems ; at the fame 

 time referring our readers for farther information on this 

 fubjeft to the articles Catoptrics, Mirror, and Spe- 

 culum. In Plate XXVI. Jig. 8. AJlronomical Injlnments, 

 let the curve GE be confidered as a portion of a convex 

 fpeculum, fonned from the centre C, and C A or C E its 

 radius ; then fuppofe DA to be a ray of light proceeding 

 from D, the radiant point, in the axis of the fpeculum., and 

 falhng on the point A, from whence it is reflefted in the di- 

 reftion of the line A Z, tending in a contrary direftion to a 

 point F, its virtual focus, in the axis of the fpeculum be- 

 hind the vertex E : then put DE=</; CAorCE = /-;. 

 C F = z ; and FE = /-|-z = r= CE. Now if we 

 fuppofe the point A to be very near to E, a point in the 

 axis, the angles at D and C will become very fmall, and 

 will, confequently, have the fame proportion to each other 

 as their oppoiite fides A C and A D have ; but A C = A E, 

 and D A may be taken =: D E without any fenfible error ; 

 hence there will be this analogy, ADC:ACD :: CE : 

 DE :: r : </. Produce now CA to I, and I A will be 

 perpendicular to the face of the fpeculum in A, the point 

 of refleftion ; and, therefore, the angles DAI and lAi? 

 will be equal. But DAI =: ^AC, and I A? = CAF, 

 as being refpeftively oppofite, therefore ^AC is equal 

 CAF: alfo s' AC = ADC + ACD = r -y d, and 

 confequently the angle CAF =: r + d. Again, in the 

 triangle C F A, when the point A is near the axis at E, the 

 angles at A and C will be very fmall, and will have the 

 fame proportion to each other as their oppofite fides F C 

 and FA, and the angle FAC : FCA :: FC : FA; 

 but in this cafe F A may be efteemed =z F E, and therefore 

 we have FAC : FCA :: FC : FE :: z : /. But we 

 have feen that the angle at C is as D A or D E, tliat is, as 



d, and 



