TELESCOPE. 



reverfc ihe numbers of/ and F, as taken above, by making 

 / = 15, and F = 36 ; and then, as before, there wiU be 



^5 X 36 _ 2- _ _ X, the negative focus of the concave 

 36 - 15 " 



lens required, which may alfo have any ratio of its curves, 

 or be a plano-concave, provided its focus be that which has 

 been here determined. . 



Likewife it mull be iccolleaed, that when a pofitive 

 focus is required from an union of two lenfes, one convex 

 and the other concave, the focus of the convex muft be 

 fliorter than that of the concave ; or, in other words, the re- 

 fractive power, depending on tlie thicknefs of the lens, when 

 the fame glafs is ufed for both lenfes, muft predominate in the 

 convex ; for it is the difterence of tlie oppofite refraftions 

 t!iat brings the rays finally to a focus : confequently, if the 

 foci are alike, the rays, being refraded alike in oppofite di- 

 rottions, will become parallel, or have what is called an 

 infinite focus : and alfo, if the focus of the concave be made 

 the fliorter of the two, the rays, after oppofite refradions, 

 will abfolutely diverge by the ditference of thefe refraftions, 

 and have an imaginai-y focus, called a virtual or negative 

 focus, at the other fide of the compound lens. 



7. If the lens given be concave, and a convex one be re- 

 quired to produce a given compound focus, which is another 

 cafe in the formation of an achromatic objeft-glafs, the 



theorem will be J- „ = .v, where / is the focus of the 



F +/ 

 concave, and might be put — /, to denote its being a nega- 

 tive focus, and * the focus of the convex lens. Let us 

 put / = 25.7, and F = 36, as above, and then there will 



b^ ^^'^ ^ 3 r= i_i!_ = 15, very nearly, for the focus x 

 36 + 25.7 61.7 



of the convex required ; which, as we have faid, muft be the 

 refrafted focus, and alfo /of a like denomination, in order 

 to make the refrafted compound focus fuitable for a tube of 

 thirty-fix inches. 



8. If tlie compound focus fhould be required to be nega- 

 tive, or to have the refraftion of the concave lens to predo- 

 minate, when the convex lens is given with the compound 



/F 

 focus, the concave may be found by this theorem 



= w, as in the laft ; but then x here is the focus of the con- 

 cave lens, which therefore will be 15 when that of the con- 

 vex is 25.7, and the negative focus, as before, 36. 



9. But if the given lens be concave, and the compound 

 focus be required negative, the focus of the convex fought 



fT 



will be had by this theorem ~ ^ = x, as in the fixth 



} Y-f 



theorem ; the focus x is here, however, that of the con- 

 vex, which in the other was that of the concave ; fo that 

 when / = 15, and F = 36, x will be again = 25.7, but 

 negative. 



In all thefe cafes, the two lenfes are fuppofed to be in con- 

 taft with each other ; but if D, the diftance between them, 

 which is a variable quantity, were given, fimilar theorems 



/F 



iniffht be formed from our general theorem - — 4;; — - 



" ^ / + F — D 



aboye explained, where, in any pofition of two convex glafles, 

 / is the focus of one lens, F the focus of the other, and D 

 the diftance between them, with a pofitive compound focus ; 

 hut if one of the two lenfes be convex, and the other concave, 



the general theorem becomes ■ 



/^ or /^ 

 7 -"F^ITD F-/-D' 



accordingly as F, put for the concave, or/, put for the con- 

 vex, is the larger: the former theorem being the *' produfl 

 divided by the fum of the foci, leftened by the dijiance," and 

 tlie latter the " produR divided by the difference of the foci, 

 leflened by the dijiance.^' Hence, by a tranfpofition of one 

 or other of the forms of this general theorem, the data and 

 poftulata may be varied as occafion may require. The firft: 

 form is applicable in cafes where Aiding eye-pieces, or a 

 Aiding fecondary objeift-glafs, are ufed in a telefcope, which, 

 plans have been recommended and adopted by Dr. Brewfter, 

 as we fliall fee hereafter. 



In confidering the theory of a telefcope, (of either the 

 refrafting or reflefting fort,) our attention muil be diretlcd 

 to two effential particulars, the image of an external objeft 

 formed at the focus of the objeft -glafs, or of the large fpe- 

 culum, as the cafe may be ; and the means by which this 

 image is rendered vifible to the eye of an obferver : and ac- 

 cordingly as the dimenfions, (hape, quality, arrangement, 

 and number of the lenfes and fpecula vary from each other, 

 may the conftruftions be faid to differ, though the efFe£t 

 to be produced be intended to be the fame. That telefcope, 

 of whatever conftruftion, muil be confidered the moft per- 

 fect, which exhibits to the eye an image of diftaat objefts 

 the moft diftindlly, as to light, colour, fliape, and propor- 

 tion ; and which, at the fame time, amplifies this image fuf- 

 ficiently to afford a minute examination of it, in a field of view- 

 that is proportionably large to contain it. That quality, 

 which appai-ently amplifies the objeft, or rather the image of 

 the objeti, by enlarging the angle fubtended at the pupil of 

 the eye, therefore called the vifual angle, is denominated 

 the poiucr of the telefcope ; and in all telefcopes, whatever 

 their other qualities may be, the light is diminijbed as the power 

 increafes, fo that in every telefcope there is a limit to its ufe- 

 ful power, which depends on the quantit)^ of light emitted 

 or refledled by the objeft to be viewed ; and it would anfwer 

 no good purpofe to increafe the power fo much, that a cor- 

 refponding deficiency of light may render the objeft invifible. 

 Hence different powers may be applied, with advantage, to 

 objefts differently illuminated ; and hence different eye-pieces 

 are ufually appropriated to the fame telefcope, particularly 

 when it is deftined for celeftial, as well as for terreftrial ob- 

 fervations. But we propofed to explain firft the theory of 

 thofe telefcopes which are uftially called refraRing or dioptric, 

 and afterwards of cata-dioptric, or thofe that magnify by the 

 aid of reJleBion. 



Under our article Lens we have faid (in feftion 5.) that 

 " the images of objefts, oppofed in any manner to a cpnvex 

 lens, are exhibited invertedly in its focus," and that " they 

 will be reprefented diilinaiy, and in their natural colours," 

 on a paper held at the oppofite fide of the glafs, at nearly 

 the diftance of its proper focus, efpecially if the room be 

 darkened ; and in feftion 7. we have faid, that " the diame- 

 ter of the image of an objctt delineated beyond a convex 

 lens, is to the objeft itfelf, in the ratio of the diftance of 

 the images to that of the objeft ;" fo that the more diftant 

 an objeft is from the lens, the fmaller is the image of that 

 objeft ; and alfo the fhorter is the focus of the lens, until 

 the diftance is fuch, that the rays fall on its furface parallel, 

 or nearly fo. Likewife (in fedtion 8.) we have (hewn, that 

 " if the eye be placed in the focus of a convex lens, an ob- 

 jeft viewed through it appears ereft and enlarged in the ratio 

 of the diftance of the objeft from the eye, to that of the 

 eye from the lens, if it be near ; but infinitely, if remote :" 

 and what is faid of an objeft itfelf, when viewed through a 



