TELESCOPE. 



of tl.c lenff s N M and G H, it is evident, fince the aberra- 

 tion is leffenodbv dividing the optic angle, th-^tthe AJinamJs 

 of virion wiU be thereby promoted ; and becaufe each of the 

 angles contribute thereto in proportion to its magnitude, 

 the ioint effect of both parts, or angles G !■/ and /G t, 

 will be as tiie prodiia or redangle under both, or as the 

 redangle of the lines 0/and /F ; but, according to our 

 former notation, T f = T - B -/; and O/-/; confe- 

 quently F / - D/"- // will be every v^here as the diftincl- 

 nefs of vifion by tlic t«o lenfes, above that ot a fingle lens 

 of the fame magnifying power. 



" Let tlie degree of diftinclnefsthus obtained be reprelentcd 

 by G = F/"— D/" — //; when this is a maximum, or the 

 greateft poiTible, the Huxions thereof will be nothing ; viz. 

 Y f— D/— 2ff= o, whence F — D = 2/; or F O = 

 2 O/; that 's, 0/=/F, or the angle G F/:i=/G F, in 

 the lijl pofition ot the lenfes, as before demonftrated. 



" Confequently, fince in that pofition we have {hewn the 

 diftinftnefs of vifion to be four times as great as by a fingle 

 lens, this will be the whole effeft of a combination of two 

 o-lalTes, and it may be fliewn that tliree glafles will produce 

 nine times the dillinftnefs, and fo on in proportion to the 

 fqutire of the mwilifr of gl"/" ; but then if we confider the ev.l 

 to be remedied is but fmall, and the damage we fufrain in lojs 

 of //?/'/ and irregularity of refraftion through fo many lenfes, 

 we may foon make the remedy worfe than the difeafe ; and 

 every thing confidn-ed, it appears probable that two lenfes 

 are better than a greater number, particularly for a celeftial 

 eye-piece." 



By fimilar reafoning we may explain the advantage of any 

 other eye-piece, as Bofcovich's, when we know the radii, the 

 pofition, and the diftanceof the lenfes that compofe it. The 

 Huygenian eye-piece, which we have faid has the foci of the 

 two plano-convex lenfes, as 3 : I, at the diftance of 2, with I 

 next the eye, and the curves exterior to the eye, is peculiai-ly 

 adapted for a reflefting telefcope that has only the fpherical 

 aberration ; but for a refracting telefcope, though achro- 

 matic, a little deviation from this form was found neceffary 

 to correct the remaining prifmatic aberration alfo. On en- 

 quiring of the beft opticians, we leai-n that the final adjuft- 

 , inent of diftance between two lenfes, in a celeftial achromatic 

 eye-piece, is made from trials in the tube of the telefcope it 

 is intended for ; becaufe this diftance, and indeed the ratio 

 of the radii of the two lenfes, wiU greatly depend on the ftate 

 of convergence of the rays, when they are incident on the 

 firft furface of the interior glafs ; and this ftate will depend 

 on the focal length of the telefcope, conjointly with the 

 aperture, and acluomatifm of the objeft-glafs : fo that it 

 would not anfwer any good purpofeto give a table of dimen- 

 fions, wliich might millead rather than afiift the young opti- 

 tian in his praftice. The form of an achromatic celeftial 

 eye-piece, compofed of two plano-convex lenfes, is repre- 

 fented in Plate XXVIII. _^^. 13, where the diftance exceeds 

 the focal length of the lens l next the eye, and in which con- 

 fequently the image is between the lenfes ; which is the ufual 

 conftruftion when the heavenly bodies are viewed without 

 any reference to the meafurenient of angles ; but as the place 

 of the image will vary in fome degree with a change of dif- 

 tance, in taking terreftrial meafures, there is another fonn, 

 commonly called Ramfden's, which is more fnitable for 

 micrometrical meafurements ; becaufe the image, being be- 

 yond both lenfes, (counting from the eye,) keeps its place, 

 as it regards any fc;Je, wire, or fpider's line, that may be ufed 

 in a micrometer : this form is given in Jig. 14. of the fame 

 plate, and has the pofition of the interior face reverfed, fo 

 that the plane face may be parallel to the contiguous image 

 to be viewed : thefe two lenfes are fometimes alike, and 



always nearly fo, in focal length ; and the diftance between 

 them is lefs than the focal length of either by fuch a quan - 

 tity, that the compound focus falls juft beyond the flat face 

 of the interior kns 2, where the image and fcale, wire, or 

 line coincide in due adjuftment "or vifion. This form has 

 likewife the advantage of reduced aberration, and is fome- 

 times called the pofitfoe eye-piece, in oppofition to the otlwr 

 form, which is therefore by fome aftronomers called the wifo'd- 

 //iii- eye-piece. This pofitive eye-piece is alfo beft adjufted 

 to the inftrument of which it is deftined to form a part ; and 

 either lens may exceed the other in focal diftance in a fmall 

 degree, as circumftances may require. 



When this eye-piece is ufed with a tranfit inftrument, ze- 

 nith fe£tor, equatorial, or circular inftrument for taking alti- 

 tudes, it is convenient to put a diagonal refleftor between the 

 lenfes, and to have the eye -lens in the. fide of the tube, for the 

 purpofe of taking obfervations in high altitudes, or even 

 in the zenith. This form is feen in Jig. 15. of the fame 

 plate, and is called a prifmatic eye-piece. 



The ierrejlriat eye-tuhe is that which gives an ered pofition 

 to the objeft, as viewed in a telefcope of the refrafting fort, 

 to which only it is apphed, though it might be applied to the 

 Caflegrainian refle6tor with equal advantage. It has been 

 feen that, originally, this eye-piece was compofed of three 

 fimilar lenfes, placed from each other relpeftively at the 

 fum of their focal diftances, as in Jig. 3. Plate XXV. In 

 this arraugament the magnifying power is not increafed, 

 unlefs the lens, T U, neareft to the eye has its focal dif- 

 tance diminiftied more than the reft : but the aberration that 

 would arife from the figure of the field-lens C D, is dimi- 

 niftied about nine times, if we difregard their thicknefs, -Dia. 

 as the fquare of the number of glafles employed between 

 the image I M, and the eye at K ; confequently, the ad- 

 vantages derived from this eye-piece of Rheita are two-fold ; 

 for, firft, it gi%'es an ereft pofition to the objeft ; and, fecondly, 

 it greatly diminiflies the quantity of fpherical aberration, 

 and confequently produces a correfponding diftinctnels j 

 but the power of this eye-piece is /imply that of one of the 

 three lenfes. To effeft an increafe of power at the fame 

 time that the two preceding advantages are preferved, various 

 arrangements of three, four, and even of five lenies, have 

 been nwde for the purpofe of conftrufting a good terreftrial 

 achromatic eye-tube ; and the ingenuity of a Dollond and 

 of a Ramfden has been exercifed fucceifively to accomplilh 

 the defired objeft. Thefe arrangements, fo far as the dimi- 

 nution of fpherical, and even of prifmatic aberration was 

 concerned, have been underftood and explained ; but the 

 total power arifing out of a number of lenfes differently 

 ftiaped, and placed at different dijlances relatively to eacli 

 other, has not been fo clearly explained ; and it fhould 

 feem, from the manner in which fuch arrangement has been 

 defcribed by different authors, tha,t the refult has generally 

 been afcertained practically rather than theoretically ; which 

 indeed muft in fome degree be the cafe whenever dow^r, or, 

 which is the fame thing in effect, whenever aftual focal dif- 

 tance, fimple or compound, is to be accurately determined. 

 We will not proceed upon the intricate plan of tracing the 

 paffage of a refrafted pencil of rays through various lenfes 

 of different refractive qualities, and placed at various inter- 

 vals, until they arrive at their laft focus, or place of the 

 image of a diftant radiant body ; neither do we propofe to 

 follow the more famihar but lefs inftruftive method of fimply 

 giving in -figures the radii and relative diftances of three, 

 four, or five lenfes, that fhall compofe an achromatic eve- 

 tube ; but, avoiding each extreme, we fliall defcribe the 

 moft improved eye-tube for erecl pofition, upon the princi- 

 ples of a compound micro/cope, which inftrument this tube 



really 



