TELESCOPE. 



ary image, now confidered as a real objeft, but that the field 

 of view is thereby circumfcribod into a fmall area. For 

 thete reafons,the Huygonian eye-piece,already explained, was 

 fuhftitutcd for the fiiigie cye-glafs, whicli fubllitution left 

 little more to be done, in the way of the improvement of the 

 Gregorian telefeope, except wliat related to the conilrudion 

 ot the fpecula, which have now been brought nearly to a 

 Hate of perfection, as we have explained, at fome length, 

 under our article Speculum. We have introduced Jig. 2. 

 for the purpofe of explaining more clearly, than we could by 

 a mere verbal defcription, the plan of the Gregorian tele- 

 feope in its mod improved Hate, in which, we repeat, the 

 fame letters indicate the fame parts as in ^^. i. In tliis 

 figure we have made the pencils of rays a b and cd to confill 

 each of three lines, for the purpofe of flicwing how the image 

 is formed at the jjoints of convergence after refleftion, and 

 alfo how the inverfion of the image is produced by the erod- 

 ing of the pencils before they converge to a point at each 

 end of the image. It may alfo be feen how the rays pafs 

 through the interior eye-glafs, before they form the fecondary 

 image between the two glaffes, as in the achromatic altrono- 

 mical telelcope, thereby conftituting this image a cata-dioptric 

 one, which before was a catoptric one, according to our defi- 

 nition. The Huygenian eye-piece is peculiarly adapted for the 

 Gregorian telefeope ; and when the fpecula have their curves 

 fo adapted as to counteratt each other's aberrations, as we 

 before recommended, and are alfo well poliflied, as well as of 

 fuitable metal, a very high power may be applied, and the 

 light by refleftion will be to that by refraftion alone nearly 

 as 5 ; 8, where the apertures are equal ; but as a refleftor is 

 capable of having a much greater aperture than any refratior 

 that can be conflrufted, it will have a proportional advan- 

 tage in the eflential quality of illumination combined with 

 power, on which union its excellence depends. It will not 

 be neeelFary to repeat here what we have faid above rcfpeft- 

 ing the manner of determining a fmgle eye-glafs, equal in 

 power to the combined eye-glafles in the Huygenian eye- 

 tube ; but it may be proper to mention here, that fuch a 

 glafs, when determined, mud be fubftituted for the com- 

 pound eye-piece, in computing the power of the telefeope 

 according to our preceding direftions. The diaphragm 

 that precludes the ftraggliug and extraneous rays from 

 coming to the eye is put where the fecondary image is 

 formed, and the aperture at the eye is obliged to be fmall in 

 this conftruftion of a telefeope, to prevent any other light 

 being admitted into the eye than what is reflefted from the 

 fmall fpeculum, and is necefTary for the formation of the 

 fecondary image. When the diameter of the fmall fpeculum, 

 and alfo the exaft fituation of the primary image, are known, 

 the aperture at the eye, that (hall admit the principal pencil, 

 may be exaftly determined by the fubjoined analogy ; ii/z. 

 as the dillance of the fmall mirror from the fecondary image, 

 is to the focal length of the nciu-eft: eye-glafs ; fo is the dia- 

 meter of the fmall fpeculum, to the necelTary aperture at the 

 eye. And to find the proper diameter of the fmall fpecu- 

 lum, or central aperture of the large one, the proportion 

 will be, as the diftance of the primary image from the large 

 fpeculum, is to its diftance from the fmall one, with incident 

 parallel rays ; fo is the diameter of the large fpeculum, to the 

 diameter of the fmall one, or of its ovin central aperture ; 

 and Vi'hen this proportion is preferved, all the n fletted light 

 will enter the fmall tube that contains the eye-glalfes, and 

 alfo the extraneous light not falhng on the larg- fpeculum, 

 if any, will be excluded. Lattly, (hould the field of view be 

 required to be equal to a given vifual angle, inch as that 

 fubtended by the diameter of the fun, this will depend on 

 the pDiuer of the inllrument, which for this purpofe mull be 



limited, as in the following example : let a reflcAing Gre- 

 gorian telefeope of four inches diameter of the large fpeculum, 

 and 17.5 inches focus, witii a hole in the centre i.i diameter, 

 (which lii confidered in praflice a good proportion,) be 

 required to have a field of view ju(l 32', when the focus of 

 the eye-glafs is two Inches ? The thing required is, tlut the 

 enlarged fecondary image of the fun (liould juil fill the aper- 

 ture in the centre of the large fpeculum. The fi/.e of the 

 primary image of the fun depends on the focal length of tlic 

 large mirror, and mud firil be found : it has been afcertained 

 tliat, in the focus of a fpeculum (or lens) of fix inches focal 

 length, the image of the fun is .05586 diameter, when he 

 meafures 32'; therefore, as it will be proportionably more in 

 a longer focus, fay as 6 : .05586 :: 1 7.5 : .1629 ; alfo, ai 

 often as this image .1629 is contained in i.i, the diameter 

 of the hole in the large fpeculum, which quotient is = 6.75^ 

 lo much docs the fmall fpeculum magnify the primiry 

 image, in converting it into a fecondary one of 1 . 1 diameter. 

 Again, if we divide the focus of tlie great fpeculum 17.5, 

 by 6.75 — I, we have 3.04, the diftance of the primary 

 image from the fmall fpeculum, which is fomewhat more 

 than its folar focus ; and alfo if we divide 4, the diameter of 

 the large fpeculuni, by the fame (6.75 — i), wo (hall have 

 .695 =: the diameter of the fun's image on the face of the 

 fmall metal, while the fecondary image will juft cover the 

 hole of the large fpeculum, as required. Now, laftly, to 

 find what is the power of the telefeope under thofe limit- 

 ations, we have 17.5 x 6.75 = 118 for the hrft part of the 



, 118 , , , 



power ; then - — = 59 = the whole power, when 2 is the 



focus of the fingle eye-glafs. ■ If the length of the focus of 

 tlie principal fpeculum were iiicreafed to 30 inches, or even 

 to 30 feet, while the aperture remains as before, no advan- 

 tage would be gained in this conftnidion from fuch length ; 

 for in the cafe of 30 inches focus, the primary image would 

 be .2793, and the power of the fmall fpeculum only 3.93 



f ], while the diftance of the primary image from the 



fmall fpeculum would be 10.24 ! l'"" diameter of the image 

 on the face of the fmall fpeculum 1.36 ; and the magnifying 



power i-^ = 59, as before. There would, indeed, be 



2 



this difadvantage, that, as the fmall fpeculum has an increafed 

 radius here, its diameter will necelfarily be fo much aug- 

 mented, as to intercept feveral of the beft rays of light, 

 which are thofe that fall near the centre. The opinion, con- 

 fequently, that a Gregorian telefeope will be improved by 

 having a long focus of the great fpeculum, with the fame 

 aperture, is erroneous. When two refledling tclefcopes per- 

 form alike, as to light and diftinftncfs, the fquare fquare roots 

 of the diameters of the fpecula muft be as the cubes of their 

 foci refpeflivcly. There can always be more power got by 

 the fmall fpeculum and eye-glafs, in even a (hort tube, than 

 the aperture will bear. 



The theory of Caflegrain's telefeope is very fimilar to that 

 of the Gregorian, the principal difference being that, in 

 Caflegrain's, the fmall fpeculum is convex inftead of con- 

 cave. When the radii ot the two fpecula and the eye-piece 

 are rcfpecSively the fame in each conftruftion, tlie powtn 

 will he the faine, though the apparent pofilion of the laft 

 image, which we have (hewn to be ered in the Gregorian, 

 is inverted in the Caftcgrainian conftrudtion ; for on exa- 

 mining Jig. 3, which explains the courfe of the rays in 

 Caflegrain's telefeope, it will be feen that the incidei.t rays 

 ab and cd, after being refieiled from the large fpeculum^ 



arc 



