TELESCOPE. 



G I H is now confidfrably enlarged. In order to explain 

 the theory of this reflcding compound microfcopc, eom- 

 pofcd of the fmall fpeculnm E F, and eye-glafs G H, more 

 particularly, which we purpofely omitted to do under the 

 term Microscope, let us fuppofe a ray of light proceeding 

 from the end h of the microfcopic objeft, or primary' image 

 h e i, and falling on the central part of the fmall fpecalum 

 at jf, it will return reflefked from this point, fothat the angle 

 of refledion on the other fide of the axis or line g e, will be 

 equal to the angle of incidence on this fide, and will there- 

 fore return in the line g e I, to the place of the conjugate 

 focu^, where the point h will be depitled at /: alfo a ray 

 coming from the point t of the fame primary image, and 

 falling on the point g, will be raflefted in a fimilar manner 

 along the line g h i, and will form the point ;', at /', in the 

 •fecondary image, which we have reprefented by a dotted 

 line. Now as the primary and fecondary images are fub- 

 tended by the fame angle hgi, or i g /, at the vertex^ of the 

 fmall fpecuUim, agreeably to the laws of cstoptrics, it is 

 cvideait that the linear magnitudes of thefe two images will 

 be direftly as their refpeclive diftances from g, the vertex of 

 the fmall fpeculum ; therefore, as often as the diftanee g h 

 is contained in the diftance g i, er the diftance g i in the 

 diftance^/; fo often will the length of the fecondary image 

 k /, exceed the length of the primary one b I. But this 

 fecondary' image i t is viewed tlirough the eye-glafs G H, 

 under the vifual angle G I H, and is faid to be again 

 magnified thereby : let us next fee what is the amount of 

 this amplification ; we have already faid that an eye at the 

 vertex g of the fmall fpeculum, would view both the primary 

 and fecondary images under the fame vifual angle hgi or 

 kg I; but by an eye at I, the vifual angle is G I H ^ 

 i K /, becaufe / K is parallel to H I, and i K to G I ; and 

 i / is the common fubtenfe of both angles ; confequently, as 

 the diftance L K, or focus of the eye-glafs G H, is to the 

 diftance of L g, or diftance of the fmall fpeculum from the 

 fecondary image; fo Js the apparent magnitude of the 

 fecondary image, or vifual angle to the eye at g, to the fame 

 with the eye at I ; and if the diftance ^ L be that at which 

 an objeft may be beft feen by the naked eye, the whole 



gk 

 power of magnifying of fuch microfcope will be = ^—: x 



gL, 



j=-|r, provided that f> i be confidered as a real objeft under 



microfcopic obfervation. But in a telefcope, the fize of h i 

 has a reference to the diftance of the objeft which it repre- 

 fents, and this circumftance muft be taken into confideration 

 in eftimating the power of the Gregorian telefcope. When 

 the eye is placed at o, the vertex of the large fpeculum, we 

 have faid, that the objeft and its primary image are feen 

 Hjider the fame vifual angle ; therefore, wherever the primary 

 image may fall in the line of the axis, the angle hoi will be 

 to the angle G I H, or kK I, as the objeft feen by the 

 naked eye is to its fecondary image, as feen through the 

 eye-glafs, and confequently the latter, divided by the former, 

 will give the power. But the vifual angles h o / and it K L 



are to each other in the compound ratio of — x — —, 



eg L K 

 which formula, exprefl"ed in meafured diftances, will be more 

 convenient for afcertaining the whole power of a Gregorian 

 telefcope, than the ratio of the vifual angles, which would 

 require previous calculation. For inftance, let o t, the dif- 

 tance of the primary image from the great fpeculum, be 

 given — 24 inches ; and eg, the diftance of the fame from the 

 fmall fpeculum, be = 3,3 ; alfo let L j-, the diftance of the 

 9 



thing, 



fecondary image from the fmall fpeculum, be = 25. y, and 

 I- K, the focus of the eye-glafs, be = 2.3 ; then we fhall 



have, agreeably to our formula, — - x -— , or, which i« the 



24 X 25.5 612 n ^ r , r 



=^-^ = = 80.0 tor the power ot 



Vi X 2-3 7-59 

 fuch a telefcope, when direfted to an objeft at fuch a dif- 

 tance as (hall make the primary image fall as we have taken 

 it. For objefts very near, the focus of the large fpeculum 

 will be long, and confequently the primary image will 

 .ipproach the Imall fpeculum as the diftance decreafes ; for 

 which rcafon, the magnifying power will increafe with 

 the diminution of diftance, and vice •uerfd ; fo that 

 the power with parallel rays, or when the telefcope is ufed 

 for celeftial purpofes, will be the fnialleil polTlble, and yet 

 this is what is ufually called the power of the telefcope, 

 which circumftance fhews the impropriety of taking the 

 power of a large telefcope from a meafure of a near terref- 

 trial diftance, which mode has been praftifed by eminent 

 aftronomers, and recommended by men of fcience. If, how- 

 ever, a correftion is applied for the want of parallelifm in the 

 incident rays, as we fhall liave occafion to do prefently, then 

 the power may be as accurately obtained at a ftiort as at a long 

 diftance. In the old conftruftion, which our Jig. i. repre- 

 fents, the piece of bent brafs at r, which fupports the fmall 

 fpeculum, is afted on by the long rod /C, that has a milled 

 nut at /, and a fcrew cut on the end C, that draws the pro- 

 jefting part N, of the piece c, along a (lit made in the tube, 

 while a contrivance in the cock M prevents the rod M N 

 from advancing or receding as the rod revolves. Hence the 

 eye-glafs G H remains fixed, and the adjuftment for diftinft 

 vifion is made by the rod M N moving the fmall fpeculum to 

 its proper diftance from the primary image h i ; and in this 

 way the fecondary image may be made to reft in any given 

 fituation beyond or (hort of the point L, fo that various eye. 

 glalTes may be ufed with the fame fpecula in fuccelTion ; or 

 different fmall fpecula may be ufed with the fame large one, 

 from which changes a variety of powers may be had with 

 fixed eye-glaflfes ; but if the eye-glaffes be inferted into a 

 fmaller fliding tube, there will be a third method of varying 

 the power, by bringing the fecondary image into the Aiding 

 tube out of the body of the large tube, fo as to increafe the 

 diftance L g, which is one of the faftors of the dividend in 

 our formula. Thus, whatever may be the arrangement of 

 the fpecula, eye-glafs, and diftance of the primary image, when 

 any three out of the four terms of the formula are given, 

 together with the whole power, the fourth may always be 

 had by a fimple calculation, which is a matter of great coHt 

 venience to the maker. If, for example, we take the power 

 80.6 = P, and the radius of curvature of the large fpeculum 

 =: 48 inches, in which cafe the primary image with parallel 



incident rays will fall at — = 24 ; and let L ^ and eg be 

 refpeftively 25.5 and 3.3, to find the focus of the eye-glafs 



that fhall produce fuch power ; we fhall have 



24 X 25.5 



3.3 X 80.6 



z= 2.3 for the focus of the eye-glafs ; or for the diftance 

 eg of the primary image from the fmall fpeculum, when ihq 



eye-glafs is given, we fhould have — -i-^ — 3.^, asbe- 



' " ^ 2.3 X 80.6 ^ ^ 



fore. But it was foon found, that a fingle eye-glafs not 

 only produces fringes of colour near its edges, arifing from 

 the prifmatic abeiration of the rays coming from the fecond- 

 ary 



