TELESCOPE. 



are prevented from coming to a point at the virtual image 

 hi, behind tlie fmall ipeculum, in confcquencc of its mter- 

 pofition, but are again rtflcftcd towards the eye m a ftate of 

 lefs rapid convergence, tiU, falling on the lens G H, they are 

 rcfraaed to a focus at L, and form the real image K/, 

 which may be coniidercd as the primary image, and is, 

 therefore, not in the fame pofition as the fecondary image, 

 which is formed in tlic Gregorian tclefcopc after the rays 

 have crojfd each other. When the rays fall on the large 

 fpeculum, they are refleaed in a ftate of convergence to- 

 wards the fmall fpeculum, becaufc coming from a diftant 

 objea ; and they enter the tube either parallel or diverging, 

 accordingly as the objeft is more or Icfs diftant ; but they 

 fall on tiie fmall fpeculum converging, fo as not to become 

 quite parallel after the fecond refleftion, but flowly con- 

 verging ; and the quantity of convergence will depend on 

 the diftauce of the virtual, or what may be called imagmary 

 focus, or image h i, from the fmall fpeculum E F, which is 

 here between/, the folar focus, and the convex fpeculum ; 

 whereas in the Gregorian inftrumcnt, the folar focus / is 

 between the concave fpeculum and image hi. In both 



conftruftions, — X v-^ is the meafure of the power; 

 eg L K. 



and it is evident that the part .p-^ is the fame in both ; 



but it is not equally clear that — is the fame, or in the 



fame ratio in both. The diftance og between the two fpe- 

 cula is lefs in CafTegrain'e inftrument than in the Gregorian, 

 by twice the folar focus of the fmall fpeculum, and by fo 

 much may the principal tube be (hotter ; therefore, it re- 

 mams to be proved that ge is to _g-o in one telefcope as ^e 

 is to go in the other, though differently pofited. In order 

 to prove this analogy, let HD {Plats XXVl. jig. ll.) 

 be a concave fpeculum, and E C a convex one, both de- 

 fcribed with the fame radius C D, and on the common axis 

 BCD; and let the point N interfeft the radius, fo as to 

 become the folar focus of each fpeculum, one really, and 

 the other virtually. Let F be a radiant point, from which 

 the ray F H is incident on the concave mirror at the point 

 H, OP to which the ray K E incident on the convex fpe- 

 culum is tending : then both thefe rays will be reflefted 

 from their refpeftivc fpecula to the fame point B in the 

 axis, and will pafs in the fame line E B. Again, let C F 

 be an objea, and the image thereof ah, formed by the con- 

 cave, will be equal to the image A B made by the convex. 

 This may be proved from our preceding theorems for con- 

 vex and concave fpecula refpeftively, w'c. — -7 ^ /, 



J, when all the figns are changed. 



and 



-dr 



dr 



2 d— r r — 2d 



For as // = F C, C 3 :=y"in the convex ; fo in the concave, 

 let F D =: t , and D B i:^ (f ; and then we have in the 

 former d : f :: 2 d -\^ r : r, and in the latter J : (p :: r — 

 la : r. But J = (/ -t- r, therefore 2« ^= 2 d -\- 2r, whence 

 r — 2l=-2d-rr; confequently d : f :: I : <p, that is, 

 C F : C B :: D F : D B ; alfo the objea and image are to 

 each other in the fame ratio with each fpeculum ; and, there- 

 fore, fince the objeft is the fame in both, the image will be 

 the fame alfo, or AB=:ai, which was to be proved. 

 After having given this demonftration, it will be unneceffary 

 to fhew how the powers may be varied at pleafure, agree- 

 ably to the variation of the radii of the fpecula and lenfes 

 that compofe the eye-piece, all which we have juft explained 

 4 



with regard to the Gregorian arrangemeot. As the inftru- 

 ment which is the fubjea of our prefent confideration in- 

 verts the objetts to which it is direfted, it is feldom ufed 

 but in aftronomical obfervations, for which it is peculiarly 

 adapted, feeing that it is capable of having greater power, 

 with the fame length of tube, than any other telefcope that 

 has been yet invented ; though with a terreftrial eye-piece, it 

 might be ufed for the examination of terreftrial objeas. 

 While we are writing our prefent article, we have before us 

 a Caffegrainian telefcope by TuUcy, of 36 inches of tube, 

 and 6i aperture, that will fnnvi Saturn or Jupiter, with 

 their moons very well defined, with a pov/er of 440 ; and 

 that will diftinaiy define the words of a page in this Cyclo- 

 pxdia, at the diftance of 210 yards with a power of 295. 



The maker of this inftrument has conftruaed two pairs 

 of telefcopes, one of each pair a Gregorian, and the other 

 a Caffegrainian, fo as to match each other exaftly in dimen- 

 fions, powers, and quality of the metals and glals, in order 

 to afcertain if one conftruaion has any advantage over the 

 other in quantity of light, under exaaiy the fame circum- 

 ftances ; and though feveral fcientific gentlemen, befides the 

 author of this article, have examined and compared diflferent 

 objeas as feen fucceffively by eacli of the two telefcopes 

 of both pairs, yet not the leaft difterence can be difcerned 

 by any obferver. When the laft glimmering of day-light 

 remained, the vanilhing objea ceaied to be vifible with 

 each like telefcope at the fame time, as nearly as could be 

 afcertained, and that v.'ith both pairs, though they arc 

 conftruaed with dimenfions greatly different the one pair 

 from the other, and vary confequently in their powers and 

 quantity of light. This experiment originated out of captain 

 Kater's paper on this fubjecl, which was publifhed in the 

 Philofophical Tranfaaions of London, in the year 1813 ; 

 and we have no hefitation in faying that the quantity of illu- 

 mination is the fame in both tonftruftions, when the dimen- 

 fions and quahties of the conftituent parts are perfeaiy fimilar. 

 Whatever may be the difperfion of light at the point of 

 croffing of the rays, in the Gregorian conftruaion, when 

 the difperfed rays are returned from the fecond fpeculum, 

 they are colleaed again, it ftiould feem, 'without lojs, cer- 

 tainly TOlhcut apparent diminution of light. This con- 

 viaion we put on record, not out of a fpirit of eontroverfy, 

 but from a love of truth. 



The firft account that w?s publiftied of the French re- 

 fleaing telefcope v/as in the fifth volume of the Philofophical 

 Tranfaaions of London, in the month of May, in the year 

 1672, almoft immediately after the account of fir Ifaac 

 Newton's conftruaion, which was gaven in the fame volume; 

 and a claim was fet up by Caffegrain as to the priority of 

 his contrivance, which, however, was not fubftantiated ; 

 nor was the matter of importance to determine, as the con- 

 ftruaions are diflimilar, and as Dr. Gregory's inftrument pre- 

 ceded both. The fuppofed advantages of Caffegrain's tele- 

 fcope over Newton's were ftated to be thefe : -d/'z. ift. That 

 the aperture was not limited to a confined number of rays 

 incident on the large concave fpeculum ; adly. That the 

 refleaion of the rays will be natural, fince it is made upon 

 the axis itfclf, and will therefore be more vivid ; 3dly. That 

 the vifion will be more pleafing, when the face is fcrcened 

 from too much light by the broad end of the tube ; and, 

 4thly. That there will be lefs difficulty in difcovering ob- 

 jeas with the eye facing them, than when turned from them. 

 If thefe are advantages, they are, however, equally belong- 

 ing to the Gregorian telefcope ; and we ftiaU prcfently have 

 occafion to ftate what was Newton's opinion on each of thefe 

 points. In this, as in the Gregorian conftruaion, the power 

 can always be increafed farther than the aperttire will bear ; 



and, 



