TELESCOPE. 



for fecuring the ufe of an exliauftcd tube, on a fuppofition 

 that tiieic would be more light wlicn the rays were rcfraftcd 

 to a focus in vacuo. Mr. Cornelius Varley, artift, now of 

 Nevvman-ftrect, London, took out a patci.i for a grapliic 

 tclefcopc, for the purpofe of delineating drawings from 

 nature, on the principle of Dr. Wollallon's camera lucida, 

 the date of which is April 5, 181 1. And on the zill of 

 May of the fame year, Dr. Brcwfter of Edinburgh, and 

 Mr. Harris, optician, of Holborn, London, jointly took 

 oyt a patent for a micrometrical, double-image, and coming- 

 up glafs, &c. which has its fcale of meafurement running 

 longitudinally along the tube. This telefcope, being on 

 a new conftruftion, will be particulai'ly defcribed here- 

 after. 



2. Theory of dioptric Tclefcopei. — Before we can properly 

 defcribe the various conftruftions of either the refrafting or 

 reflefting telefcope, it will be neceffary to explain the prin- 

 ciples on which thofc conftruftions are founded ; and for the 

 fake of order, we will confine ourfelves, in the firft place, 

 to the confideration of the elementary principles of dioptrics, 

 fo far as they ai-e connefted with the theory of the refrafting 

 telefcope. Among the various writers who have confidcred 

 this fubjeft, in both a fcientific and praftical manner, Ben- 

 jamin Martin ftands firft in our eftimation ; and as his " New 

 Elements of Optics," publilhed in 1759, are but little 

 known, by i"eafon of the fcarcenefs of this work, notwith- 

 ftanding it contains the refult of all his theoretical and prac- 

 tical inveitigations, we ihall make no fcruple in avaihng 

 ourfelves of his labours, as often as they contribute to the 

 purpofe of either illuftration or praftical application : our 

 aim being, in this article, as in fome former ones connedled 

 with it, to bring the mathematician and the mechanic into a 

 ftate of mutual underftanding. 



We propofe, therefore, to avoid as much as poffible all 

 abftrufe calculations, that have no tendency to produce 

 pradlical advantages, but to introduce, in as familiar a man- 

 ner as poffible, thofe mathematical inveftigations only, which 

 are eflentially explanatory. The firft and fundamental prin- 

 ciple in dioptrics is this, that in all uniform media, fuch as 

 air, water, glafs, &c. " the fines of incidence are in a con- 

 ftant ratio to the fines of refraAion" of any homogeneal ray 

 of light, incident on the furface of fuch refrafting medium ; 

 which principle was firft difcovered by Snell, when Huygens 

 had gone no further than to aflert, that in fmall obliquities 

 of incidence, the angle of refraftion was about one -third of 

 the angle of incidence. In the glafs which fir Ifaac Newton 

 nfed, the ratio of the fine of incidence to the fine of refrac- 

 tion was found to be 30 : zi, or nearly 3 : 2, in paffing out 

 of air into glafs : and had all kinds of glafs been found equal 

 with refpeft to their refraftive powers, the radius of convexity 

 would, in all cafes, have been equal to the focus of a double 

 convex lens of equal radii ; which equality may be confidered 

 as the bafis of all the geometrical theorems in optics, that take 

 no account of the difference of the reJraSive pomers. But 

 fince the difference of the refraftive powers of various fpeci- 

 mens of glafs has become an objeft of indifpenfible examina- 

 tion to the optician of modem times, it has become neceflary 

 to introduce into each theorem the ratio between the fine 

 of incidence and fine of refraiftion, whatever it may be found 

 to be by experiment, before the refraded focus of any indi- 

 vidual lens, depending on the quality of the glafs, in fome 

 meafure, can be determined from the georrutrical focus de- 

 pending on the radius of convexity or concavity. As we 

 have demonftrated, under our article RkfrACTION, the con- 

 ftancy of the ratio between the fines of the angles of incidence 

 and of refradlion of a mean refrafted ray ; and have alfo ex- 

 plained how the geometrical focus of any lens may be detcr- 



VoL. XXXV. 



mined with converging, parallel, and diverging rays, under 

 the term Lkns ; we will proceed to apply the doftrinc 

 arifing out of ihcfe dcmonftrations and explanations to our 

 prcfent purpofe. " Let DC (y/a/cXXIV. ^Jironomical 

 Jnjlrumnits, fig. I.) be a ray of lip\: ii.cidfiit out of any 

 medium X, upon the furface, H O, of another medium Y, 

 which we will fuppofe to be more dcnfe than X ; and from 

 the point of incidence C, let it be refradcd to F, out of its 

 firll direftion D C M. This refraftion may be confidcred as 

 arifing out of the attrafting power at the furface of the 

 medium Y, and as afting upon the ray in a p rpendiculav 

 diredtion, by which, on mechanical principles, it will ac- 

 quire fome additional force and velocity <jf motion through 

 the medium Y. Now upon the centre C defcribe the cu-cle 

 A O P H, cutting the incident ray in D ; and ilrawing the 

 diameter ACP perpendicular to HO, let DL fall pcr- 

 pendiculai- thereto, and it will be the fine of incidence. Let 

 DC or C E reprefent the fpace described in a given time 

 in tlic medium X ; and from E draw E F parallel to A B, 

 to denote the acquired force in C : then the motions in the 

 direftions C E and E F, in the fame time, being com- 

 pounded, will produce a motion in the direftion found by 

 joining C F ; for C F will be the fpace defcribed in tlie 

 medium Y, in the fame time that DC ( = C E) was pafTed 

 over in the medium X, and confequently will be the ref railed 

 ray ; and G I, perpendicular to A B, will be the fine of 

 refraftion. 



" Through F draw N M parallel to H O, and draw K E 

 perpendicular to A B ; then will BF=KE = DLbe 

 the fine of incidence; and in the fimilar triangles C I G, 

 C B F, we have C G : C F :: G I : B F. Hence it ap- 

 pears that we have the fines of the angles of incidence and 

 of refraftion B F or D L, and G I, as the velocities C F 

 and CD (=CG) in the different media inverfely, and on 

 this fuppofition they are in a conflant ratio; becaufe the velo- 

 cities are invariable, being produced by the uniform opera- 

 tion of nature. And on the contrary, if the ray F C be 

 confidered as pafGng out of a denfe medium Y, into a rare 

 medium X, it will be deflefted by the fuperior force of the 

 medium Y, into the direftion C D ; making D L : I G :: 

 C F : C D, as before. 



" Let us now conceive AMD, infig. 2, to be the curved 

 furface of a refrafting medium Y, and B a radiant point in 

 a more rare medium X, from which two rays proceed, and 

 fall upon the curve in the points M and N indefinitely near 

 to each other : thefe rays will be fo refrafted as to crofs each 

 other in a certain point F ; to determine which from the 

 given equation of the curve, the diftance of the radiant, and 

 the refraftions of the media, is that problem in dioptrics, on 

 which the various calculations and inferences depend. That 

 we may render the folution of this problem intelligible to 

 our readers, let us make the lines C M and C N the radii of 

 curvature, and confequently perpendicular to the curve at 

 the points M and N ; upon M F and N F let fall the per- 

 pendiculars C G and C^^ cutting F M in S : alfo upon the 

 incident rays B M, B N, continued, let fall the perpendi- 

 culars C E, C c ; and on the centres B and F, defcribe the 

 fmall arcs R M, MO; and put B M = d, M E = a, 

 M G = i ; the arc M R = s, and the arc M O = / ; and 

 laftly, the fine of incidence C E to that of refraftion C G, 

 as m to n, the radius of curvature being C M = r. Then 

 the triangles M E C, M R N ; M G C, M O N ; M B R, 

 Q B f, are Cmihir, as is thus evident : if from the right 

 angles R M E, C M N, you fubtraft the angle E M N, 

 there remains the angle R M N = E M C ; and if from the 

 right angles F MO, CM N, you take th^ angle Y M N, 

 there wiU remain the angle O M N = G M C. Thcfe tn- 



Gg 



glcs 



