TELESCOPE. 



porary U-lefcope, wlioii tlie principal or folar focus, from 

 adliial refradioii of the rays, was found to be 28.13 inches, 

 wliicli is thrrcfore called the rcfratied folar focus, the geo- 

 metrical focus derived from tlie radius of curvature being 

 33.7. This is the fpecinien of glafs of the greatcft denfity 

 as well as of the greateft refradive and difpcrfive powers, 

 its fpecific gravity having been repeatedly afcertained to be 

 3.466 with different hydroftatic balances of the mod deh- 

 cate conllruftion. Now if the radiant had been at a near 

 diflance, inllead of the fun being ufed, Martin has (hewn 



that the value of <7 = may be had from this theorem, 



n 



>u\^. -—J-= a (where d, r, and/, are as in our Table I. 



2 df 



of Theorems), which is demonftratcd in his Philofophia Bri- 

 tannica ; and from this theorem he determined the focal dif- 

 tancPs and quantity a of his fpecimens of glals ; but when 

 the fun is ufed as the radiant, the diftance becomes infinite ; 

 and then, neglefting rfss infinitely fmall, the left-hand term 



becomes — y , and the theorem, by ejefting d from the 

 2df 



r 



numerator and denominator, is reduced into the form — =: /, 



2a 



as in our Table I. for parallel rays with a double convex of 

 equal radii. TuUey, therefore, very properly preferred tak- 

 ing the folar focus at once, inftead of taking a meafured 

 dillance for the place of the radiant, and of calculating 

 from a long theorem, and from data that might not be per- 

 feAly correft ; his refults, therefore, muft be confidered as 

 being more fatisfatlory than Martin's. The reduced theorem 



— =/, by tranfpofition becomes — = 2 a, and alfo/ x 



2 (J = ;■ ; hence 2 a may be either a divifor or multiplier, 

 accordingly as r or /is given to find the other. Tulley has 

 called this quantity a divifor, becaufe, having the radius or 

 geometrical focus of a glafs always, from the known radius 

 of his grinding tool, he can get the refracted focus by the 

 proper divifor and a fimple calculation at any time ; which 

 mode, as we fhall fee prefently, is very ufeful in the calcu- 

 lation of the compound focus of an achromatic objeft-glafs. 

 Now to get the aftual quantity of 2 a in figures, there will 



3 3.7 

 be -„ — taken from the third and fourth vertical columns, 

 28.13 ' 



R r 



which may be called z=- or — = z a = 1. 1 98 for the faid 



divifor, one half of which is .599 = a. Put now m, as 

 before, for the fine of incidence, and n for the fine of re- 



fraftion, and we have feen above that 



n-= I, and then m = 1.599 > f^"" — 



1.599 — I 

 = 1-599' a™ -^^ = -599 



= a. Let 



I +a 



a ; therefore the fine 



of incidence is to the fine of refraftion in this firft fpecimen, 

 ifi the ratio of 1.599 = ' ; and in like manner the horizon- 

 tal columns for all the other fpecimens are filled up with very 



R 

 little trouble, when - is afcertained by fimple divifion of 



the tabular or experimental numbers With refpeft to the 



vertical column of difperfive powers, thefe powers are bed 

 afcertained by making fix equal prifms of the fame fpeci- 

 mens of glafs, and by meafuring the coloured folar fpcftra 

 of each feparately, under exaftly the fame circumftances of 

 diftance, inclination, pofition, &c. ; and as the angle of dif- 

 perfion is meafured by the coloured fpeftrum as its fubtenfe, 

 the angles of difperfion of the different fpecimens will varj- 

 with the rcfpeftive lengths of their fpeftra ; and if the re- 

 frafling angle of one of the fpecimens, the firft flint for in- 

 ftance, be diminifhed by grinding and frcfti poliftiing, until 

 its fpeftrum is of precifcly the fame length as that of any 

 other, fay the crown, then the ratio of their refrafting 

 angles will be inverfely the ratio of their difperfive powers ; 

 and a pair of analogous lenfes, one convex and the other con- 

 cave, (fuch as thofe feen in /"/a/^ XXVIII. _/ffj'. 5. and 6.) 

 will have their difperfive powers fo counteratled, that a 

 pencil of rays incident on the thick crown-glafs will emerge 

 from the thin flint colourlefs, and will proceed without colour, 

 notwithftanding the greater refradlive power of the convex 

 lens, till, by being refrafted, they finally crofs the axis in 

 which the focus is formed ; and the focal point will be more 

 or lefs diftant with a pair of lenfes fo combined, accordingly 

 as the difference of the two refrafting powers is greater or 

 fmaller. To explain this analogy between a pair of prifms 

 and a lens, either convex or concave, we will ftiew how a 

 pencil of folar rays paffing through a prifm of glafs is dif- 

 perfed at the fecond furface, fo as to form the folar fpec- 

 trum compofed of the prifmatic colours : Let a b c, in 

 Jig. 9, be a triangular piece of glafs, called a prifm, and d a 

 pencil of folar light, entering the prifm at e, in the line de B> 

 parallel to the bafe ac : on entering the glafs it will be re- 

 frafted towards this bafe, and emerge at the pointy, a little 

 nearer to c than e is to a. At this point of emergence,/, the 

 pencil will begin to difperfe into rays of different colours, 

 but whether into feven or any other number, is not our 

 prefent objedl to enquire. Let A B be a fcreen, receiving 

 the difperfed pencil in a darkened room, and /^ will be the 

 ray of mean refraftion, fh will be the red ray, or ray of 

 leaft refiaftion, and f i will be the violet ray, or ray of 

 greateft refraftion, h i being the length of the coloured fpec- 

 trum. Let this prifm be of crown-glafs ; then fubftitute 

 another of flint-glafs, exaftly in the fame fituation, and the 

 extreme rays, /; and /, will now be difperfed to H and I, and 

 the diftance between thofe new points will be the length of 

 the fpeftrum with flint-glafs. Now the angle ^/B with 

 both prifms is called the angle of deviation, or of mean re- 

 fraftion ; the angle ifh is called the angle of difperfion with 

 the crown, and I /H the fame with the flint prifm ; out 

 thefe angles of dilperfion are fubtended by the lines ih and 

 I H refpeftively, which are the lengths of their refpeftive 

 fpeftra, which therefore are the meafures of the angles of 

 difperfion of the two different prifms. Martin found thefe 

 exaftly as 3 : 5, and therefore recommended the geometrical 

 foci of the crown and flint glaffes to be altuiys in this 

 proportion ; but Tulley has found that this ratio will not be 

 accurate with all fpecimens of flint-glafs, and therefore 

 takes a different ratio, for each fpecimen of glafs that differs 

 in this quahty, from Martin's. In the fame fpecimen of 

 glafs, the angle of deviation always bear» the fame propor- 

 tion to the angle of difperfion, or diffipation as it is fome- 

 times called ; and it was the opinion of fir Ifaac Newton 

 that this is the cafe in all fpecimens ; but it remained for 

 the fenior Dollond to difcover, which is the bafis of all 

 achromatic conftruftions of an objeft-glafs, that the angles 

 of deviation may be the fame, when the angles of difperfion 

 are not the fame, and vice verfd ; and we haive a ftriking in- 

 ftance in crown and flmt glafs, in which, when the difperfive 



powei^ 



