TELESCOPE. 



powers are made to balance each other in oppofite direftions, 

 there yet remains a balance of refraflive power in favour of 

 the crown, ariiing from its greater thicknefs, which difpofes 

 colourlefs rays ilill to deviate or be refrafted, but to a more 

 diftant focus than would have been if the crown had been 

 ufed alone. This effeft may be fcen injf». lo, where a pair 

 of prifms, a and i, are infcribed in the double convex lens of 

 crown-glafs, and the pair c and c within the double concave 

 of flint : the incident rays de and ilr, at each fide of the 

 axis go, enter the convex at the points ir and e, and are re- 

 frafted towards the axis, till they meet with the inverted 

 prifms c and c of flint, when they are refraftcd in a contrary 

 diredlion, fo as to prevent their meeting at the point o of 

 the axis to which they tended, and emerge at tiie points /" 

 andy colourlefs, in confequence of the oppofite difperfions 

 which take place in the prifms ; but after emcrfion they 

 tend to a new and more diltant point O in the axis, and 

 there come to an achromatic focus. 



To render this explanation ftill more intelligible with 

 refpeft to the oppojition of two counteracting difperfions, let 

 there be two feparate prifms, placed, as m Jig. il, at a 

 diftance from each other, and inverted with refpeft to each 

 other ; let a 3 c be the prifm of crown-glafs, and ABC 

 a fimilai- one of flint-glafs ; and let two pencils of white 

 light enter thefe lenfes in oppofite direttions, one d, and the 

 other D ; then^ and G will be the rays of mean rcfraftion, 

 h and H thofe of lead, or red ; and «" and I thofe of mod, or 

 violet. Now as the refraftive power of the flint prifm 

 A B C is greater than that of the crown a b c, the mean 

 ray G in the firft will be nearer its prifm, than g, the mean 

 ray of the fecond, to its prifm ; but the angle of difperfion 

 fubtended by H I, will be greater than that fubtended by 

 h i, wliile the prifms have the fame refrafting angles C and 

 e. Now as the refraftion and difperfion in the fame prifm are 

 proportionate to the refrafting angle, thefe may be both 

 reduced to any aflignable quantity by a reduftion of the re- 

 frafting angle ; then let the fide of the prifm of flint C A 

 be ground down till it becomes C K, thereby making the 

 angle B C A, the original refrafting angle, equal B C K, the 

 new refrafting angle ; and let this fecond angle be to the firft as 

 the refraftive power of the crown is to the refraftive power of 

 the flint ; or, in other words, let the refrafting angles C and 

 f be inverfely as the refraftive powers of the two fpecimens 

 of glafs formed into prifms ; viz,, as that oi g fY : G F f; 

 and then the mean ray G will be extended to r, and F c will 

 be parallel toyC ; that is, the mean refraftion of the two 

 lenfes will be ahke, the angle G F/= ^ sf^> by being 

 alternate. In this fif.iation of the refrafting angles of the 

 oppofite prifms, the rays would both enter and emerge 

 parallel as to refradion ; but as to difperfion, that of the flint 

 would ftill predominate a little, or the angle H F I would in 

 fome meafure exceed the angle h fi : but thelo are the angles 

 we want to have equal ; therefore, to make the refrafting 

 angles C and c of the two prifms proportional to the dif- 

 perfme powers, or to the fpeftra h i and H I in_/ff . 9, let the 

 fide B C alfo of the flint prifm be groui'.d down a little to /, 

 fo that the refrafting angle I C i ot this flint, fliall be to the 

 refrafting angle a c i of the crown in this ratio of the 

 fpeftra ; and then not only will the difperfive powers of the 

 two prifms become equal, but, what is equally ntceffary, O 

 will now fall beyond c ; thai is, the refraftive power of the 

 flint by this fecond diminution of its refrafting angle, will 

 become lefs than the refraftive power of the crown, and the 

 difference of thefe powers will refraft the tranfmitted rays, as 

 in fig. 10, finally to the diftant point O, as has been ex- 

 plained, while at the fame time the rays that an-ive tliere 

 will be without colours. If now we tonceive that the re- 



VoL, XXXV, 



frafting an^le of each of the flint prifms f and c, infg. to, 

 infcribed within the concive lens c c, is fo proportioned to 

 the refrafting angle of the prifms a and b, infcribed in the 

 convex lens of crown a b, as the refrafting angle / C i of the 

 fluit prifm u\J!g. n. is to the refrafting angle a c b of the 

 CBown prifm, then the double objeft-glafs ii\ Jg. lO. will 

 be achromatic ; its lenfes being analogous to the corrrft- 

 ing prifms. Thus the theory of a double achromatic 

 objeft-glafs is within the comprehcnfion of our ordinary 

 readers ; and as the triple objeft-glafs has two thin con- 

 vex lenfes of crown, inftead of one thick, to combine with 

 the flint concave one, a farther explanation is unnecef- 

 fary, particularly if the thick double convex be fuppofcd 

 to be divided longitudinally into two plano-convexes, and 

 to be placed one on each fide of the concave : for when 

 thefe plano-convexes are formed into two curves, giving 

 the fame focal diftance each as one of the plaim-couvexes, 

 then the union of tlie three lenfes will be that reprefented in 



fS- 7- 



We may now proceed to exemplify this theory, arifiiig out 

 of Dollond's grand difcovery ; and to make the conftruftion 

 as familiar as poflible, we will avoid all fluxional calculations, 

 and explain fuch algebraical ones only, as are indifpenfable, in 

 the firft example at full length, as they occur, fo that the 

 abridgments in the fubfequent examples may be clearly in- 

 telligible. Our aim dift"ers from that of our predeceflbrs in 

 this refpeft. The illuftrious mathematicians Euler, d'Alem- 

 bert, Clairaut, Bofcovich, Klugel, and Robifon, have given 

 formulae for the calculation of achromatic objeft-glaflcs, that 

 are above the compreheiifion of ordinary opticians ; and Dr. 

 Brewfter has calculated tables, according to thefe formulx, 

 of the different curves that fuit a certain fpecimen only of flint- 

 glafs, and that fuch as is not to be found, at Icaft in Eng- 

 land ; viz. that which has its fines of the Z. of incidence 

 and of the L of refraftion as 1.604 '■ '• Befides, the cal- 

 culations tabulated are not in a praftical form in Table II., 

 the radius of the convex being ftiorter than that of its 

 contiguous concave. On the contrary, we propofe to 

 take glafs that falls in our way, and to calculate in a 

 familiar manner the radii of curvature that fliall fuit fpe- 

 cimens already within our reach. In (hort, our predeceflort 

 fliew how achromatic objeft-glaffes may be made, if proper 

 glafs could be obtained ; and we wiU explain how achromatic 

 objeft-glafles are made, and in the befi manner, vAth glaft 

 of our own manufafture. 



Example i I^et it be required to form a double objeft- 



glafs of thirty inches focal length, from the fecond flint-glafi 

 and crown-glafs given in Tullcy's table of experimental re- 

 fults ? In the crown-glafs, the ratio of the fines of the 

 angles of incidence and of refraftion (m ; n) is 1.528 : 1 { 

 and in the flint-glafs it is 1-5735 : I ; while the ratio 

 of their difperfive powers are .500 ; ,762, or I ; 1.524. 

 The firft ftep is to determine the ratio of the geometri- 

 cal focus of the firft or crown-glafs, to the compound 

 focus of the propofed pair of glafles, in order that the 

 radii of this lens may be kuown, before its proper com- 

 panion, the flint lens, have its focus determined. It will be 

 convenient to call the radius of the convex I, and as it is pro- 

 pofed to have it a double convex, the geometrical focus will 

 alfo be I ; but as the compound focus of both lenfes is 

 the refraded focus always, the geometrical focus I niuft be 

 turned into the re frafted focus alfo, in order to have both of 

 the fame denomination : but to do tliis we want the divifor, 

 which mav be taken from the table, or derived from 



— n . 1.528 — i.ooo 



X J ; thus — — 



n 1 .000 



li 



,528 X 2 = 1.056, ih*- 

 divifor 



