TELESCOPE. 



= r ; and the refult of our calculation will (land thus ; 



wz. 



^. „ w y*- =2i.35l F=j8-24.an'lA= 1.93 



F.rft convex B | ^ ^ ^^^ J ^ T = .2432- 



-, ^ fV = 13.9 1 'F = 13.9, and 'A = 



Concav* C |,j^ ^ ,^_^ I ,.4715 X 'T = .2432. 



fr = 21.357 F= 18.24, and A = 1.93 

 IR == 15.93 J X T = .2432. 

 fF X F 



Second convex 



Alfo 



= i3 



9.12 



LF+ F 



f'F X (?) 

 And - - - |,p3-^ = * - 30-0 



It is hardly leceffary to obferve, that the quantities T and 

 'T arc here given in numbers, for the fake of illiiftration ; 

 but when the quadratic equation is worked, thofe fymbols 

 mav be externiinated, and their values involved in the 

 procelb 



A t .b:.- of radii for triple objeft-glaires, in which the 

 two convex lenfes of crown-glafs, and the one of flint, have 

 rcfpeftively the fame refraftive and difperfive powers as in 

 Table I. and V = 'R. 



Table VIII Radii of triple achromatic Objeft-glafles. 



ample ; but let the radii of the concave be unequal ; r/a, 

 '/• : 'R :: I : 1.23, and in the befl pofition ? 



In this example we propofc to abridge the work thus ; 



fu-ll, 'A - 1.507 X 'T and z = '.883, and '-^ = ^°-^ 



» .883 



= 1.33 X 'T = 'A con-efted ; then — -^^f ,^-^— ) = 

 ^^ 1.524 V'F rat./ 



.873 X T for the proportional aberration of the fubftituted 



lens E, as before ; which is an impoffible quantity. The 



focus of this fubftituted lens, as in thelail example, is 9. 1 2, 



and confequently 9.12 x 2 = l8.24is again the focus of one 



of the two convex lenfes tq be ufed, that of the concayc 



13.0 



being, as before, 13.0 (for ^is — Q.12) ; whence')- 



1.524 ' 



and 'R will be 12.6 and 15.5 refpcftivcly. T, as before, t:^ 

 = .126, and 'T = -1653 (by calculation) ; hence'T x 1.33 

 = .2198 is the ahfolute aberration of the concave lens, as 

 well as that of each of the two convexes of 18.24 focus; 



therefore' — ^ = 1-745 X T = A of one of thofe lenfes, 

 .126 



and the root of the quadratic arifing out of this equation of 

 A, gives the ratio of the radii, where R is unity, thas ; as 

 R : r ;: I : I.I ; and the rational focus, by the proper theo- 



r 1 '8.24 . T, r 1 



rem, is 1.048 ; coniequently ^ = 17.401s =: R of each 



convex lens, and 17.40 x i.i = 19.1413 = r; fo that 

 we have now the fubjoined refults ; ti'fx,. 



Convex 



„ fr = 19.147 F = 18.24, a"<i A = i'747 



^ tR = 17-40]" X T = .2198. 



p fV = 12.60") 'F = 13-9, and 'A = 1.33 



^ I'R - 15.50J X 'T = .2198. 



Convex D \' = ^'^•'4 ^ = '^•'+' '"'^ ^ = '-7+7 

 |R = 17.403 



Concave 



X T = .2198. 



Alfo 



fc5 = 9.12 for the compound 



focus of B and D. 



And 



("<!)=: 30.0 for the compound 

 " I focus of B, C, and D. 



The following is a table of radii for triple objeft-glafles, 

 where the refraftive and difperfive powers are as in the laft 

 example, but where the radii of the concave are unequal, wsu 

 '/•:'R :: I : i.l. 



Example 9. — Let it be required to conftru^ another 

 triple objea-glafs of 30 mches focal length, witll^crown and 

 flint-glafs cxaftly fimilar to what was ufed in the laft es- 



Table 



