TELESCOPE. 



proper quantitv for the fum of both the convex lenfcs ; then 

 'T being found = ..^,6. and T = .112 in each convex, we 

 (hM have A = 1.668 x 2 X .112 = .1871 for each con-, 

 vex, and 'A = 1.376 X .136 = -1871 alfo, for the concave, 

 and confequently the ratio of r : R as 1. 01 : I ; then by 

 ulniK the proper theorems, as before dn-eded, thefe radn 

 W.11 come out r = 20.,". =>"d R = 20.37 m each convex, 

 while the concave will have each of its radn = 16.9, as 

 originally affumed ; and if the difperfive was great enough 

 for the refractive power, as above fpecified, not only vyould 

 the objea-glafs be acbromalic, but its focal length would be 

 = 30. But we llnd the geometrical F = 10.24, ^"'^ '■'^' 



f,,aed F = ^J = 9-696, and r« = T^"^= "^-'"^ " 



, . , , 'F X F ^ . 1 4.107 X 9-696 _ 

 'F refrafted, and j^—-^^ = *, gives — ^^^ _ 9.696 - 



' 3^-78 1 _ J ^.gj.y ^jj^j^. . and hence we infer, that the 

 4.451 

 difperfive and refradive powers are irrational in this 

 calculation, and the excefs in the focal length is double 

 the quantity with thefe two convex lenfes, B and D, 

 to what we found it with one, in a double objeft-glafs, 

 in our former examination. We are not however dif- 

 pofed to depreciate the mathematical labours of a man, 

 whofe memory «-ill always be dear to every lover of 

 fcience, and whofe article Telescope in particular has 

 obtained tlie enconaium of an eminent contemporary mathe- 

 matician ; but we have felt it our duty to point out the 

 fource of inaccuracy, which, by entering into the data, has 

 affefted the refult of long and tedious calculations, and may 

 have given much trouble to many, as we know it has done to 

 fome opticians, who have attempted to copy thofe refults in 

 praftice. The learned profeffor has indeed ftated, as he 

 proceeds, that the value of certain appreciable quantities has 

 been neglefted, to fimplify the procefs ; and if thofe 

 quantities had affefted the focal diftance more, and the ratio 

 of the radii r : R, and alfo that of F : 'F lefs, the refulting 

 prifmatic and fpherical correftions might have been more 

 perfeft, even with a defeft of difperfive power, than we now 

 find them. We have not room, however, to enter farther 

 into particulars. 



From Dr. Brewfter's experiments, made in his " Trea- 

 tife on New Philofophical Inftruments," it appears that 

 \he green ray is not always in the middle of the folar fpeftrum, 

 and that with rock-cryllal it is at the oppoiite fide of the 

 middle from what it is in glafs ; hence TuUey infers, that if 

 (rlafs could be found of the fame difperfive power as rock- 

 cryllal has, the intermediate colours might be correfted 

 as well as the extreme colours ; and that the fecondary 

 fpeftrum woiJd difappear. To effctl this improvement, 

 the convex lens of rock-cryflal mull be at one fide of the 

 concave of flint, and the convex of crown or other glafs, 

 with equal difperfive power to that of the cryftal, muft be 

 at the other fide. This objetl is worthy of the optician's 

 future confideration and purfuit. ' 



Cekjlial achromatic Eyc-pifces We have already explained, 



in the former part of this feftion, how the focus of two 

 glafles, placed at a gi-ueit dijlance from each other, may be 

 afcertained, and alio what is the focus of a fingle imaginary 

 lens that fhall be equal to them both in power : we propofe 

 therefore prefently to return to the fame figure, {J!g. 8. 

 Plate'KXlV.) in order to (hew what the advantage will be 

 in point of diflinclnefs, which is as effential a quality in an 

 eye-piece as power. But, in the firil place, let us fuppofe 

 '^^fis- 1°- t^e points I, 2, and 3, fo many points of an ob- 



8 



jeft, of which the image is formed at F, after pafling 

 through any lens A B ; then as the point I has rays ilTuing 

 from it, that fall on every part of the lens, and as thefe 

 rays are differently refraifted at different diflanccs from the 

 axis, both towards A and towards B, there will be feveral 

 iinages of this point at the focus F, lying contiguous to each 

 other ; but the rays that come to a focus, after paffing in 

 and near the central part of the glafs, will form their images 

 very clofely together, fo as very nearly to coincide. The 

 fame will be true of the points 2 and 3 feparately confidered, 

 under the fame circuraflances, fo that while the fingle lens 

 A B continues to produce both prifmatic and fpherical 

 aberrations, there will be a confufion or indijlindnefs in the 

 image, arifing from a promifcuous mixture of a number of 

 contiguous and nearly coincident images arifing out ot the 

 fpherical figure of the lens, as well as fringes of colour 

 arifing out of the difperfion of the differently refrangible 

 rays. This indiftinftnefs is more confiderable in a lens ufed 

 as an objeft-glafs, than as an eye-piece ; becaufe the image 

 formed Ijy it becomes an obje<3; to be viewed by means of 

 the eye-piece, and therefore any diftortion, confufion, or 

 colouration that exifts in the image, will be magnified by the 

 eye-piece ; and the greater the magnifpng power, the greater 

 will be the evil produced thereby. To obviate this confe- 

 quence, which will exift partially, even when the beft com- 

 pound objeft-glafs is ufed that art can accompHfh, the fingle 

 eye-glafs has been laid afide, and a fyftem of glaffes fubfti- 

 tuted, that will admit of a high power in the eye-piece, with- 

 out a proportionate increafe of indiftinftnefs or of colour 

 in viewing the image. The firfl arrangement of two glaffes, 

 as a fubftitute for one, to be ufed as a celeflial eye-piece, 

 where invcrfion of the objeft is not material, was calculated 

 and appHcd by the ingenious Huygens, who, not aware that 

 the prifmatic aberration could be cured by an oppofition of 

 difperfive powers, according to DoUond's noble difcovery, 

 devifcd the method of reducing the quantity of fpherical 

 aberration by dimjion ; and the refult of his inveiligations 

 was, that two plano-convex lenfes, (which have each but 

 little aberration in their befl pofitions,) when placed at fuch 

 a diflance from each other that their focal points, for pa- 

 rallel rays, might coincide, would have fuch a compound 

 focus, as would not only greatly increafe the power, but Hill 

 more diminifh the fpherical aberration. An arrangement of 

 this fort was put into the hands of W. Molyneux by Mr. 

 Flamftead in the year 1686, of which Molyneux determined 

 the compound focus, depending on the radii of curvature of 

 the two glaffes and the diftance between them, in the man- 

 iier we have above explained. But the firfl mathematician 

 who gave the rationale of the advantage to be derived from 

 a combination of lenfes, as they have reference to the fphe- 

 rical- aberration, was fir Ifaac Newton, whofe method of 

 explaining it Martin has given in his New Elements of Op- 

 tics, parti, p. 27, thus: " Let NBM {fig. 9.) be the 

 fpherical furface of a plano-convex lens N G M B ; C the 

 centre ; C B the radius or femi-diameter taken in the axis ; 

 A N an incident ray ; and N K the fame refrafted, cutting 

 the axis produced in the point K. Alfo let F be the focus 

 of parallel rays which pafs through the glafs infinitely near 

 to the axis : let F D be a perpendicular to the axis in the 

 point F, then will K F be the curve or difference of the 

 focal diftance of parallel rays which are incident near the 

 axis, and at the diftance G N, the femi-aperture of the 

 lens. This is called the aberration of the extreme ray in 

 longitude. Again, let any ray (fln) be incident on the other 

 fide the lens, at the diftance b G, the refrafted part of this 

 ray, nd, will interfeft the other refrafted ray ND in the point 

 Q, at the perpendicular diftance Q O from the axis. This 



is 



