T E L 



and by trigonometry, in the triangle QF'"R'", we have 



, ,', "'"QP" 1 



= a 



160 



TEL 



sin. gK'"N ' 



sin. R'"QF'" 

 s j n g 



the focal distance of the compound lens. 



These values being reduced to what they become when 

 the incident ray I'Q is infinitely near the axis of the 

 lenses; that is, when the angles are substituted for their 

 sines, there may be obtained 



It' -! S *S _ i 



MF 



N I " 



. 



NF'~ 



i 



' an 



MF-/ 



y sy 



NF" 



, 



~ 



By means of thec equations, eliminating the quantities 

 MF," NF', and NF". and neglecting powers of / above the 



first. there may he obtained a value of m : then diffe- 



rentiating tliis value with respect to f i. ft', and NF"', and 

 making the resulting value of the differential of NK"' 

 equal to zero (which is a condition necessar)' in order that 

 the chromatic dispersion may be corrected for rays near 



the axis), there may be obtained a value of jr> + g>. Again 



on substituting - - for R, and -^-~ 

 found, there will result 



for 8, as above 



Now the value of NF'" may be directly computed from 

 the formula; first investigated ; afterwards assuming dif- 

 ferent values of R', and substituting them in the last 

 equation, let the corresponding values of S' be found. 

 With these values of S' find corresponding values of 



(sin R'"QF" "\ 

 ' QK"'N +1 ) ' ^^ **' ^ ^'"' anl ^ proceeding 

 according to the usual methods of trial and error, there 

 will at length be found a value of NF'" agreeing with 

 that which was computed by the direct process : the four 

 radii will then, consequently, be determined. 



Investigations relating to the dispersion of light, and 

 rules for computing the radii of curvature for achromatic 

 object-glasses, will also be found in an essay by Mr. P. 

 Barlow of Woolwich, printed in the ' Philosophical Trans- 

 actions' for lsJ7. 



Though on thus uniting the red and violet light by 

 lenses of crown and flint glass the chromatic dispersion 

 is in a great measure corrected, yet when the image is 

 examined, it is found to be surrounded by a green-coloured 

 fringe. The difficulty of procuring flint glass of sufficient 

 purity is also a serious impediment to the perfection of 

 achromatic lenses for telescopes ; and though great ra- 

 wards have been offered for glass which shall be free 

 from defects, the exertions of artists have hitherto been 

 almost without success. Occasionally however flint glass 

 is obtained nearly homogeneous, and the opticians of 

 Germany appear, in this respect, to have been more fortu- 

 nate than those of England. 



The late Dr. Kitchie obtained a disc of flint glass which 

 was. bv Mr. Dollond, formed into an object-glass nearly 

 7 J inches in diameter. It was applied to a telescope 12 

 feet long, and bore a magnifying power equal to 700 times : 

 it is said to have had scarcely any spherical aberration, 

 and to have been very free from colour. (Mem. Atr. 

 .Soc., 1840.) 



In the ' Transactions' of the Royal Society of Edinburgh, 

 1791, there is given an account of some experiments made 

 by Dr. Blair, from which he was led to the discovery of a 

 fluid medium, which, being applied between lenses of 

 crown glass, renders the compound lens completely achro- 

 matic. By adding liquid muriatic acid to chloride of 

 antimony, or sal ammoniac to chloride of mercury, he 

 succeeded in obtaining a spectrum inmhich the coloured 

 ravs in each pencil followed the same law of dispersion as 

 takes place in crown glass. Therefore, confining a small 



quantity of either of these himids between the convex 

 .surfaces of two plano-con\e\ lenses, or between those of 

 a piano and a convex meniscus K-i.-. of crown gla*. Pi 

 Blair obtained an object-glass in which the chromatio 

 aberration was entirely destroyed ; and he is said to have 

 thus constructed one of.) inches local length, and as much 

 a- :> inchi-s in diameter or aperture. Object-gkoe* 10 

 made were lor some years on sale in 1-ondon ; hut either 

 from the crystallization of the fluids, or the negligence 

 of the artists in compounding them, the telescopes hecamc 

 imperfect, and gradually fell into disuse. 



l)r. Sir l)a\id Jircwster, in his ' Treatise on New Phi- 

 losophical Instruments,' recommends the employment of 

 sulphuric acid and oil of cassia for the composition of 

 fluid lenses, by which the secondary spectrum may he 

 destroyed ; the acid being, of all known substances, that 

 which exerts the greatest, and the oil that which exerts 

 the least action on the green coloured rays. Then'. 

 tion of the chromatic dispersion hy means of fluids has 

 also recently l>een attempted by Mr" Barlow, who, in com- 

 bination with a convex lens of crown glass, used a couca\ e 

 lens, consisting of sulphuret of carbon between two u r : 

 (like that of a watch , of each of which the two faces were 

 of equal curvature : this fluid has nearly the same refrac- 

 tive index as flint glass, and its dispersive power is more 

 than double that of the latter material. The crown glass 

 lens and the fluid lens, instead of being close together. 

 were placed at a considerable distance from one another, 

 by which disposition an increased magnifying power might 

 have been obtained without increasing the length of the 

 telescope. Probably from imperfections in the fan;: 

 the glasses, the images of objects were found to be not 

 well defined ; and the construction, in consequence, has 

 not been adopted. 



The image formed by the great speculum of a reflecting 

 telescope is free from the inconveniences attending the 

 chromatic aberration of light ; for the angles of incidi nee 

 being equal to that of reflection, in any pencil coming 

 from a point in an object, all the rays will converge to 

 one point at the place where the image is formed. If the 

 surface of the speculum were that which is formed by the 

 revolution of a parabola about its axis, then all the rays in 

 any pencil proceeding from a very remote object, as one 

 of the celestial bodies, and being incident on the speculum 

 in a direction parallel to the axis, would, by the nature of 

 the parabola, converge accurately in the focus of the 

 curve; and on this account, an effort is always made to 

 give to the reflecting surface of the speculum a parabo- 

 loidal figure. The advantage does not how ever hold good 

 with the pencils which fall on the mirror in directions 

 oblique to the axis; and therefore that figure is of less 

 importance, when the telescope is to he used for viewing 

 terrestrial objects, than when it is to be employed lor l 

 nomica.1 purposes : for then, on account of the great dis- 

 tance of the objects, the several pencils of light fall on the 

 mirror with a very small obliquity to its axis. 



The telescope imented by Galileo consisted of one con- 

 vex lens AB, and of a concave lens CD ; the distance be- 

 tween them being equal to the difference between the 

 focal lengths of the two lenses. In this instrument, if the 



object OP were so remote that the raj's in each -pencil of 

 light might be considered as parallel to one another, there 

 would hi' formed at its principal focus an inverted iinairc 

 op, of that object by Hie union of the rays in each pencil 

 in one point; then the concave Un* being placed between 

 AB and that image, in such a situation that its principal 

 focus may coincide with the place of that image, th< 

 in each pencil will, by the refracting power of the lens, be 

 made to emerge parallel to one another; and in this 

 case, by the optical properties of the eye, distinct vision 

 is obtained. 



The line OXo is the axis of the pencil of light from O ; 

 and, as this passes through the ci ntw \ of the lens AH 

 without refraction, the anirle X\ is equal to half the 

 angle under which OP would be observed by an eye at X 



