M TKl.ESCOPE. 



and by trigonometry, in UM triangle 4 r "' ii"', we hare 



TKLB8COPK 



100 



the focal distance of tho compound leu. 



These value* being reduced to what they become when tho Inoidant 

 ray i-Q i* infinitely near the xi of the lenses ; that U, when the angle* 

 are mibtitiiU>d for their sine*, there may be obtained 



r 



By mean* of these equation*, eliminating the quantitie* ur, NF', and 

 XP', and neglecting powers of t above the first, there may be obtained a 



value of ^p; : then differentiating this value with respect to to M, M' 



and HP"', and making the resulting value of the differential of xr'" 

 equal to zero (which is a condition necessary in order that the chro- 

 matic dispersion may be corrected for rays near the axis), there may be 



1 1 2(^-1) 



obtained a value of , + -,. Again on substituting - for n, 



BO r* 



for B, a* above found, there will reult 



about iU axil, then all the ray* in any pencil proceeding from a very 

 remote object, a* one of the celestial bodies, and being incident on the 

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

 he parabola, converge accurately in the focus of the curve ; and on 

 hi* account, an effort is always made to give to the reflecting surface 

 of the speculum a paraboloidal figure. The advantage does not, how- 

 ever, hold good with the pencils which fall on the mirror in din 

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

 when the telescope i* to be used for viewing terrestrial objects, than 

 when it i* to be employed for astronomical purposes ; for then, on 

 account of the great distance of the objects, the several pencils of light 

 all on the mirror with a very small obliquity to it* axis. 



The telescope invented by Galileo consisted of one convex lens, A n, 

 fg. 6, and of a concave lens, c i> ; the distance between them being equal 

 a the difference between the focal lengths of the two lenses. In this 

 nstniment, if the object o r were so remote that the rays in each 



Fig. }. 



Now the value of Vf'" may be directly computed from the formula; 

 first investigated ; afterwards assuming different values of R', and sub- 

 stituting them in the last equation, let the corresponding values of 

 ts' be found. With these values of a' find corresponding values of 



5PT * ] ) ; Uut "' of ""'' and P roceedin * accordin 8 * **"> 



usual method* of trial and error, there will at length be found a value 

 ' agreeing with that which was computed by the direct process : 

 the four radii will then, consequently, be determined. 



Investigation* relating to the dispersion of light, and rules for com- 

 puting the radii of curvature for achromatic object-glasses, will also be 

 f mnd in an essay by Mr. P. Barlow of Woolwich, printed in the ' Philo- 

 sophical Transactions ' for 1827. 



Thuugh on thus uniting the red and violet light by lenses of crown 

 and Hint glass the chromatic dispersion is in a great measure corrected, 

 lien the image is examined, it U found to be surrounded by a 

 green-coloured fringe. The difficulty of procuring flint glass of miffi- 

 eient purity is also a serious impediment to the perfection of achro- 

 matic lenses for telescopes. The steps that have from time to time 

 been taken to remedy this evil are noticed in the following article on 

 the history of the telescope, [TlLESOOPK, HISTORY or,] but we may 

 here mention that in the ' Transactions' of the Royal Society of K.lin- 

 tmrjih, 1791, there I* given an account of some experiments made by 

 I >r. I'.Uir, from which he wan led to the discovery of the fluid medium, 

 which, being applied twtween lease* of crown glass, renders the com- 

 pound lens completely achromatic. By adding liquid muriatic add to 

 chloride of antimony, or sal ammoniac to chloride of mercury, he 

 mooeeded in obtaining a spectrum in which the coloured rays in each 

 pencil followed the same law of dispersion as takes place in crown 

 Klaat. Therefore, confining a small quantity of either of the*e liquids 

 between the convex surface* of two plano-convex lenses, or between 

 those of a piano and a convex meniscus lens, of crown glass, Dr. Blair 

 obtained an object-glass in which the chromatic aberration was entirely 

 destroyed; and he is said to have thus constructed one of 9 im-he* 

 focal length, and a* much as 8 inches in diameter or aperture. Object- 

 sIsssH so mad* wen for some yean on sale in London ; but either 

 from the crystallisation of the fluids, or the negligence of the artist* in 

 compounding them, the telescopes became imperfect, and gradually 

 f.-ll into disuse. 



Dr. (Sir David) Brewster, in hi* ' Treatise on New Philosophical 

 Instrument*,' recommends the employment of sulphuric acid and <l "t 

 cuvua for UM composition of fluid lenses, by which the secoii'lan 

 pectnim may be destroyed ; the acid being, of all known substances 

 that which exerts the greatest, and the oil that which exert* the least 

 action on UM green-coloured ray*. The correction of the chromatic 

 dispersion by mean* of fluids was alao attempted by Mr. Barlow, a* 

 noticed in the following article, But probably from imperfection* in 

 the form* of the glmms, UM image* of object* were found to be not wet 

 defined ; aad the construction, in consequence, ha* not been adopted. 

 The imag> formed by the great speculum of a reflecting telescope ii 

 free from the inconveniences *<mding the chromatic aberration o 

 light ; fur UM angle* of incidence bring equal to those of reflection, in 

 any pencil coming from a point in an object, all the ray* will converge 



If 



to one point * **" P*** wber * im W formed. If the surface of 

 UM speculum were that which is formed by the revolution of a parabola 



pencil of light might be considered a* parallel to one another, 

 would be formed at its principal focus an inverted image (o p) of that 

 object by the union of the rays in each pencil in one point ; then the 

 concave lens being placed between A B and that image, in such a 

 situation that its principal focus may coincide with the place of that 

 image, the rays 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 tie eye, distinct vision is obtained. 



The line o x o is the axis of the pencil of light from o ; and, as this 

 passes through the centre X of the lens AB without refr.u-tion, the 

 angle z X o is equal to half the angle under which o e would be observed 

 by an eye at x when no telescope is interposed, while (ro n parallel to 

 T o being the direction of a ray in that axis after refraction in c i > 

 is half the angle under which o P is seen in the telescope : the ratio 

 between these angles is therefore the measure of the magnifying power 

 of the telescope ; and since the angles are to one another as Y z is to 



x z, nearly, it follows that nearly expresses the magnifying power. 



Y 7. 



This is the construction of what is called an opera glass ; ami the 

 Galilean telescope is now used chiefly for viewing objects within a 

 theatre, or an apartment, since if considerable magnifying power wen- 

 given to it the extent of the field of view would be very small. 



A simple telescope may also be constructed by means of two convex 

 lenses, fig. 6, which are placed at a distance from one another equal to 

 the sum of their focal lengths. For the image being formed at the focus 

 z, of the lens A R, which is nearest to the object, as in the Galilean 

 telescope, and being supposed to be a plan. ! ,.- li^ht also being 



Fi. 6. 



supposed to be homogeneous, the rays of each pencil, after crossing at 

 the focus and proceeding from thence in .t .liv.-n.-mt -i 

 allowed to fall upon the surface of the secon<l 1ms, .p. may he r.-i . 

 in the latter so as to pass out from thence in parallel directions ; ami 

 consequently distinct vision of the object may be obtaiueil by.. 

 situated so as to receive the pencils. 



If x o be the direction of the axis of a pencil of light coming from 

 O, one extremity of the object o r, which is supposed to be so remote 

 that all the rays in each pencil may be considered as parallel ' 

 another ; then the angle z x o is half the angk- un.ler whirli tlie ohj. <-t 

 o P would be seen by an eye at x without a telescope, while (lie i 

 that pencil entering the eye at p. in the direction n E, which is i 

 to o T, the angle z YO is half the angle under whi.-li : ' >ject is 



seen when viewed through the telescope. Now these angles are to one 



another nearly as z Y to z x ; therefore will express nearly the 



magnifying power of the instrument. As the pencils of light from o 

 and p cross the axis of the eye at E before they are unit, d on the 

 retina, the image of the object o r is formed in the eye in a ] 

 contrary to that which is formed when the object is viewed without 

 the telescope ; therefore, on looking through the latter, the object o P 

 appears to be inverted. 



But the image formed at op, instead of being a plane, is nearly on a 

 portion of a spherical surface whoso centre is at x ; and, on the other 



