101 



TELESCOPE. 



TELESCOPE. 



102 



hand, in order that the rays in each pencil may after refraction men 

 be parallel to one another, they ought to diverge from a point nearly 

 in the surface of a sphere whose centre is at Y, the two spherica 

 surfaces being in contact at z : consequently when the distance 

 between the lenses is such that the crossing of the rays in a penci] 

 parallel to the axis takes place exactly at z, the crossing z in one of the 

 oblique pencils will be at a certain distance from the point /, at which 

 it ought to be to permit the rays in it to go out of c D parallel to one 

 another ; the rays of the pencils which proceed from the margin of the 

 object will not then emerge parallel to one another, and consequently 

 that margin will not be distinctly seen. Moreover, from the unequal 

 refrangibility of the different kinds of light, the rays in each pencil 

 will be decomposed in passing through the lens c D, so that though the 

 chromatic aberration were perfectly corrected in the image at p o, it 

 would exist in the image which is formed in the eye by the rays 

 emerging from c D. 



The spherical aberration can only be diminished by diminishing the 

 inclination at which the rays in the marginal pencils fall upon the 

 surface of the lens after having crossed at the focus of the object- 

 glass ; that is, by using a lens of less convexity or of greater focal length ; 

 adding a second eye-glass in order finally to render the rays hi each 

 pencil parallel to one another. Thus, if it be required to preserve the 



Fig. 7. , 



.M II li 



! magnifying power and field of view as might be obtained with any 

 jle eye-glass ; let, as before, X,/jr. 7, be the place of the object-glass, 

 op the image formed by it, and let c D be the place of the single eye- 

 glass : then draw a line o q go as to bisect the angle DOT, which may 

 be considered as the whole refraction produced by the lens c D : let o, 

 on the right or left of op, be the assumed place of what is called the 

 'ia, and draw o n perpendicular to x Y, the axis of the telescope, 

 meeting x D in B ; also through n draw M H K parallel to o q, cutting 

 o o, or o o produced, in H : again draw M x perpendicular to the axis of 

 the telescope, and M R parallel to o i ; also draw R s perpendicular to 

 the axis. Lastly, draw G u parallel to o q to meet x o in n, and u v 

 perpendicular to the axis. Then, from the principles of optics, if a 

 lens be placed at o, having its focal length equal to i; v, and another at 

 R, whose focal length is B N ; the ray x n u will by refraction in the 

 first lens take the direction H 8, and by refraction in the second lens it 

 will take the direction 8 T parallel to o Y or O E : thus the present 

 visual angle s T R will be equal to D E Y, which was obtained with the 

 single eye-glass. 



This is called the Iluijghenian eye-piece, and it U that which is gene- 

 rally used for astronomical telescopes : the object seen through it is 

 inverted, as in the last-mentioned telescope. 



If the places o and K of the two eye-glasses are given (G B being very 

 near op ; its focal length being also known), and it be required to find 

 the focal length of R 8 so that the red and violet rays in each pencil 

 may emerge from it parallel to one another, that length might be 

 determined in the following manner. In a pencil of rays crossing each 

 other at n, //. 8, let am be the direction of_a mean ray,andnr, uv those 



Fig. 8. 



of a red and a violet ray ; these last will make with one another an angle 

 equal to about ,', of the angle D HOT, which may be supposed to be known. 

 Jfi.w, by optical principles, if these rays are to emerge from R s in 

 directions parallel to one another, the focal lengths of the lens for red 

 ami violet rays, namely, R T and R/ must be to one another as 28 to 

 27, and the foci f and / must be in places determined by perpendi- 

 culars drawn to the axis from points w and w, in which the line R w 

 supposed to be drawn parallel to rr' or if', meets Br and B ; that is, 

 by finding the position of a line to be drawn from R to cut the given 

 . .so that R w may be to Rio an 28 to 27. For this purpose, 

 having drawn the straight line II R, the angles u H w, R nw will In- 

 known ; li-t them be represented by a and 6; also let the angle H it w 

 be represented by 9 : then by trigonometry we shall have, after a few 

 reductions, 27 cotan. a 28 cotan. 4 = cotau. 9. 



In order to afford a view of objects in the same position as they 

 appear to have when seen by the naked eye, a telescope may be formed 

 with three lenses besides the object-glass. In the construction of this 



instrument, if attention is paid only to the rays which suffer a mean 

 refraction, the first eye-glass, or that which is nearest to the object-end 

 of the telescope, may be placed between the image formed by the 

 object lens and the eye, with the foci of the two lenses in coincidence ; 

 by this means the rays in each pencil will emerge from the first eye- 

 glass in directions parallel to one another, those of the pencils which 

 are oblique to the axis of the telescope crossing each other at some 

 point in the latter axis. A second eye-glass is then placed at any 

 convenient distance from the former, beyond the place where the 

 oblique pencils cross each other ; and by this lens a second image is 

 formed in a position contrary to that which is formed by the object 

 lens. Lastly, the third lens being placed between this image and the 

 eye at a distance from the former equal to its focal length, the rays in 

 the several pencils will emerge parallel to one another, and an erect 

 image of the object will thus be formed in the eye. 



The ratio between the angles under which an object would be seen 

 by the naked eye, and that by which it is seen in the telescope, is com- 

 pounded of the ratios of the focal lengths of the several lenses ; 

 thus, if : 'uj the focal length of the object-lens, /', /",/'" those of 

 the eye-lenses, reckoned in order towards the eye, the expression 



F ./" 



T, p^> will denote the magnifying power. 



But both the spherical aberration and the chromatic dispersion in 

 such a telescope are very considerable ; and before the invention of the 

 achromatic object-glass, Mr. Dollond endeavoured to diminish the 

 former by an eye-tube consisting of five lenses disposed so as to divide 

 the bendings of the pencils nearly equally between them. Such 

 telescopes are not now used ; and Mr. Dollond succeeded at length in 

 constructing telescopes with four eye-glasses, from which both dis- 

 tortion and colour are removed as much perhaps as a removal ia 

 possible. 



This is accomplished by placing the first eye-glass beyond the imago 

 formed by the object-glass, and at a distance from it less than the 

 focal length of that eye-glass : by this disposition the rays of mean 

 refrangibility in each pencil which diverges from the image are not, 

 after refraction, parallel to one another, but go on with diminished 

 divergency. A little way beyond the place where the axes of tho 

 oblique pencils cross the axis of the telescope there is placed the 

 second eye-glass, which is of such focal length that the mean refrangi- 

 ble rays in each pencil, after passing through it, meet in a point, and 

 thus a second image of the object is formed near the eye : the use of 

 these two lenses, therefore, is to cause the second image to be formed 

 by a gradual convergence of the rays in each pencil. But the several 

 pencils of rays are intercepted by the third eye-glass (commonly called 

 the field-glass), and the second image is thereby formed rather nearer 

 to the first than it would be without such field-lens : from this image 

 the rays hi each pencil diverge, and by the refractive power of tho 

 fourth eye-glass they are made to enter the eye in parallel directions : 

 thus distinct vision of the external object is obtained. The field-glass 

 might have been placed between the eye and the second image, as in 

 the Huyghenian eye-piece before described ; but the aberration arising 

 from the spherical form of the glasses is a little less by the construc- 

 tion just mentioned. 



Now, in each pencil, the red and violet rays which had been united 

 at the image formed by the object-glass, and which there crossed each 

 other, go on from thence diverging from each other till, on the oppo- 

 site side of the axis of the telescope, they fall upon the surface of the 

 second eye-glass : after passing through this lens, the violet ray, which 

 Is always more refracted than the red ray, gradually converges towards 

 the latter, and at length meets it in some place short of that at which 

 the rays of mean refraction unite to form the second image. The 

 practice is to fix the third or field-glass exactly or nearly at the place 

 where the red and violet rays so unite in ail the pencils; for the 

 different coloured rays crossing each other in that place, they aro 

 finally, by the refractive power of the fourth eye-glass, made to enter 

 the eye in parallel directions, and thus afford a view of the object 

 nearly or wholly free from colour. 



In forming the eye-glasses of telescopes it may be observed that 

 they should be such as will allow the incident and emergent pencils of 

 rays to be nearly equally inclined to their surfaces : on this account 

 the first and fourth eye-glasses are of the plano-convex form ; the 

 Bat side of that which is nearest to the object-glass being towards the 

 latter, and that of the other towards the eye. 



Besides the power of magnifying objects, that of affording distinct 

 vision with given quantities of light is often an essential requisite in a 

 telescope, particularly to naval men, who have occasion during the 

 obscurity of the night to keep in view a ship of which they may be in 

 chase. This subject was investigated by the late Sir William Herschel, 

 and an account of his researches on what he calls the " space-pene- 

 .rating power of telescopes " was printed in the ' Philosophical Transac- 

 tions ' for 1800. 



Herschel states that he was aware of this property of telescopes as 

 early as the year 1777, when he had constructed a Newtonian telescope 

 vith a speculum whose focal length was 20 feet : for, ou directing the 

 nstrument to a church-steeple at a considerable distance, he could 

 distinguish the hour by the clock, though with the naked eye he could 

 not see the steeple itself. In order to obtain a formula for the space- 



