TEL 



161 



TEL 



when no telescope is interposed, while (inn parallel to Yo 

 being the direction of a ray in that axis after refraction in 

 CD) ZYo is half the angle under which OP is seen in the 

 telescope : the ratio between these angles is therefore the 

 measure of the magnifying power of the telescope ; anc 

 since the angles are to one another as YZ is to XZ, nearly 



XZ 



it follows that = nearly expresses the magnifying power 



This is the construction of what is called an opera glass, 

 and the Galilean telescope is now used chiefly for viewing 

 objects within a theatre, or an apartment, since if consider- 

 able magnifying power were given to it the extent of the 

 field of view would be very small. 



A simple telescope may also be constructed by means ol 

 two convex lenses, which are placed at a distance from 

 one another equal to the sum of their foeal lengths. For 

 the imasre being formed at the focus Z, of the fens AB, 

 which is nearest to the object, as in the Galilean telescope, 



and being supposed to be a plane surface, the light also 

 bcinir supposed to be homogeneous; the rays of each 

 pencil, after crossing at the focus and proceeding from 

 thence in a divergent state, on being allowed to fall upon 

 tin surface of the second lens CD, may be refracted in the 

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

 and consequently distinct vision of the object may be ob- 

 tained by an eye situated so as to receive the pencils. 



If Xo be the direction of the axis of a pencil of lisrhf 

 coining from O, one extremity of the object OP, which is 

 supposed to be so remote that all the rays in each pencil 

 maybe considered as parallel to one another; then the 

 anirlc ZXo is half the angle under which the object Ol' 

 would lie seen by an eye at X without a telescope, while 

 the rays of that pencil entering the eye at K in the direc- 

 tion D'E, which is parallel to oY, the angle 'L\<> is half 

 the angle under which the same object is seen when 

 viewed through the telescope. Now these angles are to 



one another nearly as ZY to ZX ; therefore ^FTF will ex- 

 press nearly the magnifying power of the instrument. A> 

 the pencils of light fromO and P cross the axis of the eve 

 at E before they are united on the retina, the image of the 

 object OP is formed in the eye in a position contrary to 

 that which is formed when the object is viewed without 

 the telescope ; therefore, on looking through the latter, the 

 object OP appears to be inverted. 



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

 nearly on a portion of a spherical surface whose centre is 

 at X ; and, on the other hand, in order that the ray.s in 

 each pencil may after refraction in CD 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 spherical 

 surfaces being in contact at Z : consequently when the 

 distance between the lenses is such that the crossing of 

 the rays in a pencil 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 z', at which it ought 

 to be to permit the rays in it to go out of CD 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 CD, so that 

 though the chromatic aberration were perfectly corrected 

 in the image at po, it would exist in the image which is 

 formed in the eye by the rays emerging from CD. 



The spherical aberration can only be diminished by 

 diminishing the inclination at which the rays in the mar- 

 ginal pencils fall upon the surface of the lens after ha\ing 

 the focus of the object-glass; that is, by using 

 a lens of le>-s convexity or of greater focal length : adding 



ond eye-glass in "order finally to render the n 

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

 to preserve the same magnifying power and field of view 

 P. C., No. 1508. 



as might be obtained with any single eye-glass ; let, as 

 before, X be the place of the object-glass, op the image 

 formed by it, and let CD be the place of the single eye- 

 glass : then draw a line oQ so as to bisect the angle DoY 



c 

 P 



which may be considered as the whole refraction pro- 

 duced by the lens CD : let G, on the right or left of op, be 

 the assumed place of what is called the field-glass, and 

 draw GH perpendicular to XY, the axis of the telescope, 

 meeting XD in H ; also through H draw MHK parallel to 

 oQ, cutting Go, or Go produced, in M : again draw MN 

 perpendicular to the axis of the telescope, and MR paral- 

 lel to oY ; also draw RS perpendicular to the axis. I^astly, 

 draw GU parallel to oQ to meet Xo in U, and UV per- 

 pendicular to the axis. Then, from the principles of 

 optics, if a lens be placed at G, having its focal length 

 equal to GV, and another at R, whose focal length is RN ; 

 the ray XoH will by refraction in the first lens take the 

 direction HS, and by refraction in the second lens it will 

 take the direction ST parallel to oY or DE : thus the present 

 visual angle STR will be equal to DEY, which was ob- 

 tained with the single eye-glass. 



Thjs is called the Huygenian eye-piece, and it is that 

 which is generally used for astronomical telescopes: the 

 object seen through it is inverted, as in the last-mentioned 

 telescope. 



If the places G and R of the two eye-glasses arc given 

 (GH being very near op ; its focal length being also 

 known 1 !, and it be required to find the focal length of RS 

 so that the red and violet rays in each pencil may emerge 

 from it parallel to one another, that length might he de- 

 termined in the following manner. In a pencil of rays 

 misMng each other at H, let H/ be the direction of a 

 mean ray, and Hr, Ht> those of a red and a violet ray ; 

 these last will make with one another an angle equal to 



ibout ^ of the angle DHm, which may be supposed to be 

 \nown. Now, by optical principles, if these rays are to 

 emerge from RS in directions parallel to one another, the 

 bcal lengths of the lens for red and violet rays, viz. RF 

 ind R/must be to one another as 28 to 27, and the foci F 

 and / must be in places determined by perpendiculars 

 drawn to the axis from points W and if, in which the line 

 [IW supposed to be drawn parallel to rr' or vv', meets Hr 

 ind IIu; that is, by finding the position of a line to be 

 drawn from R to cut the given lines H;-, He, so that RW 

 may be to R' as 28 to 27. For this purpose, having 

 drawn the straight line HR, the angles RHW, RH' will 

 ie known ; let them be represented by a and b ; also let 

 the angle HRW be represented by 6 : then by trigono- 

 metry we shall have, after a few reductions, 27 cotan. a 

 28 cotan. 6 = cotan. 0. 



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



as they appear to have when seen by the naked eye, a 



elescope may be formed with three lenses besides the 



object-glass. In the construetion of this instrument, if 



attention is paid only to the rays which suffer a mean re- 



..n, the first eye-glass, or that which is nearest to the 



>l>ject-end of the telescope, may be placed between the 



inauc, formed by the object lens and the eye, with the foci 



of the two lenses in coincidence ; by this means the rays 



n each pencil will emerge from the first eye-glass m 



liiections parallel to one another, those of the pencils 



vhieh are oblique to the axis of the telescope crossing 



each other at some point in the latter axis. A second 



yc-glass is then placed at any convenient distance from 



he former, beyond the place where the oblique pencils 



ross each other; and by this lens a second image is 



VOL. XXIV. Y 



