OPTICAL INSTRUMENTS. 



11 



the object-lens, which may be the same 

 focus as that in fig. 16, eee three lenses 

 of equal power. Now, if the focus of 

 each eye-lens e is two inches, as in the 

 former case, then each eye-glass must 

 be placed at a fixed distance of 4 inches 

 from each other ; and the distance be- 

 tween the object-lens o, and the nearest 

 eye-lens, will be 1 inches, this distance 

 increasing as the objects to be viewed 

 approach the instrument. The power 

 of day-telescopes may be calculated in 

 the same manner as the astronomical ; 

 for the two additional lenses produce 

 no effect in the amplification of the 

 objects. 



(18.) The magnifying power of tele- 

 scopes may be ascertained without a 

 knowledge of the foci of the glasses, by 

 means of a dynameter ; this apparatus 

 simply consists of a strip of mother- 

 of-pearl, marked with equal divisions, 

 from the T o to T^O of an inch apart, 

 according to the accuracy required ; 

 this measure is attached to a magnifying 

 lens in its focus, in order to make the 

 small divisions more apparent. When 

 the power of a telescope is required, the 

 person must measure the clear aperture 

 of the object-glass ; then holding the 

 pearl dynameter next the eye-glass, let 

 him observe how many divisions the 

 small circle of light occupies when the 

 instrument is directed to a bright ob- 

 ject. Then by dividing the diameter of 

 the object-glass by the diameter of this 

 circle of light, the power will be ob- 

 tained. 



CHAPTER V. Aberration of Reflectors 

 and of Lenses Glass and Diamond 

 compared Huy gens' Eye Piece 

 Ramsderis Eye Piece Newton" s 

 Parabolic Lenses Chromatic Dis- 

 persion. 



(19.) The field of vision, or number 

 of objects seen by the telescopes^g-s..^ 

 and 16, is very limited, the eye-lenses 

 not being sufficiently large, as is shown 

 by the dotted lines i i mfig. 1 5, which do 

 not enter the eye lens e, and are not 

 received by the eye. Now, if the dia- 

 meters of these lenses were increased, 

 the objects would be rendered indistinct, 

 arising from the rays, spread over the 

 surface of the lens from any point in 

 the object, not being collected again in 

 another point after refraction. This 

 error is occasioned by the figure of the 

 lens, and is called the spherical aberra- 

 tion by figure. 



As a lens is formed with two sur- 

 faces, and, consequently, has two re- 

 fractions, we shall first investigate the 

 aberration of a spherical reflecting sur- 

 face. 



In (2) the focus of a concave sphe- 

 rical reflector was stated to be half 

 the radius distant from its surface ; this, 

 however, is only the case with parallel 

 rays near the centre. When we are 

 desirous of employing specula for 

 telescopes, they require to be made of 

 the parabolic or hyperbolic form, to 

 unite all the rays to one point : the rays 

 that fall on the extreme parts of a sphe- 

 rical reflector, forming an image nearer 

 the speculum than those that fall on its 

 centre. In fig. 17, F is the focus of cen- 



Fig. 17. 



tral rays, and the point/ the focus of the 

 extreme rays A C, while, along the axis 

 from / to F, images from the different 

 parts of the reflector will be formed of 

 the same object ; these, not coinciding, 

 will confuse one another. The quantity 

 F/is called the longitudinal aberration, 

 and will be equal to half the aperture of 

 the speculum squared (a b) 2 , divided by 

 4 times the radius of curvature (d b), or 

 a b 2 . 



^ nearly, in specula whose sur- 

 face is spherical.* 



This spherical aberration produces an 

 indistinctness of vision, by spreading 

 out every mathematical point of the 

 object into a small spot in its picture ; 

 which spots, by mixing with each other, 

 confuse the whole. The diameter of 

 this circle of confusion, at the focus of 

 central rays F, over which every point is 

 spread, will be LK (fig. 17.) ; and when 

 the aperture of the reflector is mode- 

 rate it equals the cube of the aperture, 

 divided by the square of the radius 



The focus of rays reflected by any curve will be 

 equal to half "the distance of the tangent from the 

 centre or half d D for A a. 



