Page:Optics.djvu/156

 object or first image at the center of the great mirror: but since the focal length of the mirror is half its radius, this is the same thing as the angle of the first image seen from the mirror. The magnifying power may then be measured by

In order to exhibit this more conveniently, we will put $p′q′⁄pq·Aq⁄Aq′$, $eq′⁄eq·Aq⁄Cq′$, $f$ for the focal lengths of the great and small mirror and the lens respectively, $f′$ for the distance of the mirrors, which is about the length of the telescope.

Then is $F$, $l$, since

$eq=q$ is the focal length of the lens, $eq′=q′$. $1⁄q$ is nearly equal to $=1⁄q′+1⁄f′$ or $eq′⁄eq$, and $q′⁄q$ about the same thing as $=q′+f′⁄f′$ or $Cq′$, so that the magnifying power is nearly

To determine the field of view in this telescope we must join the corresponding extremities of the eye glass and the small reflector; this will mark the extreme points of the second image, and the angle subtended by it at the eye glass, divided by the magnifying power, will show the extent of view taken in at once by the instrument.

This telescope, which was the first reflecting one invented, is found in practice very preferable to Newton's, and in general to Dr. Herschel's, whose construction is fit only for a very large instrument. In the first place it is more convenient than either, as the observer has the object in view before him, and can easily direct the instrument to it; but it has one more solid advantage which is this: the metallic specula never can be worked perfectly true, so