REFLECTING TELESCOPE, 89 



at a distance from the vertex, on a mirror of this form, must 

 (as in the case of a mirror of greater radius, i. e. of less cur- 

 vature) have its focus formed farther from it, than if it. 

 were incident near the middle or vertex, wiiere the curva- 

 ture i ". the mirror is that of a circle of lesser radius. 



And thus it is/ievident, that, as the several pencils, re- These error* 

 fleeted by the great mirror, when it is spherical or hyper- ^^^ "jV^^'^l 

 bolical, do not converge, each to a single point, but to a gj^^n gp^^.^, 

 series of points, whose length is the depth of the focus of the lum. 

 mirror; so, neither do these pencils, in proceeding on to 

 the little mirror, diverge each from a single point, but from 

 the same series of points. So that, though the little mirror 

 were formed truly elliptical, it would not make each of 

 these pencils converge again (at the place of the second 

 image, formed behind the first eye-glass) to single points, 

 but to another scries of points ; by which the rays of con- 

 tiguous pencils would be blended with one another, and 

 make the objecf which is viewed, by means of these pencils, 

 so transmitted to the eye, and, by it, refracted to a third 

 scries of points, near the retina, at the bottom of the eye, 

 appear hazy and indistinct. 



These remarks will be applied to our present purpose, by Inductions, 

 considering : 



First. That the rays, reflected by the several annuli, ia 

 the surface of the great mirror, will fall on the annuli of 

 the same order, in the little mirror ; the rays from the 

 outer, inner, or intermediate annuli of the one, proceeding 

 to the like annuli in the other. 



Secondly. That the fartjicr the focus, or point of con- 

 vergence, of any annulus of the great mirror, is distant from 

 that mirror, the nearer will be the point of divergence of 

 this part of the whole pencil, (among the series of such 

 points), to the little mirror. Also, that the interval, be- 

 tween any one point in the series and this mirror, cannot be 

 altered, by moving the mirror, without altering the intervals 

 of all the rest; which, after the telescope is brought to the 

 distinctest vision, cannot be permitted. 



Thirdly. That, if the focus of any annulus, of the g^eat Rationale of 

 jnirror, be farther from it, than those of the other annuli the figure of 

 and, consequently, nearer to the little mirror than those • ^^^ '°^^^-°**''. 

 the rays, issuing from it, to this mirror, will not be reflected 



Vol. XVI.^Feb. 1807* H by 



