416 LECTURE XXXV. 



tion. A small portion, however, of any of these curves, differs very 

 little from a circle; and a spherical surface is ahuost universally substituted 

 in practice for all of them, except that the mirrors of large reflecting tele- 

 scopes are sometimes made parabolical. 



The principal focus of a spherical reflecting surface, whether convex or 

 concave, is half way between the surface and its centre. If a luminous point 

 be placed in the centre of a concave mirror, the rays will all return to the same 

 point; if the point be beyond the centre, the image will be between the centre 

 and the principal focus, its distance from that focus being always inversely as 

 that of the radiant point. Such a focus is never absolutely perfect, for the 

 rays are never collected from the whole surface of the mirror into the same 

 point, except when both the point and its image are in the centre: but, 

 provided that the surface be only a small portion of that of the whole sphere, 

 the aberration will be too small to be easily observed : and the same is true 

 of the foci produced by refracting surfaces. (Plate XXVII. Fig. 377, 

 378.) 



When a ray of light passes through two surfaces forming an angle with 

 each other, including a denser medium, as in the case of a prism of glass, 

 it is always deflected from the angle in which the two surfaces meet. A 

 greater number of surfaces, placed in different directions, constitute what is 

 sometimes called a multiplying glass, each of them bending the rays of light 

 into a diff'erent direction. (Plate XX VII. Fig. 379, 380.) ' 



A lens is a detached portion of a transparent substance, of which the op- 

 posite sides are regular polished surfaces, of such forms as may be described 

 by lines revolving round a common axis. These lines may be portions of 

 circles, of ellipses, hyperbolas, or of any other curves, or they may be right 

 lines. But in general, one of the sides is a portion of a spherical surface, and 

 the other either a portion of a spherical surface or a plane; whence we have 

 double convex, double concave, planoconvex, planoconcave, and meniscus 

 lenses. The figures of all these are sufficiently described by their names, 

 except that the term meniscus, which properly implies a little m oon or 

 crescent, is applied in general to all lenses which are convex on the one side, 



