4: THEORY OF THE MICROSCOPE. 



actual theories of Gauss, with some abridgments and modifications, 

 which will facilitate their comprehension by non-mathematical 

 readers. It will be sufficient, here, if we summarize the most 

 important of his conclusions, and demonstrate the points of differ- 

 ence and analogy which exist between an infinitely-thin lens and 

 systems of lenses. 



An infinitely-thin convex lens (that is, one whose thickness 

 as compared with its radii of curvature may be disregarded) has 

 the property of transmitting rays which are directed to its optical 

 centre without refraction, and of uniting incident parallel rays in 

 one point, the principal focus. 



If a & (Fig. 2) is the givpn lens, C C' its axis (that is, the line in 

 which the centres of curvature lie), E its optical centre, and F F* 

 two points at a distance from the lens equal to its focal length, 

 through which two planes are drawn at right angles to the axis ; 

 then the rays which start from a point in the plane F will emerge 

 from the lens as parallel rays, and, conversely, rays which are 

 parallel when they enter the lens will be united in one point in 

 the plane F*. To every incident cone of rays, whose apex lies 

 in the plane F, there corresponds an emergent cylinder of rays, and 

 to every incident cylinder of rays a corresponding cone of rays 

 whose apex lies in the plane F*. If the rays, in addition to being 

 parallel to each other, are parallel to the axis of the lens, then 

 their point of union is situated on the axis at the other side of the 

 lens, that is, at F or F*. 



On this property, coupled with that possessed by spherical 

 surfaces of so refracting rays proceeding from a point that they 

 (or their prolongations) again intersect in a point, is based the 



