198 president's address. 



refracted to another point on the axis /x times further into the 

 glass, viz., one-and-a-half inches from the surface; this second 

 point is called the geometrical focus. This geometrical focus is 

 only true for rays very close to the axis ; rays that are more 

 distant from the axis are aberrated. In this respect refraction 

 differs from reflection, because there is no aberration in a ray 

 reflected at a plane surface. The effect of aberration is to send 

 the ray further into the glass than the position of the geome- 

 trical focus. If the point where any particular ray strikes the 

 plane surface of the glass is distant y from the axis then the 

 aberration of that ray will be T \ y 2 ; therefore, if y in our 

 example is one inch, then that ray will be refracted to a point 

 T 5 ^ inch further into the glass than the geometrical focus, viz.. 

 T9167 inch from the surface. 



This kind of aberration is called positive. Sometimes rays 

 are brought to a focus less distant from the surface than the 

 geometrical focus, in which case the aberration is known as 

 negative.* 



Now let us suppose that instead of a plane surface we have a 

 convex spherical surface of very long radius, the radius being 

 so great that the surface is almost plane, we can see then that 

 the aberration will be similar both in direction and nearly in 

 amount to what it was before, but it will now be called spherical 

 aberration. Next let us make the curve more convex by 

 shortening the radius until the radius is equal to the focus of 

 the incident light, viz., one inch. The incident light now falls 

 on the glass normally or perpendicular to the surface ; there is 

 therefore neither refraction nor aberration ; the rays pass 

 through the glass and meet the axis aplanatically at the centre 

 of curvature. So we see that the rays which were refracted 

 nearly two inches into the glass block get nearer and nearer to 

 the surface as the curvature is deepened until they arrive at the 

 centre of curvature, which is also the point to which the in- 

 cident light converges ; at the same time the aberration, which 



Some writers, however, reverse these terms. In hardly any other science 



does such a difference of nomenclature exist. In some works Hie focus of a 

 converging, or common biconvex, lens, will be called negative. The utmost 

 confusion prevails with regard to the signs attached to conjugate foci and 

 radii of lenses. Changes are sometimes made in the nomenclature of the 

 signs in the same book without any intimation in the text ! 



