150 MICROSCOPIC VISION. 



1. The photometric value of the term. 



The radiation of light from any surface diminishes in 

 proportion to the cosine of the inclination of the raj^s to 

 the normal. This fact may be easily demonstrated by the 

 uniform illumination of a gas globe, for if beams radiating 

 obliquely from the surface were as luminous as similar 

 beams radiating normally, the consequence would be that 

 the peripheral portions of the globe would be far brighter 

 than its central portion. If, for example, we were to cover 

 a spherical football with postage stamps, we should see 

 a great many more postage stamps at the periphery, where 

 they would be inclined obliquely towards us, than in the 

 centre, where they would be in a plane perpendicular to the 

 line of sight. Now if each postage stamp sent one ray to 

 the eye, and the oblique rays were equal in intensity to 

 the direct rays, the periphery must appear much brighter 

 than the centre. But such is not the case ; spherical 

 objects when uniformly illuminated appear equally bright 

 all over, therefore the emission from every point of their 

 surfaces must diminish in the proportion of the cosine of 

 the inclination of the ray to the normal. This means that 

 the amount of light radiating from a point in a homogeneous 

 medium varies as (sin u)^ the square of the sine of the 

 semi-angle of the solid cone. The next point is that the 

 radiation of energy such as light or heat in different media 

 varies as {n^) the square of the refractive index of the 

 media. Therefore the total effect of radiation in any 

 medium is proportional to {n sin if)^, that is, the square of 

 the numerical aperture. 



We now come to that which may appropriately be called 

 the Magna Charta of Microscopy, or the Lagrange, Helm- 

 holtz. Abbe theorem. 



Let u and ti' be the angles of convergence of any ray on 



