504 Dr. G. J. Stoney on Microscopic Vision. 



written 



g=-?r, . . . . . . . (5) 



M 



and G (called by Abbe NA) = jB, . . . (G) 



B being the radius to the border of the disk of light seen on 

 looking down the tube. It appears from these formulae that 

 the grasp of any particular beam is simply proportional to the 

 radius in image x out to the punctum into which that beam 

 is concentrated ; so that we may put the above formulae into 

 the simple form of words — g is proportional to r, on the same 

 scale on which G (the numerical aperture of the objective) 

 is represented by R (the radius of the disk of light seen on 

 looking down the tube of the microscope). This excessively 

 simple rule will be found of great use in carrying on practical 

 microscopical work. It may be symbolized by the equation 



'•=§' (7) 



Image C is in the medium c continued downwards. It 

 therefore lies in a plane parallel to and close to the objective 

 plane, but not necessarily coincident with it. Let us call 

 this plane the image plane, in order to give it a name. We 

 have spoken of the image as lying in this plane, but the phrase 

 must here be understood in a generalized sense. What is 

 meant is, not that the image is flat, but that the image plane 

 is related to image C in the same way that the objective 

 plane is related to the microscopic object. 



Consider now one of the beams that form image C. The 

 positions in that beam that are in the phase at the time t, 

 are a system of parallel planes transverse to the beam and 

 separated by intervals of A/ from one another. These planes 

 intersect the image plane in a system of parallel lines, which 

 are separated from one another by intervals 5=X'/sin a } a being 



* In dealing with such matters as are discussed in this section, the 

 reader should note that g, g', &c, the grasps of individual beams, though 

 of cypher dimensions are not mere numbers. They are directed quantities, 

 each standing out in some definite longitude, perpendicularly to the optic 

 axis. Each accordingly consists of a vector combined with a scalar. It 

 is thus that they can be fully represented both in direction and magnitude 

 by the radii r, r', &c. in image x, the radii from the optic axis out to 

 the pun eta of their respective beams. It is otherwise with G, the grasp 

 or numerical aperture of an objective, the direction of which is immaterial, 

 and of which, therefore, the scalar part is the only one to which we need 

 pay attention. G is adequately represented by R, where II is the length 

 of a radius of image x irrespective of its direction. 



