Dr. Gr. J. Stone J on Microscopic Vision. 



501 



Under these circumstances the light after reversal will 

 form image C, L e. standard image No. 2, in the extension 

 downwards of medium c. If the light be allowed to advance 

 farther down, and then to suffer another reversal, it will in its 

 subsequent upward journey re-form standard image No, 2, 

 and then continuing past it, will fall upon the front of the 

 objective in exactly the same state as the light that came 

 from the microscopic object would have done. We shall 

 find the state of things which is here sketched to be much 

 the most convenient for our purpose. 



We may accordingly remove everything that lies below the 

 objective except medium c 9 which is to be extended down- 

 wards, and we may substitute image C («. e. standard image 

 No. 2, formed as above described in medium c after two 

 reversals) for everything so removed. We have thus only to 

 picture to ourselves image G as present in its proper position 

 in medium c and as emitting its light upwards. This light 

 is resolvable into beams of uniform plane waves, each of 

 which has its own axial ray, viz. : that ray of the beam which 

 starts from o, the point where image C is pierced by the axis of 

 the microscope. Accordingly all axial rays diverge from o, 

 and after passing through the objective they all converge to, or 

 rather nearly to, another point s on the optic axis, at D. If 



-Ok*--- — - 



a and /3 are the angles which one of these rays (or one of 

 these beams *) makes with the optic axis at o and s, then 

 Lagrange's theorem states that 



n sin a=M sin ft, (1) 



where M is the number of times that the linear dimensions of 

 image D are larger than those of image C, and where n sin a 

 is that which Abbe calls (when applied to the most inclined 

 ray from o which the objective can admit) the " Numerical 

 Aperture " of the objective, symbolizing it by the letters N A. 

 These — the name and the symbol — are a too limited name, 

 and an inconvenient symbol. I therefore propose instead to 



* We may speak of a and /3 as the inclinations either of the axial ray, 

 or of the beam to which it belongs. With some objectives image x lies 

 inside the objective, with some eyepieces D lies inside the eyepiece ; and 

 the diagram &c. will need to be modified accordingly. 



Phil Mag. S. 5. Vol. 42. No. 259. Dec. 1896. 2 N 



