286 EDWARD M. NELSON ON 



it was probably compiled partly from opticians' catalogues. My 

 own list was formed on a plan which, was theoretical, not practical. 

 The plan, consisting of two parts, was very simple ; the first 

 part was to find out the resolving power of the human eye. This 

 was determined from observations of my own sight to be l/250th 

 of an inch at 10 in. The second part of the plan was to find 

 out the N.A. necessary to resolve this amount with a given 

 objective, when used with an eyepiece multiplying by 10 for a 

 long tube {C eyepiece) or 15 for the short tube. In addition, 

 a term " Optical Index " was introduced ^ ; this was obtained by 

 multiplying the N.A. by 1,000, to clear it of decimals, and dividing 

 by the initial magnifying power. Example : — Nominal 2 in., 

 initial magnifying power 6-67 (actually, therefore, a 1| in.), 

 N.A. 0-167, multiply by 1000 = 167, divide by 6-67 = 25 = 

 Optical Index. If the lens was a good one it would resolve, 

 say, 16,700 lines to the inch. Its magnifying power with a 

 C eyepiece would be 66*7, and consequently an eye capable of 

 seeing 250 lines to the inch would be required to observe that 

 resolution, since 66-7 multiplied by 250 = 16,700. Therefore, 

 object glasses to fulfil the conditions of this plan must have an 

 optical index of 25. This rule may be put in other words, viz. 

 each objective must have N.A. 0-25 for each increase in initial 

 magnifying power of 10. Examples, 1 in., N.A. 0-25 ; 1/2 in., 

 N.A. 0-5; 1/4 in., N.A. 1-0; 1/10 in., N.A. 2-5. The higher 

 powers are, however, impossible of construction, hence the plan 

 must be called theoretical. This plan was adversely criticised 

 at the time (40 years ago), but since then this eye-limit has been 

 adopted by oculists, and with the lower powers the N.A. limit 

 has been exceeded. 



The reason for introducing the term " optical index " was for 

 the purpose of providing microscopists with a term similar to 

 that used by photographers, who call the speeds (squares of the 

 aperture) of their lenses U.S. 1, 2, 3, etc. — unity being, as all 

 know, //4. Now //4 is the same as N.A. 0-125, or the aperture 

 that a lens, whose initial magnifying power is 5 (a nominal 3 in.), 

 should possess. 2 



1 Journ. R.M.S. 1893, p. 12. 



2 The precise difference between optical index and x, in f/x, consists 

 in f/x being based on a tangent whereas optical index is based on a 

 sine. With low ratios the difference is negligible, because the sines and 



