ency of an objective. When applied to objective 

 mountings or used in tables it is abbreviated to 

 N. A. The formula by which computations are 

 made is N.A.=( sine u) in which N. A. is numerical 

 aperture, n the index of refraction of front 

 medium and u one-half the angle of aperture. 

 Since the media are air, water or oil it is necessary 

 to know the refractive index of each, which is 1.0 

 for air, 1.33 for water, 1.5 for oil and for the ordi- 

 nary crown glass the index is the same as for oil. 



To illustrate this formula better we will take an 

 example. A dry objective inch focus has an 

 angular aperture of 100 degrees. By reference to 

 a logarithmic table we find that one-half of the 

 sine of 100 degrees is 0.766 and we know that n, 

 the medium in front of the objective being air, 

 has a value equal to 1.0. The formula then is, in 

 figures, N. A.=n or 1.0 X u or 0.766=0.766. 



To make this computation we have all figures 

 except that of angular aperture at hand. This 

 must be determined and the method for accomp- 

 lishing it will be given in a succeeding chapter. 



As a rule the designation as to power and 

 numerical aperture engraved on the mounting of 

 an objective from a responsible firm can be relied 

 upon as being quite close, the variations seldom 

 being greater than is incident to accurate human 

 handi-work and such variations as do occur, have 

 little influence on the optical capacity. It is mani- 



