AND A SIMPLE APERTOMETER DERIVED THEREFROM. 7 



of 0*1, 0*2, 0*3, and so on. These circles would, as is obvious 

 from a consideration of equation 11, project into the upper focal 

 plane of any objective as a number of equi- distant, concentric 

 circles, but they would not, in general, be of equal thickness. 

 To secure this object, it is necessary to calculate, for each circle 

 on the diagram, a thickness which corresponds to an equal 

 increment of the N.A. Thus, instead of calculating the radius of 

 a circle to project as equivalent to a N.A. of 0*5, say, it is better 

 to calculate for 049 and 0*51, draw the two circles, and blacken 

 the space between them. The difference between the N.A. 

 represented by the circle of the inner edge of any line and that 

 represented by the circle of the outer edge is thus in every case 

 equal to 0*02 N.A. The following table has been calculated in 

 this way for a value of A = 1> anc ^ f° r N.A.'s commencing at 

 0*1 and proceeding by steps of 0"1 to 0'9. 



To use this table for the calculation of the radii of the N.A. 

 circles for any other value of A , it is only necessary to remember 

 that R must be read in the unit selected for A, and must be 

 multiplied by it. Thus if A be taken as 2 inches, each number 

 under r must be multiplied by 2, to obtain the desired radii in 

 inches, Similarly, if A be taken in centimetres, R must be 



