often exceeded in photography, where actual magnification can be in- 

 creased at will by increasing the distance between eyepiece and film. 

 Moreover, the residual aberrations of most lenses cause the image to 

 degenerate long before the theoretical limit of magnification is reached. 

 In general practice, the old rule that "the useful limit of magnification 

 is one thousand times the N.A." is a useful one to follow. For example, a 

 X45 objective working at an N.A. of 0.85 will be stretched beyond its 

 useful limit with a x20 eyepiece but will probably stand a Xl5 eye- 

 piece. 



Two methods of designating the primary magnifications of objectives 

 are still in use. The obviously intelligent one, followed by most contem- 

 porary manufacturers, is to engrave the actual figure on the lens barrel. 

 The older method, still all too frequently seen, and given for comparison 

 in the table of magnifications, is to engrave the "equivalent focus." When 

 this equivalent focus is given in inches— e.g., % in., % in., % in.— it has 

 some actual meaning. The equivalence, in this case, is to the magnifica- 

 tion of a simple lens at a distance of 10 in. A simple lens of 1 in. focal 

 length will cast an image magnified ten times at a distance of 10 in. 

 Similarly a %-in. lens will give a X20 image at the same distance, or a 

 %-in. lens a Xl5 image. It is therefore relatively easy, when a lens has 

 E.F. y 6 in. engraved on the barrel, mentally to convert to X60. The 

 engraving of E.F. in terms of millimeters is a stupidity of Teutonic origin 

 that should never have originated and is unforgivable when used by 

 American manufacturers. To interpret, for example, E.F. 2 mm, it is first 



