Possibilities oj Future Development 121 



where the energy of the beam electrons, V, has to be substituted 

 in volts. As an example, if we realize at the axis a charge density 

 twice Hull's value, and assume V = 60 kV, Ho = 1,650 gauss 

 will be required to make Le = 1 cm. Therefore, if L = 5 cm, the 



off-axis distance of the trajectory will be reduced to 2e"^ = y^ 



' 1 

 with H = 3,300 gauss even to yTTvvS- The reduction of the focal 



length of the composite lens as compared with the focal length 

 of the first lens is of the same order. Therefore, it does not 

 appear impossible to realize focal lengths of the order of one M-, 

 and magnifications of the order of 100,000 with a throw of only 

 10 cm. 



The focal depth of an objective can be defined as the axial 

 interval or object thickness A^ which can be simultaneously 

 focused within the resolution limit d^. A simple consideration 

 gives. 



dr 



A^ = - (49) 



a 



In present-day microscopes d^ is not less than 25 A, and a not 

 more than 5 X ^0~^, therefore, the focal depth is not less than 

 about 5,000 A or half a micron.* But if Cf can be reduced 



to — — , dr will be reduced to V^.l = 0.316 and a increased in the 



same ratio, which means that the focal depth is reduced by a 

 factor 10, i.e., to about 500 A. This is a considerable advantage 

 in exploring details of objects, but it raises certain difftculties. 

 It might appear that it is an easy matter to keep an objective 



focused within about ^ of its focal length, as it is possible to 



* Practically, often of the order of 10 |^. 



