382 JAMES HILLIER 



ing power but rather that the light used, being periodic in nature, 

 obeyed the laws of diffraction. On calculating the diffraction effects 

 for a microscope, Abbe found that it was incapable of resolving details 

 in the object separated by much less than half the wavelength of the 

 illumination used. While there has been much discussion in the 

 literature as to the precise meaning of Abbe's theory, and as to the 

 exact method by which it should be applied, the fact remains that his 

 well known formula d = 0.61X/(n sin a) provides a reasonably ac- 

 curate estimate of the resolving power of a microscope system (n is the 

 refractive index of the medium in which the object is placed, a is the 

 angle subtended at a point in the specimen by a radius of the objec- 

 tive, and X is the wavelength of the light used) . The common param- 

 eters for an optical microscope using visible light and a good oil 

 immersion objective lead to a resolving power of approximately 0.2 

 M (2000 A.). If we standardize on 0.2 mm. as the resolving power of 

 an unaided eye at a viewing distance of 25 cm., it is apparent that 

 the useful magnification of such a system is approximately 1000 X. 



It is immediately obvious that there are many structures found 

 in nature that are beyond the resolving power of such a microscope — 

 the finer structures of cells and bacteria, the entire particle in the 

 case of a virus or a large molecule, have dimensions that lie below 

 200 m/x (2000 A.). At the same time many of these materials have 

 heterogeneous physical structures that cannot be investigated at all 

 successfully by any of the indirect statistical techniques of biochem- 

 istrj^ and biophysics. 



Owing to the natural limitations of refractive materials it has 

 has not been possible to make any outstanding increase in the resolv- 

 ing power by increasing the numerical aperture of the objective 

 system. The remaining possibility, that of using a radiation with a 

 shorter wavelength, was exploited very shortly after Abbe's work. 

 Unfortunately, here too the properties of existing refractive materials 

 have prevented the use of radiation beyond the ultraviolet region. 

 With the ultraviolet microscope resolving powers of better than 

 1000 A. or, in other words, useful magnifications greater than 2000 X 

 are not possible. This was indeed a small gain compared to the two 

 orders of magnitude that were really desirable. 



The electronic solution of the problem came through a rather in- 

 volved series of developments by physicists who were primarily 

 interested in the study of the properties of electrons and electron 

 beams. By the year 1924, it was well known that cathode ray beams 



