2 The Electron Microscope 



by means of reflecting elements, it can no longer be expected 

 that the X-ray supermicroscope will ever materialize. 



The way for the supermicroscope was opened in the years 

 1924—1926 by three discoveries. In 1924, de Broglie put forward 

 his bold hypothesis of electronic waves. In 1925, Schrodinger 

 discovered wave mechanics by combining de Broglie's ideas with 

 Hamilton's analogy of dynamics and optics. Finally, in 1926, 

 H. Busch discovered the lens property of axially symmetric 

 electric and magnetic fields, and laid the foundations of geo- 

 metrical electron optics. 



It was a sheer coincidence that Busch 's discovery followed 

 so soon on the heels of the other two. \Mien Busch worked out 

 the electron trajectories in axially symmetric fields, he did not 

 think either of wave mechanics, or of the Hamiltonian analogy. 

 Only when he had finished his paper, and showed it to a theo- 

 retical physicist, did he hear the exclamation : *'\Miat a nice 

 illustration of the Hamiltonian analogy !" It may be remembered 

 that Sir William Hamilton wrote his celebrated Memoirs ^ al- 

 most exactly a hundred years before. It is amusing to think that 

 during these hundred years many hundreds of able students 

 studied the Hamiltonian theory of dynamics, and apparently 

 there was not one to ask himself: "Well, if there is such a close 

 analogy between dynamics and optics, what is the dynamical 

 analog of a lens?" Presumably for most students, the Hamil- 

 tonian analogy was merely something to be acknowledged wnth 

 a passing nod en route to the esoteric mysteries of Canonical 

 Transformations and the Last Multiplier. 



Lest experimental physicists might feel inclined to smile at 

 the impractical attitude of mathematicians, it may be recalled 

 that experimenters had in their hand an electron lens for more 

 than 25 years (1899-1926), without noticing that it was one. 

 This was the so-called concentrating coil of cathode-ray tubes, or 

 Braun tubes as they were called at that time. The only thing 

 that can be said in excuse of these experimenters is that their 

 tubes were gas-discharge devices, and if anything queer hap- 

 pened in them, it was easy to blame it on the gas discharge. Only 

 Busch was sufficiently impressed with the ctu'ious effects of the 



