198 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1944 
the spacings between their atoms. Von Laue suggested that if a beam 
of light were directed across a crystal and made to strike a photo- 
graphic plate, there would appear a spray of narrow rays each com- 
posed of a single wave train instead of the broad fanlike arrange- 
ment of the grating, and a pattern of starlike spots where the rays 
come in contact with the plate instead of the dark irregular blot 
when a grating is used. Of course, the rays are disposed according 
to the spacings of the atoms in the lattice and according to the char- 
acter of the lattice. Von Laue confirmed this idea for waves short 
enough to be so diffracted and then advanced the theory that this 
principle might hold true for X-rays as well, which theory was almost 
immediately confirmed by Friedrich and Knipping. Shortly after 
Schroedinger began to develop De Broglie’s wave theory of electrons, 
Elsasser conceived the idea that possibly these tiny particles might 
also be diffracted by crystals, and Doctors Davisson and Germer, of the 
Bell Telephone Research Laboratories, using as part of their appara- 
tus an electron gun, set out to test and to prove this theory. Due to 
their experiments and those of G. P. Thomson, it was established 
beyond a doubt that electron beams are diffracted just as are X-ray 
beams. However, it was also demonstrated in the course of these ex- 
periments that electrons of slow speeds and feeble kinetic energies are 
unable to penetrate the crystals. It was Thomson who utilized faster 
electrons and demonstrated that not only are electrons diffracted like 
X-rays, but like X-rays also they make an imprint upon a photographic 
plate at increased speeds. These three men, together with others, then 
measured the wave lengths which they compared with the momenta 
of these electrons by their diffraction. To these experiments and 
measurements were then applied the following rules of correlation: 
“Energy (/) is proportional to frequency (v), and momentum (Pp) is 
inversely proportional to wavelength (lambda), the same constant (2) 
appearing in both relations. (Frequency is interpreted as the velocity 
(V) of the waves divided by their wavelength.)” These rules can be 
applied mathematically to the electron microscope to illustrate better 
the principles of its operation. In making use of the first rule, how- 
ever, it is necessary to substitute “voltage” for “frequency,” and in so 
doing, therefore, the rules of correlation explain the increase of energy 
in relation to the increase of voltage as well as the increase of speed of 
electrons in relation to the decrease or shortening of wave length when 
we say the higher the voltage, the greater the speed; hence, the shorter 
the wave length of electrons. It is interesting to note in passing that 
a 150-volt electron has a wave length of one Angstrom unit, this being 
more than 10-° times smaller than the wave length of visible or 
ultraviolet light. 
Because the wave lengths utilized in an electron microscope are so 
much shorter than those employed in an ordinary light microscope, 
