86 
THE QUANTUM [ V i. 2 
accustomed to a material magnet setting with its axis in opposi 
tion to the field, but with these elementary magnets the case is 
different. Let us consider, then, an atom possessing a magnetic 
moment ± M, with the vector in the direction of the field, i.e. 
either in the parallel or in the anti-parallel position. When the 
field is not homogeneous such an atom will experience a 
mechanical force proportional to the magnetic moment and to 
0H 
the gradient of the field, i.e. to — where H is the field 
os 
strength, and s is distance measured in the direction of the field 
gradient. We know that a simple magnet placed in a uniform 
field merely turns on its axis but does not move bodily. When 
the field is not uniform, forces tending to produce translation do 
arise, and are determined by the product of M and the gradient 
of the field. 
Let a stream of these magnetic atoms impinge and make 
a record on a plate perpendicular to their direction of motion. 
Then if the stream has a circular cross section, in the absence 
of a field the trace will be a small circle. When the field is 
applied, two circles should be seen if it be supposed that all 
the atoms have the same velocity, for the magnetic moment 
in the direction of the field may be either positive or negative. 
If, however, the velocities are distributed according to Maxwell’s 
law, the traces will be elongated, but there should be a minimum 
effect in the undisplaced position. 
On the classical theory all orientations are equally prob 
able, and it can be shown that with Maxwellian distribution of 
velocities there should be an intensity maximum in the zero 
position. 
Here then, there is a marked difference between the results 
given by the two theories, and this affords a crucial method for 
distinguishing between them. 
2. The Experiments of Gerlach and Stern 
Striking confirmation of the theory of quantization in space 
(“ direction quantization ”) has been afforded by the wonderful 
experiments of Gerlach and Stern.* A stream of atoms of 
vaporized silver was allowed to flow in a high vacuum of the 
order io~ 4 to io~ 5 mm. of mercury, past the edge of the wedge- 
shaped pole of an electromagnet which produced a strong but 
non-uniform magnetic field. The silver atoms were deposited 
as a thin invisible layer on a glass plate placed immediately 
* Gerlach and Stern, Zeits. f. Physik, vol. 8, p. no, 1921 ; vol. 9> 
pp. 349 and 353, 1922.