112 BELL SYSTEM TECHNICAL JOURNAL 



must exactly balance one another. In this region Compton sug- 

 gests that the gas is in the state of thermal ionization defined and 

 described by Saha, in which at all times a certain constant percentage 

 of the atoms, depending only on their ionizing-potential and on the 

 temperature, is ionized. If the temperature of the central region of 

 the carbon arc is about 4000°, and the ionizing-potential of the gas 

 about 8 volts, the proportion of ionized molecules will be about right. 



According to one of the newer and stranger developments of the 

 quantum-theory, an atom possessing magnetic moment and sub- 

 merged in a magnetic field is not at liberty to orient itself in any 

 direction whatever, not even momentarily; it may set itself only at 

 certain specified inclinations, such that the cosine of the angle be- 

 tween the direction of its magnetic axis and the direction of the field 

 will have one of certain specified values. Imagine for example, an 

 atom consisting of a single electron revolving in a one-quantum orbit 

 (the smallest possible orbit) about a centre which itself is not magnetic; 

 such a centre might be a simple nucleus, or a nucleus surrounded by 

 a number of electrons moving in orbits so inclined to each other that 

 their magnetic moments cancel one another out. The magnetic 

 moment of such an atom is eh/^irm (e the charge and m the mass of 

 the electron) ; its magnetic axis is perpendicular to the plane of the 

 orbit of the electron. According to the theory, the magnetic axis 

 must point exactly with or exactly against the magnetic field; the 

 cosine of the angle must be +1 or — 1. This was verified last year 

 by Gerlach, who projected a ray of silver atoms (shooting off from a 

 hot rapidly-evaporating silver filament through a small hole) across 

 a magnetic field with an extremely steep field-gradient. The ray 

 divided itself into two, one consisting of atoms with their north 

 magnetic poles pointing directly up the field, the other of atoms 

 turned through 180° relatively to the first set; there was quantitative 

 agreement with the theory. If the outside electron moves in a two- 

 quantum orbit, the magnetic moment of the atom is 2 eh/^irm, and 

 the cosine of the angle may take the values ±1 and the valuesi^; 

 if in a w-quantum orbit, the moment is neh/^irm and the permissible 

 values for the cosine are =bl/«, ±2/«, ±w/w. 6 



The theory also accounts for the normal Zeeman effect. It remains 



to be settled whether the magnetic moments of actual paramagnetic 



substances can be calculated from it. According to the accepted 



6 The condition governing the angle is, that the integrals of (a) the angular mo- 

 mentum of the electron in its orbit, and (b) the projection of the angular momentum 

 on the plane normal to the field, taken around a complete cycle of the orbital motion, 

 must both separately be integer-multiples of the quantum-constant h. The latter 

 integer-multiple cannot be zero, according to Gerlach 's experiment and Sommerfeld's 

 theory. 



