OOTOBEE 12, 1917] 



SCIENCE 



349 



electron moves in a strong magnetic field, 

 it follows a spiral path around a line of 

 force. This motion in a spiral path radi- 

 ates energy with a frequency that depends 

 on the strength of the field, and is therefore 

 variable. It is easily shown that in a case 

 where the spiral is tightly wound around 

 a line of magnetic force, the frequencj'^ is 

 given by the equation 



■ Ml 



(2) 



From this equation it appears that the 

 frequency is independent of the velocity of 

 the electron and of the radius of the spiral 

 and that it is practicallj'' proportional to 

 the strength of the magnetic field; and 

 since H varies continuously, the frequency 

 can have all possible values (up to a maxi- 

 mum), which gives the radiation the char- 

 acter of a continuous spectrum. 



Let us combine this conception of gen- 

 eral X-radiation with the experimental fact 

 that the maximum frequency due to the 

 impact of an electron against an atom is 

 given by equation (1). Suppose the elec- 

 tron to be traveling very nearly along the 

 line of force coming from a very great dis- 

 tance, where its velocity is v and let x be 

 its distance from any fixed point at the 

 time t; let -P be the total force acting on 

 the electron in the direction of the weaker 

 magnetic field. Then we can show easilj- 

 that 



h e dH 



2ir m dx 



(3) 



We find, therefore, that a force of repul- 

 sion acting on the electron, the magnitude 

 of which is represented by equation (3), 

 will explain why an electron of given ki- 

 netic energy can not produce radiation 

 higher than that given by equation (1). 



A force such as that represented by equa- 

 tion (3) should hold an electron in equi- 

 librium at a distance somewhat smaller 

 than 10"^ from an atomic nucleus, if the 



nucleus had a charge e and the magnetic 

 moment attributed to atoms and magneton.s. 

 Such a force would play an important role 

 in determining the size and compressibility 

 of atoms, the conduction of heat and spe- 

 cific heats, and a great variety of phe- 

 nomena. "William Duane 

 Hakvahd Univeksity 



THE RELATIONS OF MAGNETISM TO 

 MOLECULAR STRUCTURE 



Maxwell's classical theory of electricity 

 and magnetism contributes little to our 

 knowledge of molecular structure. For the 

 portion of it which deals with material sub- 

 stances is exhibited in terms of quantities 

 for which the process of definition wipes 

 out structural distinctions. It is only 

 through molecular theories of magnetism 

 that magnetic phenomena may be corre- 

 lated with molecular structure. 



Langevin's theory of magnetism ap- 

 pears to be the soundest attempt to formu- 

 late such a theory. He hypothecates the 

 existence in the molecules of every sub- 

 stance of groups of electronic orbits which 

 by virtue of the peculiarities of the struc- 

 ture of the molecules may be so arranged 

 that the resultant magnetic field due to the 

 electronic orbits in a given molecule at 

 points without the molecule may or may 

 not vanish. In the former case the mole- 

 cule is diamagnetic, in the latter magnetic. 



The effect of the application of a mag- 

 netic field to a diamagnetic substance is to 

 change the orbital velocity of any electron. 

 This change is in the proper direction to ac- 

 count for the diamagnetic polaritj^ of the 

 substance. Langevin's theory leads to an 

 expression for diamagnetic susceptibilitj'' 

 which does not involve the temperature, in 

 agreement with Curie's law for diamagnet- 

 ism. Numerous exceptions to this law ex- 

 ist, but the exceptions may probably all be 

 taken care of by a slight extension of 

 Langevin's theory as proposed by Oxley. 



