668 HELL SYSTEM TECHXICAL JOVRXAL 



motion of the electron nexer (|iiite ri'jx'als itself. Such a system is 

 called conditionally periodic. 



When we come to consider the atom-models proposed for atoms 

 with more than one electron, we shall make use of these ideas; but 

 that will not occur before the Third Fart of this article. However, 

 one application can be made to the theory of hydrogen and ionized 

 lu'liimi. 



73. Motion, in an Inverse-square Central Field, of an Electron of Which 

 the Mass Varies as Prescribed by the Theory of Relativity 



According to "relati\istic mechanics," as distinguished from 

 "Newtonian mechanics," the mass m of an electron (or an\t]iing 

 else) varies with its speed v in the manner 



m=mo/\^l—v-/c^ (45) 



and the force F acting upon it produces an acceleration dv/dt given 

 not b\ the familiar equation force = massXacceleration, but by the 

 ccjuation 



F = d(mv),dt (4()) 



If we suppose the electron revolving in a perfect inverse-square 

 field about the nucleus, and apply these equations of relativistic 

 mechanics, we arrive at the same result as though we had used the 

 equations of Newtonian mechanics, but had assumed that the field 

 acting upon the electron is the sum of an inverse-square attraction 

 and an inverse-cube attraction. Specifically, the result is formally 

 ecjuivalent to the result attained by continuing to use Newtonian 

 mechanics, and assuming that the potential energy of the atom- 

 model is given by (43) with the following value inserted for the con- 

 stant C: 



C=-e-E'/2moC- (47) 



The orbit is a rosette; and all the general remarks made in section J2 

 about rosette orbits nia\- be repeated for this case. 



74. Motion of an Electron in a Field Compounded of an Inverse-square 

 Central Electric Field and an Uniform Magnetic Field 



Here we ha\e a famous theorem of Larnior's to help us. According 

 to this theorem, a magnetic field // acting upon a re\olving electron, 

 or a system of revolving electrons, produces no other effect than a 



