270 Mr. W. Sutherland on the 



of the periods of vibration of the negative and positive 

 electron respectively. So far as we have now gone, we could 

 represent the motion of an electron Q as compounded of a 

 circular motion round P with angular velocity (m + ft) 27r/co 7 

 while P revolves round the centre of the atom with 

 velocity co. It is the former of these motions that interests us. 

 Now it must be the relative motion of negative and positive 

 electrons which causes the electromagnetic phenomena of light. 

 We can best represent the motions of the two electrons by 

 taking their centre of inertia to be travelling in an orbit 

 which is nearly a circle with the centre of the atom as centre, 

 while the negative electron travels in a circle round the centre 

 of inertia with frequency (m + //,]) 2 7t/g), and the positive with 

 frequency (m + /^ 2 )27t/cj. The relative motion of the radius- 

 vectors of the two electrons then gives the type shown to be 

 necessary by the kinematical analysis in section 3. From the 

 equations (12) and (13) expressing Rydberg's laws according 

 to that analysis it follows, that a series in a spectrum arises 

 from the several relative motions obtained from the motion of 

 period (1 + ^)277-/0) of the one electron, and the motions of 

 periods (1-f )a 2 )27r/G>, (2 + /x 2 )27r/o> .... {in + /* 2 ) 27r/co of the 

 other. This carries the kinematical analysis of the Balmer- 

 Rydberg formula a stage forward. The positive and negative 

 electrons are forced by the ordinary elastic vibrations of the 

 atom to execute vibrations of a certain type, and the com- 

 binations of two such motions in the relative motions of the 

 two electrons produce the series of motions defined by the 

 formula. The fundamental angular velocities of the electrons 

 round their centre of inertia are q)/(1+/jLi) and a)/(l + /i 2 )- 

 But equation (13) must carry us into a fuller understanding 

 of the formula. Dynamically it has not yet been directly 

 investigated to my knowledge, although Zeeman's discovery 

 of the splitting up of spectral lines in a magnetic field has 

 elicited important attempts to give a dynamical theory of the 

 motion of an electron, which would correspond to Stoney's 

 kinematics and account for the Zeeman effect. In these 

 theories (Lorentz's, Larmor's, Preston's) the electron is 

 supposed to describe an ellipse under a central force, and the 

 elliptic orbit being caused to precess by magnetic force gives 

 the doubling or trebling of a spectral line as explained by 

 Stoney. But in these theories a single electron or its- 

 equivalent is studied; whereas if the radiation of atoms is due 

 to the relative motion of positive and negative electron, and 

 if both motions are independently affected by a magnetic field, 

 the theoretical explanation of the Zeeman effect must become 

 more complicated, and be capable of yielding the more 



