272 Mr. W. Sutherland on the 



with velocity A/(H-/Lt]) 2 and the motion of the positive with 

 velocities 



A/QL + ^Xl+ALa) A/(l + / a 1 )(m + ^ 2 ) J 



; and to the motion of the positive electron with velocity 

 A/(i +/X2) 2 an( l the motions of the negative with velocities 



A/(l + ^)(l+>0 AKl + fjL^im + fAi), 



The Diffuse series arises in the same way as the Sharp, 

 except that the value of fi associated with m is or an 

 integer. 



Our analysis has brought us to a fundamental constant 

 angular velocity A for all electrons round the centre of any 

 : atom of any element. The electrical apparatus which produces 

 all spectra is the same. In free sether the positive and negative 

 electron revolving with angular velocity A round their centre 

 of inertia form what I have proposed to call the neutron, the 

 electric doublet, which gives the sether its chief electric and 

 magnetic properties. Near an atom the tw T o parts of the 

 neutron have their motions controlled mechanically by the 

 atom in the manner just discussed in accounting for B/ydberg's 

 Laws. 



It appears from the facts of Section 1 that in the hydrogen 

 atom the fundamental period and the harmonics of periods 1/2, 

 1/3 .... 1/w up to a certain value of m are all multiples of the 

 period of rotation of an electron. Near the hydrogen atom 

 .an electron has a large number of alternative orbits between 

 two collisions with the atom. The chief lines in the ordinary 

 spectrum of hydrogen are caused by one electron's travelling- 

 round the atom twice between two collisions, while the other 

 travels three times .... m times round it between two 

 collisions, both having the same angular velocity A. This 

 is the primary spectrum of hydrogen or the Diffuse Series. 

 For the Sharp series we have 3^ . . . . (2m + l)/2 revolutions 

 of the one electron between two collisions to 2 of the other ; 

 for the Principal series 1J revolutions of one electron and m 

 of the other. The other lines of the secondary spectrum o£ 

 hydrogen are due to two revolutions of one electron between 

 two collisions, and p + r/s revolutions of the other between 

 .two collisions. 



In the Alkali metals the relations between the values of fx 

 in Table III. exhibit some system. In the Diffuse series of Li 

 and Na /jl is or an integer, so that the atoms of these metals 

 have mechanical periods of vibration which are multiples of 

 the period of revolution of one of the electrons. With the K 



