Spectra of the Elements, and Structure of the Atom. 557 



acceleration, or else change the laws of force between electrons 

 altogether, while preserving the law between electron and 

 nucleus. 



Electronic arrangements in an Atom. 



It follows from the preceding considerations that if the 

 more complex atoms have the number of electrons which, 

 from the results of experiments on scattering, seem necessary, 

 these electrons must either form a single ring, or rings in 

 parallel planes. This does not imply that those of any single 

 ring actually move in a circle. Accepting Bohr's view that 

 the dynamical equilibrium of an electron in the atom, while 

 involving an acceleration, centrifugal or other, does not 

 involve a consequent radiation, we can make the orbits 

 elliptical. Returning, for example, to the equation for the 

 orbits of three electrons about a nucleus, let us suppose that 

 they remain at the corners of a variable equilateral triangle. 

 Then any orbit is given by 



d 2 Ul e 2 / XT 1 \ 



and its most general form is an ellipse, if the electron remains 

 in the atom. Imagine, more generally, a system of n electrons 

 describing a set of equal ellipses, with a common focus at 

 which the nucleus is situated, and with their successive major 

 axes inclined at equal angles 2irjn to each other. If the 

 electrons are at corresponding points at any instant, they are 

 at the corners of a regular polygon inscribed in a circle. 

 Thus at any single moment they form a ring, and even on the 

 older electrodynamics, such a system has little radiation, for 

 the vector sum of the accelerations is zero if there is more 



than one electron. The figure shows the case of two electrons 

 P and Q. In the general case, if r is the instantaneous 

 distance of an electron from the nucleus, the radial force on 

 it is 



-i(*-\*) 



where S» = £ t cosec 



Phil. Mag. S. 6. Yol. 27. No. 160. April 1914. 



rir 

 n 



