Orbits in the Field of a Doublet. 1013 



and it takes an infinite time to leave the system. The path 

 again lies between bounding rays 6— + «, but 



cos oi = cos l — r l 2 V l 2 /2fi, 



and therefore a is greater than 7r/2 ; the orbit is therefore 

 confined to an oblique-angled sector of the plane. The 

 path in general touches the bounding rays a finite number 

 of times or not at all and has a certain straight line as 

 asymptote. No velocity of projection towards the origin, 

 however large, enables the particle to re.ich the doublet, or 

 prevents it continually increasing its distance from the 

 origin, possibly after it has approached within a certain 

 distance of the doublet. 



(d) When the transverse velocity is such that 



2^<r 1 2/V 1 2 -2/^cos6' 1 



the orbit is not restricted to any sector of the plane. The 

 particle again approaches the doublet if the radial velocity 

 of projection is towards the origin, but it never reaches it : 

 in this case it ultimately recedes from the doublet. When 

 the radial velocity of projection is positive it straightway 

 recedes from the doublet. While the distance of the particle 

 of the doublet is changing in this way, the angular distance 

 of the particle from its initial position steadily increases, and 

 it finally proceeds to infinity in the direction of a certain 

 line, after a finite number of circumscribings of the origin. 



A g 



r^Y, -2/i cos 6 1 



increases, the orbit becomes more and more like the orbit in 

 the limiting case when 



? . 1 2y i 2__2 A tcos6' 1 



is infinite ; in this case the particle circumscribes the 

 doublet in the same sense, for ever, while its distance from 

 the doublet increases without limit. 



The main interest of the results lies probably in the 

 electrification of neutral atoms in a vacuum tube — the 

 neutral atom being taken, as usual, in its first approxi- 

 mation as a doublet. All the formulae deduced involve, 

 essentially, a critical velocity of an electron, which deter- 

 mines whether it leaves the atom in whose proximity it 

 finds itself, or whether it stays. On the Quantum Theory, 

 the criteria which determine the actual capture of such 

 an electron by an atom have not yet been defined, and the 

 fact that an electron " stays/' according to this analysis, 



