September 21, 1917] 



SCIENCE 



277 



time the frequency of its vibration is un- 

 disturbed. Hence the spectrum lines given 

 out by rarefied gases, in which an atom is 

 only ' ' occasionally ' ' close to another, are 

 comparatively clean and sharp. With in- 

 crease of pressure the free path is decreased 

 and the total interval of disturbance length- 

 ened to practically the same fractional ex- 

 tent. If, for instance, the pressure is 

 doubled, temperature remaining constant, 

 the free path is halved, atomic "collisions," 

 total duration of an atom's close proximity 

 to others, and, therefore, quantity of shifted 

 light all are at least doubled. Hence with 

 increase of pressure a spectral line must 

 spread (independent of the Doppler effect) 

 and its maximum intensity shift to the red. 



Under very heavy pressures the atoms 

 are always within mutually disturbing dis- 

 tances, and therefore under such conditions 

 their lines gradually merge into a contin- 

 uous spectrum. 



It might seem that atoms with such 

 strong magnetic fields necessarily would 

 cluster into rods and rings, like iron filings 

 in a magnetic field. In short, that at any 

 attainable temperature, a gas consisting of 

 such atoms would collapse into — who knows 

 what? 



To test this point consider an extreme 

 case. Let two atoms, each consisting of a 

 single circular ring of 5 X 10* electrons 

 and an equivalent positive nucleus at its 

 center, face each other on a common axis, 

 and let the orbital revolution of their rings 

 have the frequency of yellow light of wave- 

 length .6/a: Find the electric and magnetic 

 forces between them. 



The magnetic flux through either ring 

 due to the presence of the other is given by 

 the expression 



in which i is the strength of the current, 

 r the radius of the I'ing, and x the distance 



between the centers. Hence the magnetic 

 force between the rings is found by the 

 equation 



Assume the electronic charge to be 4.774 

 X 10-^°, MiUikan's value, and let r = 10-^ 

 cm. Then when 



X = r, 

 Fmagnctio = 1.6.561 dynes, 



lOr lOOr 



91.39 X 10-6 dyne, 9.37 X IQ-s dyne. 



The electric force between the two atom 

 models consists of four parts; namely, 

 attraction between each nucleus and its 

 neighbor's ring, repulsion between the 

 nuclei and repulsion beween the rings. 

 The problem of computing this force is 

 not so simple as, at first sight, it is 

 likely to appear. However, a general solu- 

 tion of the problem of the rings (rings 

 of different radii and linear densities) in the 

 form of a converging series has 'been kindly 

 furnished by Professor R. S. Woodward. 

 A similar solution of the somewhat simpler 

 problem presented by duplicate atom mod- 

 els gives the following total electric forces 

 (repulsions) 'between them: 

 X = r, 



Felectrio = 3578 X 10' djiics, 



lOr lOOr 



34.186 dynes, 6.45 X IQ-s dyne. 



Of course it is not assumed that any such 

 force as that computed for x^r, about 

 3.65 kilograms, actually exists between any 

 two atoms. Neither does it seem probable 

 that atoms can get so close that their cen- 

 ters are separated by only a single atomic 

 radius. However, the calculations appear 

 to prove that the electric forces between any 

 atomic models of the kind here assumed 

 would be more than sufficient to prevent 

 collapse through the interaction of their 

 powerful magnetic fields. 



