Fundamental Constant of Atomic Vibration. 3 



dental results of imperfections in the empirical formula, it is 

 evident that b tends to a limiting value which is a funda- 

 mental constant. In the paper cited I have suggested that 

 with V for the velocity of light in vacuum Yb is to be re- 

 garded as a frequency of vibration or rotation which is 

 nearly the same in all atoms. In "The Electric Origin of 

 Molecular Attraction" (Phil. Mag. [6] iv. 1902, p. 625) at 

 section 4 an attempt was made to show that the frequency 

 of rotation of a pair of electrons in the Na atom is identical 

 with this fundamental Yb, whose value is 33 x 10 14 . But 

 that attempt gave better numerical agreement than it ought, 

 because the best available estimates of molecular diameters 

 at that date were too small, and introduced a compensating 

 error which masked tlie incompleteness of the theory then 

 sketched. But by means of the conception of the internal 

 electric field of the atom we can make the discussion of Vb 

 more definite, and then test it by more definite molecular 

 data. 



From the theory of the text-books for a uniformly magne- 

 tized sphere (e. g. J. J. Thomson's Elements of El. and 

 Magn.) we can specify the field of force of a uniformly 

 electrized sphere of moment es as that due to a potential 

 ylr = (es cos#)/?' 2 at a point r, 6, outside the sphere, while 

 inside the sphere the electric intensity has the constant value 

 es/a z parallel to the direction of electrization, the radius of 

 the sphere being a. This constant internal field is very 

 important. Even when the electrization is not uniform and 

 the intensity not constant, for a first approximation we can 

 assume a uniform electrization equal to the average value 

 of the actual and associate with it a constant average 

 intensity. 



Evidently in the atom we have a region of electric force 

 suitable for maintaining simple harmonic motion of electrons. 

 Consider a negative electron \j and a positive # in positions 

 of static equilibrium within the sphere, the charge of each 

 being e. As a pair they will be at rest in unstable equili- 

 brium anywhere within the sphere so long as the line joining 

 them is parallel to the electrization, and of such a length z 

 that ■e i /z 2 = e 2 s/a*, and the moment ez is oppositely directed 

 to es. This pair floats in the internal electric field of the 

 sphere just as a magnet would float in a cavity in a gravi- 

 tationless Earth, and if suitably constrained it can vibrate as 

 the magnet would. It differs from the magnet inasmuch as 

 its length is also determined by the strength of the electric 

 field. Let us take the pair of electrons to such a position 

 that their midpoint is at the centre of the sphere, and each 



B2 



