Fundamental Constant of Atomic Vibration. 5 



being about 10 ~ 21 , the values in J. J. Thomson's list ranging 

 from 0*639 to 1*865 times this. According to Rutherford 

 * = 4-65 x lO" 10 , and to Planck e = 4*69 x 10" 10 . Using the 

 former we get 11 = 0*795 x 10~ 8 . Now in a short note follow- 

 ing I have recalculated the molecular diameters of Phil. Mag. 

 [6] xvii. 1909, p. 320, on the basis of the value of e just 

 used, and these values will be used elsewhere in the present 

 paper. 



Tbe diameter of the hydrogen molecule is 2*17 x 10~ 8 , and 

 the radius of the hydrogen atom is this divided by 2 4 '' 3 , and 

 is 0*861 x 10" 8 . Thus R is smaller than the smallest radius 

 ascertained by the kinetic theory. But there are smaller 

 atoms than that of hydrogen, for the volume of a gramme- 

 atom of Li in its compounds is about 2 and of Be is about 1, 

 whereas according to the value given above for a in the 

 hydrogen atom with 2*77 x 10 19 for the number of molecules 

 in a c.c. of. hydrogen under standard conditions the volume 

 of a gramme-atom of H is 



(2 x 0*861 x 10- 8 ) 3 x 2 x 2*77 x 10 19 = 3*176. 



Hence a for Li is (2/3* 1 7 6) 13 times that for H and is 

 0*739 x lO" 8 , and for Be a = 0*586 x 10" 8 . These values for 

 the two smallest known atoms are less than R as calculated 

 above. These two exceptions show that we cannot stipulate 

 for R being less than a, and that the constraining power of 

 the atom over the positive electron may extend beyond the 

 atom of combined Li or Be. However, the fact that R is of 

 the order of magnitude of atomic radii is encouraging. 



If we now consider (1) more closely we see that it has 

 some important bearings. The rigidity of the atom due to 

 its electrization is 



U 3 (2ay W 



(Phil. Mag. [6] vii. 1901, p. 417), this being the electric 

 energy per unit volume of the atom. So (1) informs us that 

 the electric energy of the atom per unit volume or its rigidity 

 is equal to the electric energy of the special pair of electrons 

 per unit volume of the sphere of radius R or the rigidity of 

 that sphere d ne to the presence of the electrons. In " Further 

 Studies on Molecular Force" (Phil. Mag. [5] xxxix. 1895, 

 p. 1) it is shown that for non-metals in compounds (M 2 /)£, 

 which is proportional to es t is proportional to a 3 nearly. 

 Hence from (1) if R is constant, r is also nearly constant. 

 In the non-metals then the central atomic vibrator is nearly 

 the same in the different elements. The internal electric 



