1034 Dr. A. C. Crehore on 



Perhaps as good an estimate as any of the distance between 

 the two atoms in the hydrogen molecule has been made by 

 E. C. Kemble *, who, however, assumes a dumbbell form of 

 molecule, which by hypothesis has a different amount of 

 freedom from the molecule above described. The above 

 molecule is free, to rotate around a circle of latitude at 

 39° 49', but is not free to change this latitude without en- 

 countering a restoring force. Kemble makes use of the 

 kinetic theory of gases combined with the quantum theory 

 and arrives at a moment of inertia for the dumbbell, 2*0 X 10~ 41 

 gm. cm. 2 , from which value it appears that the distance 

 between the two atoms is about *5 x 10~ 8 cm. A slightly 

 larger value of P than double that used for fig. 3 will give 

 the equilibrium distance that is estimated from Kemble's 

 result, but it seems desirable to revise his estimate in order 

 to adapt it to this form of atomic model. 



In concluding this part of the subject attention is directed 

 to the fact that, except for numerical coefficients which are 

 not very large, the values of the successive terms of the 

 series for the electrostatic force are as Mr -6 , b 6 r~ s , b % r~ l ° y 

 etc., thus making the ratio of any term to the next following' 

 a constant, b~ 2 r 2 at a given distance, r. If r is of the order 

 of 10~ 8 cm., since b is of the order 10~ 13 cm., the ratio is of 

 the order 10 26-16 = 10 10 , and the terms, therefore, decrease at a 

 very rapid rate. Were it not for the fact that there exists a 

 peculiar reason connected with the shape of the electron that 

 makes the numerical coefficients of the r~ 6 and r -8 terms 

 simultaneously very small, it would be quite unnecessary to 

 consider the use of the r~ 10 term at all. This same pecu- 

 liarity does not apply to the coefficients of the r~ 10 , r~ 12 , and 

 subsequent terms, and as a consequence they follow the 

 general rule above cited. Hence the r~ 12 and all following 

 terms are quite negligible. The following Table I. gives 

 the approximate values of the terms within the brace of (17) 

 near the position of stable equilibrium for the two cases 

 where P has the value used in making fig. 3 and for double 

 this value. For the larger of the two values of P it is seen 

 from this Table that the gravitational or r~ 2 term is becom- 

 ing negligibly small in comparison with the other three 

 terms. That is to say, the use of the electrostatic force 

 alone is quite sufficient to cause a stable position to exist in 

 the region of *5 x 10 ~ 8 cm. so far as the translational forces 

 between the two atoms are concerned. The internal moment 

 of the force which tends to keep the two atom's axes parallel 



* Phys. Rev. Feb. 1918, p. 156. 



