54 SCIENCE PROGRESS 



gas are set in rotation. The linear velocities of the molecules 

 may have any value, the distribution of velocities amongst the 

 molecules being given by Maxwell's laws. On the other hand, 

 the angular velocity of the molecule according to the Quantum 

 Theory must be one of a definite series of values which are 

 determined by Planck's constant h and the moment of inertia / 

 of the molecule. Since these molecular rotations modify the 

 absorption frequencies, this gives rise to the series of bands 

 characteristic of absorption spectra. It can be shown that the 

 frequency difference ^v between successive bands is given by 

 the formula : 



ov = — J 



when c is the velocity of light. 



We can measure this frequency difference and calculate the 

 moment of inertia / of the molecule. Therefore, since we know 

 the masses of the hydrogen and chlorine atoms, we can calculate 

 their distance apart. The substitution of chlorine for fluorine, 

 or bromine for chlorine, increases this distance between the 

 atomic centres. 



The determination of the size of the atom from the average 

 length of the free path in a gas, and from the Van der Waal's 

 constant b, corresponds to an estimate of the shortest distance 

 between the atomic centres when the strong repulsive forces 

 come into play which cause the atoms to rebound from each 

 other. On the other hand, the determination of inter-atomic 

 distances by means of crystal analysis, or by such information 

 as may be obtained from absorption spectra, tells us the distance 

 between the atomic centres when the atoms are linked in 

 chemical combination. In some cases we suppose the molecule 

 to consist of separate structures held together by electrostatic 

 forces, in others that the fusion of structure takes place which 

 has been termed the holding of electrons in common. The 

 relations between the inter-atomic distances in crystals have 

 been interpreted by supposing that the atoms were spheres in 

 contact with each other, but it is not to be expected that the 

 diameters of the spheres found in this way will correspond with 

 those given by the Kinetic Theory. We are on surer ground, 

 however, in comparing the increase in atomic dimension given 

 by all these methods when we substitute for an atom the 

 corresponding atom in the next period of Mendeleef's table. 

 Both crystal analysis and Rankine's work on the viscosity of 

 molecules confirm the view that the atoms near the end of any 

 one period have nearly the same structural dimensions. We can, 

 for instance, compare the difference in o- for argon and krypton 

 given by the Kinetic Theory, with the increase in inter-atomic 



