Rate of Recombination of Ions in Gases. 145 



to increase the apparent diameter of the molecule in a certain 

 ratio. 



Objection may be raised to the assumption of a definite size 

 for molecules on the ground that it is too specialized. The only- 

 alternative seems to be the view of centres of force developed by 

 Maxwell*. One objection to the consideration of molecules as 

 mere centres of force is urged by Mr Sutherland f. Another is 

 the values of the ratio of the specific heats for mono- and diatomic 

 molecules which seem to indicate a definite geometrical distribu- 

 tion of mass points. A further objection lies in the great 

 mathematical difficulties furnished by this view which makes its 

 application to any particular case almost impossible. In addition 

 to this the excellent agreement of Mr Sutherland's results with 

 the experimental determination of the variation of viscosity of 

 gases with temperature furnishes a strong argument in favour of 

 molecules of definite shape. 



Even if molecules really consist of an aggregation of centres 

 of force, in some cases the view which regards them as hard 

 spheres possesses a definite meaning. Looking at a molecule as 

 a centre of repulsive force varying extremely rapidly with the 

 distance, it has a certain mean free path aud therefore a certain 

 apparent sphere of action whose radius is, say, 8. If now a field 

 of force which varies much less rapidly with the distance is super- 

 posed on the first, the number of molecules which are deflected 

 through a given angle will be changed. If the second force is 

 attractive a greater number, if repulsive a smaller number, of 

 molecules will be pulled into the stronger part of the field, so that 

 the number of deflections through a given angle would in the first 

 case be greater, in the second, smaller than before. The actual 

 alteration will be much the same as if the molecules were hard 

 spheres of mean radius 8 attracting or repelling one another with 

 the second system of forces. As an imaginary illustration we 

 might take the case of a gas containing positive and negative ions, 

 which are supposed to have the following constitution. A positive 

 ion is to be regarded as a molecule from which a corpuscle has 

 been taken away and a negative ion a molecule to which a cor- 

 puscle has been added. The number of collisions between ions of 

 opposite signs could then be calculated, assuming that the mole- 

 cules were rigid spheres of radius equal to that given by experi- 

 ments on viscosity, attracting one another according to the inverse 

 square law : the result thus obtained would then be true, at any 

 rate approximately, even if the molecules were really pure centres 

 of force. 



Turning to the actual calculation, we shall assume that the 



* Scientific Papers, n. 35. 

 t Phil. Mag. xxxvi. 509. 



