634 



TRANSACTIONS OF SECTION A. 



Department of General Physics. 



1 



The foUowiug Papers were read : — 



A Suggestion with regard to the Meaning of Valency. By H. Bateman. 



Starting with the hypothesis that an atom contains a large number of charged 

 particles some evidence can be brought forward in support of the Tiew that 

 changes can take place in the configuration or state of motion of the particles 

 which do not involve a corresponding change in the spectrum. 



Let a sphere be described round each particle as centre, and let tlie radii of 

 the spheres be chosen so that there are a number of contacts between the 

 difl'erent spheres. We shall suppose that a node of the vibrations exists at a 

 point of contact when two spheres touch externally, provided the particles at 

 their centres carry similar charges, and when two spheres touch internally, 

 provided the particles carry opposite charges. 



Now a number of spheres, the members of which have a certain number of 

 contacts with one another, is transformed into another system with the same 

 number of contacts by any couformal transformation of space. 



Diagram I. — Expulsion of a particle or group of particles from an atom. 



Fig. I. 



Fig. 2. 



Fie. 3. 



Fig. 4. 



Diagram II. — Kayless change (the shaded region may be occupied 

 by any number of spheres). 



Fig 1. 



Fig. 2. 



Fig. 3. 



An infinitesimal transformation of this type may be built up from twoi 

 inversions where the spheres of inversion are very nearly coincident. Four 

 parameters are required for the specification of each sphere, so that the total 

 number of variables in the transformation is eight. The correspondence between 

 this number and the maximum valency of an atom suggests that there may be 

 a group of conformal transformations associated with an atom involving arbitrary 

 parameters in number equal to the valency of the atom. A succession of 

 infinitesimal transformations would correspond to a motion of the charged 

 particles within the atom, so that on this view the valency would represent 

 the number of degrees of freedom for a departure from a given configuration or 

 state of motion of the charged particles contained in the atom. 



When two atoms combine each can be supposed to lose a number of degrees 

 of freedom, a 'bond' of the chemist corresponding to a pair of equations involving 

 the valency coordinates, and one or more equations involving only the positional 

 coordinates. 



To show that the periods of vibration of the atom are unchanged by a con- 

 formal transformation we may fix our attention on a particular sphere S which 

 always passes through a node N in the course of the vibrations. The correspond- 



