Manchester Memoirs, Vol. liii. (1908), No. 3. 3 



to connect n with the number of atoms in the molecule,* 

 but the experiments of Capstick f and others indicate 

 that the properties of the constituent elements must be 

 taken into account. 



A set of rules leading to numbers showing a fair 

 agreement with the experimental ones, may be con- 

 structed on the hypothesis that an atom in a chemically 

 active state possesses a number of degrees of freedom 

 represented by 3+ the valency exhibited by the atom 

 under the circumstances.^ When a number of atoms are 

 in a state of combination, the number of degrees of 

 freedom of a molecule of the compound may be calculated 

 by adding together the numbers that must be ascribed to 

 each atom, and subtracting the number of conditions that 

 must be satisfied in order that the geometrical relations 

 peculiar to a stable configuration or state of motion may 

 remain permanent. 



To take a simple geometrical illustration we shall 

 consider two ideal spherical atoms each of which contains 

 a ring of electrons. In the state of combination we shall 

 suppose that the system is stable when the spheres are in 

 contact (one condition) and the planes of the two rings 

 are parallel (two conditions). Thus in this ideal state of 

 combination three geometrical conditions have to be 

 satisfied if the stable state is to remain permanent, this 

 involves a loss of three degrees of freedom for the 

 combination. 



When the molecules of a gas contain only one atom, 

 as in the case of Mercury, Helium, Krypton, Argon, the 



* Naumann, Annalen der Chemie, vol. 143, p. 284, 1S67, also J. J. 

 Thomson in Watts' "Dictionary of Chemistry," vol. i, p. 89. 



t Phil. Tratis., vol. 186, p. 564, 1895 ; vol. 185, p. I, 1894. 



+ The author was led to make this hypothesis from considerations quite 

 apart from the law of equipartition. An account of these will be given in 

 another paper. 



