450 Lord Rayleigh on the Finite Vibrations of a 



such that two atoms on collision may rotate round their 

 centre of" gravity with their previous velocity of translation, 

 separated by a distance equal to their diameter. It appears, 

 therefore, that the value of <r x is really a complex quantity, 

 and its apparent variations cannot be ascribed to the molecule 

 behaving simply as a centre of force. This method of deter- 

 mining the law of force surrounding a molecule is therefore 

 scarcely admissible. 



Some information whether the shape of a molecule changes 

 with temperature can be obtained from the following con- 

 siderations. The writer has shown from the phenomena of 

 surface-tension that the attraction between two molecules in 



a. liquid is given by the expression ^ (2m 1/2 ) . K, where K 



is a constant which has the same value for all liquids at 

 corresponding states and z is the distance of separation of 

 the molecules. Now since corresponding temperatures are 

 not equal to one another, this suggests that the dependence 

 of K on temperature is not direct but indirect ; that is, it is 

 not due to a decrease of the attractive power of each atom, 

 but to a change in their configuration. A change in con- 

 figuration produces a change in the law of force. If the 

 energy of rotation of a molecule increases with the energy 

 of translation, as is usually supposed, the molecule would 

 contract with rise of temperature if there is equilibrium 

 between the forces of attraction and the centrifugal forces. 

 It seems probable that this is what happens. 



Cambridge, May 16, 1910. 



XLIV. Note on the Finite Vibrations of a System about a 

 Configuration of Equilibrium. By Lord Rayleigh, O.M., 

 F.B.S* 



THE theory of the infinitesimal free vibrations of a system, 

 depending on any number of independent coordinates, 

 about a position of stable equilibrium has long been familiar. 

 In my book on the ' Theory of Sound ' (2nd ed. vol. ii. p. 480) 

 I have shown how to continue the approximation when the 

 motion can no longer be regarded as extremely small, and 

 the following conclusions were arrived at : — 



(a) The solution obtained by this process is periodic, and 

 the frequency is an even function of the amplitude (Hx) of 

 the principal term (H x cosnt). 



* Communicated by the Author. 



