410 VAX DKB WAALS ON THE CONTINUITY 



When the motion of a material system is such that the sum of the 

 momenta of inertia of the system about three axes at right angles to each 

 ither through ita centre of mass does not vary by more than small quantities 

 from a constant value, the system is said to be in a state of stationary motion. 

 The motion of the solar system satisfies this condition, and so does the motion 

 of the molecules of a gas contained in a vessel. 



The kinetic energy of a particle is half the product of its mass into the 

 aquare of ita velocity, and the kinetic energy of a system is the sum of the 

 kinetic energy of its parts. 



When an attraction or repulsion exists between two points, half the pro- 

 duct of this stress into the distance between the two points is called the 

 Virial of the stress, and is reckoned positive when the stress is an attraction, 

 and negative when it is a repulsion. The virial of a system is the sum of 

 the virial of the stresses which exist in it. 



If the system is subjected to the external stress of the pressure of the 

 ides of a vessel in which it is contained, the amount of virial due to this 

 external stress is three halves of the product of the pressure into the volume 

 of the vessel. 



The virial due to internal stresses must be added to this. 



The theorem of Clausius may now be written 



12 (in?) = $pV+&$(Rr). 

 The left-hand member denotes the kinetic energy. 



On the right hand, in the first term, p is the external pressure on unit 

 of area, and V is the volume of the vessel. 



The second term represents the virial arising from the action between every 

 pair of particles, whether belonging to different molecules or to the same mole- 

 cule. K is the attraction between the particles, and r is the distance between 

 them. The double symbol of summation is used because every pair of points 

 must be taken into account, those between which there is no stress contributing, 

 of course, nothing to the virial. 



As an example of the generality of this theorem, we may mention that 

 in any framed structure consisting of struts and ties, the sum of the products 

 of the pressure in each strut into its length, exceeds the sum of the products 

 of the tension of each tie into its length, by the product of the weight of 

 the whole structure into the height of its centre of gravity above the founda- 



