. ATOM. 



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

 product of this atwei into the distance between the two points is called the 

 onu/ of the ihMB, 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 ririala of the stresses which exist in it. If the system is subjected to 

 the external stress of the pressure of the sides of a vessel in which it is 

 contained, this stress will introduce an amount of virial $pV, where p is the 

 imniiirn on unit of area and V is the volume of the vessel. 



The theorem of Clausius may now be stated as follows : In a material 

 ayvtem in ft state of stationary motion the time-average of the kinetic energy 

 it equal to the time-average of the virial. In the case of a fluid enclosed in a 



where the first term denotes the kinetic energy, and is half the sum of 

 the product of each mass into the mean square of its velocity. In the 

 second term, p is the pressure on unit of surface of the vessel, whose volume 

 is F, and the third term expresses the virial due to the internal actions 

 between the parts of the system. A double symbol of summation is used, 

 because every pair of parts between which any action exists must be taken 

 into account. We have next to shew that in gases the principal part of the 

 pressure arises from the motion of the small parts of the medium, and not 

 from a repulsion between them. 



In the first place, if the pressure of a gas arises from the repulsion of 

 its parts, the law of repulsion must be inversely as the distance. For, con- 

 sider a cube filled with the gas at pressure p, and let the cube expand till 

 each side is n times its former length. The pressure on unit of surface ac- 

 cording to Boyle's law is now ^ , and since the area of a face of the cube 



is ' times what it was, the whole pressure on the face of the cube is - of 



n 



it* original value. But since everything has been expanded symmetrically, the 

 distance between corresponding parts of the air is now n times what it was, 

 and the force is n times less than it was. Hence the force must vary inversely 

 as the distance. 



But Newton has shewn (Prindpia, Book i. Prop. 93) that this law is 

 inadmissible, as it makes the effect of the distant parts of the medium on a 



