MOLECULAR CONSTITUTION OF BODIES. 421 



The dynamical principles necessary for this study were developed by the 

 fathers of dynamics, from Galileo and Newton to Lagrange and Laplace ; but 

 the special adaptation of these principles to molecular studies has been to a 

 great extent the work of Prof. Clausius of Bonn, who has recently laid us 

 under still deeper obligations by giving us, in addition to the results of his 

 elaborate calculations, a new dynamical idea, by the aid of which I hope we 

 shall be able to establish several important conclusions without much symbolical 

 calculation. 



The equation of Clausius, to which I must now call your attention, is of 

 the following form : 



Here p denotes the pressure of a fluid, and V the volume of the vessel 

 which contains it. The product pV, in the case of gases at constant tempera- 

 ture, remains, as Boyle's Law tells us, nearly constant for different volumes 

 and pressures. This member of the equation, therefore, is the product of two 

 quantities, each of which can be directly measured. 



The other member of the equation consists of two terms, the first depending 

 on the motion of the particles, and the second on the forces with which they 

 act on each other. 



The quantity T is the kinetic energy of the system, or, in other words, 

 that part of the energy which is due to the motion of the parts of the 

 system. 



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

 square of its velocity, and the kinetic energy of the system is the sum of the 

 kinetic energy of its parts. 



In the second term, r is the distance between any two particles, and R 

 is the attraction between them. (If the force is a repulsion or a pressure, R 

 is to be reckoned negative.) 



The quantity $Rr, or half the product of the attraction into the distance 

 across which the attraction is exerted, is defined by Clausius as the virial of 

 the attraction. (In the case of pressure or repulsion, the virial is negative.) 



The importance of this quantity was first pointed out by Clausius, who, by 

 giving it a name, has greatly facilitated the application of his method to phy- 

 sical exposition. 



The virial of the system is the sum of the virials belonging to every pair 

 of particles which exist in the system. This is expressed by the double sum 



