Page:Chance, love, and logic - philosophical essays (IA chancelovelogicp00peir 0).pdf/284

 a system of particles so that none of them are removed to indefinitely great distances nor acquire indefinitely great velocities. The kinetic energy of a particle is the work which would be required to bring it to rest, independently of any forces which may be acting upon it. The virial of a pair of particles is half the work which the force which actually operates between them would do if, being independent of the distance, it were to bring them together. The equation of the virial is

1/2[sum]mv^2 = 1/2[sum][sum]Rr.

Here m is the mass of a particle, v its velocity, R is the attraction between two particles, and r is the distance between them. The sign [sum] on the left hand side signifies that the values of mv^2 are to be summed for all the particles, and [sum][sum] on the right hand side signifies that the values of Rr are to be summed for all the pairs of particles. If there is an external pressure P (as from the atmosphere) upon the system, and the volume of vacant space within the boundary of that pressure is V, then the virial must be understood as including 3/2PV, so that the equation is

1/2[sum]mv^2 = 3/2PV + 1/2[sum][sum]Rr.

There is strong (if not demonstrative) reason for thinking that the temperature of any body above the absolute zero (-273° C.), is proportional to the average kinetic energy

system. This is much like the sense in which we speak of the Calvinistic system of theology, the Kantian system of philosophy, etc. (B.) It means the aggregate of the planets considered as all moving in somewhat the same way, as the solar system; and hence any aggregate of particles moving under mutual forces. (C.) It means a number of forces acting simultaneously upon a number of particles.]
 * [Footnote: a theory of the motions of the stars; as the Ptolemaic system, the Copernican