502 Lord Rayleigh on the Pressure of 



As to the preponderance of attractive over repulsive virial, 

 I think that the conclusion is correct, although Sutherland's 

 argument, quoted above, omits reference to the essential 

 consideration of the time for which any particular value of 

 the virial prevails. If we fix our attention upon a pair of 

 particles, acting as simple centres of force, which encounter 

 one another, the corresponding virial varies from moment to 

 moment, but the mean contribution to the total may be 

 represented bv ,~ , , 



the integration being taken over the whole range for which 

 p4>{p) i s sensible. Since only relative motion is in question, 

 the centre of gravity of the two particles may be supposed to 

 be at rest and the problem becomes one of " central forces/' 

 In the usual notation we have 



d' 2 r 



so that 



v denoting the resultant velocity. At the upper limit dr/dt 

 is equal to the velocity at co , say V, and at the lower limit 

 dr/dt= — V. Hence 



\P.r.dt='2rY-yvd^ .... (28) 



so that the mean virial is closely connected with the " action " 

 in the orbit. 



For a simple illustration it will be more convenient to 

 make 6 the independent variable. Thus by (26) 



i P. r.dt = | ^F.i*.d0 (2D) 



Suppose for example that 



P = /^- :3 (30) 



Then f-^ ,. ix f , n fi „ ,. y y, 



j ?.,,/,= y^y 



where 6 represents twice the vectorial angle between the 

 initial asymptote and the apse. If h be given, a comparison 

 between repellent and attractive forces (fi given in magnitude 

 but variable in sign) shows that (31) is greater in the case 



