Gases and the Equation of Virial. 



503 



o£ attraction (fig. 1), so that i£ attractive and repellent forces 

 occur indifferently the average effect corresponds to attraction. 



0, centre of force ; C D, asymptote ; A, B, apses. 



In the case of the particular law (30) we can carry out the 

 calculation. If, as usual, u = r~ 1 , the equation of the orbit is 



tj-ii ii 



<76N+"=/r"' 



(32) 



jjl being positive in the case of attraction ; whence, if jjl be 



8maU > w =Usin s/(l-fj,h- 2 )0. . . . 



In (33) H=0, or r=oo, when = and when 



<9 = 7th- y/(l-fi/i- 3 ) ; . . . 

 .so that from (31) 



.... (35) 



(33) 



(34) 



J 



F.r.dt= 



v/(/r-/x) 



The solutions (33), (35) hold if /t be numerically less than 

 A 2 , and (35) shows that when p changes sign the virial of 

 attraction preponderates. This conclusion is accentuated by 

 the consideration of what occurs if fi exceed /r numerically. 

 Equations (33;, (35) -till hold if fi be negative, i. e. if the 

 force be repulsive. But when /ju is positive, the form 

 changes. Thus if fi=h 2 , we have 



m=U0, ..... . (36) 



