404 
The Solar System [ch. xyi 
Discussing the equipotentials il = constant in the manner adopted in 
§ 229 we find that, whatever the values of M and M' may be, the equipotentials 
surrounding the point M are at first spheres, but give place to open equi 
potentials at a certain distance from M. Fig. 61 shews the equipotentials 
drawn for the special case of M ' = 2 ilf. The last closed equipotential is 
drawn thick, and its whole volume is found by quadrature to be equal 
to that of a sphere of radius 0 - 348 R. 
Similarly fig. 62 shews the equipotentials drawn for the limiting case of 
M'/M = oo. The mass M' is now of course at infinity. The outermost 
curve constitutes the last closed equipotential, and its volume is found by 
/ j|/ 
quadrature to be that of a sphere of radius 0*72 i^jp) R- 
The critical equipotential occurs when S' is at a distance R which bears a 
certain ratio to the undisturbed radius of S. From the figures just given it 
is found that the critical values of R are 
/M'\& 
when M'/M = 2, R = 2-87 r 0 = 2-28 r 0 (377 3), 
when M'/M = oo, R = 1 ‘ 75 (m) r ° (377-4).