stars in an encounter. The velocity of fall from infinity alone is \J2 times 
that appropriate to a circular orbit, so that when two stars meet, the value of 
v must be greater than that assumed above by a factor of at least \/2. 
As a consequence the value of R necessary for break-up is less than 84 per 
cent, of that given by equation (376-2). But this still does not differ very 
greatly from the simple equilibrium value given by formula (375'1), at any 
rate so long as the masses M and M' are comparable. 
Equation (3751) would however suggest that the limiting distance for 
tidal break-up could be made very large by taking M' very large compared 
with M. This is true on an equilibrium theory of the tides but equation 
(376*2) shews it is not so when dynamical factors are taken into account. 
When M' is very large the two stars shoot past one another with such 
a high relative velocity that the more intense tidal forces have very little 
time in which to operate ; the shortness of the time of action neutralises the 
intensity of the forces. 
377 . When there is great central condensation of mass the problem 
assumes a different form. Let us consider the extreme case of a body whose 
model (§ 229), so that its gravitational potential is always 7 Mfr. 
If this mass is under the influence of its own gravitation, and also of a 
tidal field of force of potential V T , the total gravitation potential il is 
given by 
il = ^ + V T (377-1). 
r > 
Let the tidal force originate in a second star S' which may be treated as 
a point of mass M' at a distance R. If r' denotes distance from this point, 
the whole potential of S' is 7 M'/r', but only a part of this produces tidal 
forces. Part goes in producing the acceleration 7 M'/R 2 of S, which may be 
supposed to originate from a field of force of potential yxM'/R 2 . Subtracting 
this, the effective tide generating potential is 
and the total potential il is 
Following an equilibrium theory of the tides, the boundary of the surface 
of S must be one of the system of equipotentials XI = constant. The tidal 
disruption of S will commence when, if ever, there is no closed equipotential 
capable of containing the whole volume of S.