400 
The Solar System [ch. xvi 
from those postulated by the planetesimal hypothesis. This investigation 
further suggested that mere tidal action of itself would suffice to explain the 
origin of the solar system, without calling in the various complicated and 
wholly hypothetical mechanisms of intermittent eruptions, of smaller erup 
tions to form satellites, of planetesimals, and so on, and led me to put forward 
the simple tidal theory which follows. 
The Dynamical Tidal Theory. 
374 . Just as with rotation, the effects produced in a star by tidal action 
prove to be very different according as the star is of fairly uniform density or 
is arranged so as to have high central condensation of mass. 
Tidal Effects in an Incompressible Mass. 
375 . Let us examine first the effects which would be produced in a liquid 
star of homogeneous incompressible matter. 
Following Roche, we examined in §206 the effect produced on a small 
mass S of approaching too near to a big mass S' around which S was supposed 
to revolve in orbital motion. If S and S' were of the same density we found 
that S could not approach to within 245 radii of S' without being broken 
up. At this distance the difference in the gravitational pull of S' on the 
nearer and further halves of S became so great that the attraction of the two 
halves of S for one another failed to keep S together as a single body. The 
mass S accordingly broke in two, and as the broken halves found themselves 
again torn to pieces in precisely the same way, the process of disruption 
continued indefinitely. 
A similar situation arises when the two masses only approach one another 
for a short time and then recede again, as happens in an ordinary gravitational 
encounter between two stars whose orbits happen to pass fairly close to one 
another. 
When a second star S' approaches the star S whose behaviour we are 
considering, its first effect is to raise tides of the ordinary kind on S. First 
suppose that the distance R between S' and S changes very slowly, so that an 
equilibrium theory is adequate to follow the changes in the tides. In this case 
the equations of equilibrium are precisely of the type already discussed in 
§206; they are in fact equations (206-6) with co 2 put equal to zero, /4 still 
denoting 7 M'/R 3 . 
A discussion of the general type already given in § 206* shews that the 
configuration of S remains stable until it has assumed the shape of a prolate 
spheroid of eccentricity e = 0-8826, the value of R at this stage being 
R = 2198 (¿gy r * (375-1), 
* Fora full account of the whole investigation see the paper already mentioned (p. 391), or 
Problems of Cosmogony and Stellar Dynamics, pp. 43 ff, 118 ff.