405 
377 - 379 ] The Birth of Planets 
As soon as R becomes less than these critical values, no closed equi- 
potential is capable of containing the whole mass of S. A certain amount 
begins to spill out through the sharp pointed conical end of the last closed 
equipotential, and the tidal disruption of S has begun. 
We may notice that the critical values of R determined by equations 
(377-3) and (377-4) do not differ widely from that given by equation (375-1), 
although the two equations just obtained refer to a body with extreme con 
densation of mass, while the earlier equation referred to a body having no 
central condensation of mass at all. 
The Birth of Planets. 
378 . The matter which is ejected through the funnel-shaped end of the 
last closed equipotential may scatter into space and fall back into the star S 
unless it is of sufficient amount for its own gravitation to keep it together. 
If it is of sufficient mass to cohere under its own gravitation, it will form a 
long filament, pointing approximately towards the tide-generating mass S', 
or possibly two long filaments starting out from antipodal points of S, the 
two filaments not generally being symmetrical, and the more massive pointing 
towards S\ Plate XVI shews two photographs of actual nebulae whose 
configurations may or may not be due to tidal action but which in any case 
serve to indicate the type of motion which theory predicts ought to occur 
under the action of sufficiently intense tidal forces. 
The long filament or filaments of matter just described cannot be stable 
so long as their density remains approximately uniform. They form suitable 
subjects for the action of gravitational instability of the kind discussed 
in § 314. As the result of the operation of gravitational instability, con 
densations will form round which the whole matter of the filaments will 
ultimately condense into detailed masses. These condensations have an 
average mass M equal to \ 0 ¿ p, where X is given by formula (316 - 2), so that 
' *>•'* (378,1 >- 
Table XXX (p. 350) shews that with reasonable values for the density 
and molecular velocity of the ejected matter, each condensation would have a 
mass of the order of magnitude of the actual masses of the planets. It is 
suggested that the planets originated out of such condensations. 
379 . In both the extreme cases of an incompressible mass of uniform 
density and of a mass with its density distributed as in Roche’s model, we 
have found that a sufficiently close encounter with another star will result in 
the break up of the mass into detached pieces. In the former case, however, 
the final broken up pieces are each of a mass comparable with that of the 
parent star; in the latter case, the fragments which are pulled off by tidal 
action are of comparatively insignificant mass, so that the mass of the parent