OF ROTATTNO LIQUID CYLINDERS. 
103 
In thi.s table the quantities of which the numerical values are doubtful are 
marked with a query. A single query indicates a probable error of 1 or per 
cent. ; a double query indicates that the error may be comparable witli the quantity 
itself 
Let us examine the state of things just after separation has taken place. The 
satellite is descrilhng an orbit about the primary, both bodies rotating with the same 
angular velocity. This angular velocity is, to within a few per cent., given hy 
wV27rp=-43.(131). 
If the satellite exerted no attraction upon the primary, tlie figure of the primary 
would be a figure of equilibrium under the influence of a rotation given by (131). 
The force exerted by the satellite may be divided into two parts, a uniform force 
in the direction 6 — 0, and a tide-generating force of tlie usual kind. If the former 
of these existed alone, the configuration of the primary would still be one of 
equililjrium under a rotation of amount given by (131). We therefore see tliat the 
actual cohfigui-atinn of the inimary may Ije regarded as a configuration of ecpiilibrium 
under ivdation given by (131), disturbed by the tide-generating potential which is 
caused by the satellite. 
Since this tide-generating potential is small, except in the immediate neighbour¬ 
hood of the satellite, it ought to be possible to remove the tides from the surface 
of the primary, and form a pretty good idea of the configuration which would be 
the configuration of tlie primary except for tidal disturbance. If this is done witli 
the primary of fig. G, it will be found that the remaining curve is a very good 
ellipse. We may therefore conjecture that curve (9) is an ellipse deformed by the 
tidal influence of its satellite. 
Now the ellqise corresponding to the amount of rotation given by (131) is 
curve 4 of the preceding table. We see that the axes are in the ratio y/5 1, and 
this is in good agreement with the ellijise olitained hy removing the tides in fig. G. 
The momentum of the ellipse of unit area of whlcli the axes are in the ratio .^/S ; 1 
(curve 4) is ‘44. If we reduce this so as to api)ly to an ellijise of area '93 instead of 
to one of unit ai'ea, we find an angular momentum of '38. Since this ellipse must be 
supposed to rotate not about its centre, bnt about the centre of gravity of itself and 
a satellite about one-fifteenth of its mass, situated at the end of its axis, this angular 
momentum must he increased to aliout ‘39. The small discrepancy between this and 
the value ’40 obtained for curve 9 may be accounted for pai'tly by 'errors of 
approximation, and partly by the increase of momentuhi caused by the tidal 
deformation of tlie ellipse. 
We can check our result in another way. The equation of the ellipse being 
ax^ -f- /u/” = 1.(1G2), 
the force at x, 0, a point near the extremity of the major axis and outside the ellipse, 
