512 
MR. G. H. DARWIN ON THE 
which represents the general nature of the surface for the case where the ^-satellite 
revolves negatively and the ^/-satellite positively. But of course the figure would not 
he drawn correctly to scale. 
The contours for the remaining quadrant, in which both satellites revolve nega¬ 
tively would somewhat resemble a family of rectangular hyperbolas with the axes as 
asymptotes. I have not thought it worth while to construct them, but the physical 
interpretation is obviously that both satellites always must approach the planet. 
II. 
A DISCUSSION OF THE EFFECTS OF TIDAL FRICTION WITH REFERENCE TO THE 
EYOLUTION OF THE SOLAR SYSTEM. 
§ 6. General consideration of the 'problem presented by the solar system. 
In a series of previous papers I have traced out the changes in the manner of motion 
of the earth and moon which must have been caused by tidal friction. By adopting 
the hypothesis that tidal friction has been the most important element in the history 
of those bodies, we are led to coordinate together all the elements in their motions in 
a manner so remarkable, that the conclusion can hardly be avoided that the hypothesis 
contains a great amount of truth. 
Under these circumstances it is natural to inquire whether the same agency may not 
have been equally important in the evolution of the other planetary sub-systems, and 
of the solar system as a whole. 
This inquiry necessarily leads on to wide speculations, but I shall endeavour to 
derive as much guidance as possible from numerical data. 
In the first part of the present paper the theory of the tidal friction of a planet, 
attended by several satellites, has been treated. 
It would, at first sight, seem natural to replace this planet by the sun, and the 
satellites by the planets, and to obtain an approximate numerical solution. We might 
suppose that such a solution would afford indications as to whether tidal friction has 
or has not been a largely efficient cause in modifying the solar system. 
The problem here suggested for solution differs, however, in certain points from that 
actually presented by the solar system, and it will now be shown that these differences 
are such as would render the solution of no avail. 
The planets are not particles, as the suggested problem would suppose them to be, 
but they are rotating spheroids in which tides are being raised both by then’ own 
satellites and by the sun. They are, therefore, subject to a complicated tidal friction; 
the reaction of the tides raised by the satellites goes to expand the orbits of the 
satellites, but the reaction of the tide raised in the planet by the sun, and that raised 
