528 
MR. G. H. DARWIN ON THE 
expression for the rate of loss of rotational momentum ; Hud is large compared with I: 
so long as the rotation of the planet is fast compared with the orbital motion of the 
planet about the sun, and since this factor is always positive, it always increases as the 
contraction increases. 
For planets remote from the sun, where contraction has played by far the more 
important part, (3 will be very nearly equal to -f, and for those nearer to the sun (3 
will be small (or it might be negative if the tidal retardation exceeds the contractional 
acceleration). 
We thus have one factor always increasing and the other always diminishing, and 
the importance of the increasing factor is greater for planets remote from than for 
those near to the sun. 
If jS be small it is difficult to say how the two rates will vary as the contraction 
proceeds. But if (3 does not differ very much from § both rates are probably 
initially small, then rise to a maximum and then diminish. 
Hence it may be concluded as probable that in the history of a contracting planetary 
mass, which is sufficiently far from the sun to allow contraction to be a more important 
factor than tidal friction, both the rate of loss of rotational momentum and of loss of 
rotation, due to solar tidal friction, were initially small, rose to a maximum and then 
diminished. 
These considerations are important as showing that the efficiency of solar tidal 
friction was probably greater in the past than at present. 
We now come to (y)— 
The effect of the genesis of a satellite on the evolu tion. 
This subject is necessarily in part obscure, and the conclusions must in so far be open 
to doubt. 
When a satellite separates from a planetary mass, it seems probable that that part 
of the planetary mass, which before the change had the greatest angular momentum, 
is lost by the planet. Hence the rotational momentum of the planet suffers a dimi¬ 
nution, and the mass is also diminished. An inspection of the expressions in the last 
paragraphs show T s that it is probable that the loss of a satellite diminishes the rate 
of loss of planetary rotational momentum, but slightly increases the rate of loss of 
rotation due to solar tidal friction. 
Now if the satellite be large the effect of the tides raised by the satellite in the 
planet is to cause a much more powerful reduction of planetary rotation than was 
effected by the sun. The rotational momentum thus removed from the planet 
reappears in the orbital momentum of its satellite. And the reduction of rotation 
of the planet causes a reduction of rate of solar tidal effects, by diminishing the 
angular velocity of the planet’s rotation relatively to the sun. 
The first and immediate effect of the separation of a satellite is no doubt highly 
speculative, but the second effect seems to follow undoubtedly, whatever be the mode 
of separation of the satellite. 
