526 
MR. G. H. DARWIN ON THE 
It has been already shown-that «=——— —, and 
J r 19 X 47T yUU °a 
TT 2x3 (f 2x3 A 8 
Hence —= -— 77.— ;- y~ 
5xl9x47r/i«u ox19x47t ecu 
Therefore the rate of reduction of planetary rotation is proportional to /]% 7 wm - 3 v. 
The coefficient of friction v is quite unknown, but we shall obtain indications of the 
relative importance of tidal retardation in the several planets by supposing v to be the 
same in all. If we multiply this expression by rna?, we obtain an expression to which 
the rate of reduction of rotational momentum is proportional. By means of the data 
used in the preceding section I find the following results. 
Table III. 
PJanet. 
Number to which, 
tidal retardation 
is proportional. 
Number to which 
rate of destruction 
of rotational 
momentum is 
proportional. 
Mercury 
1000 - (?) 
9-1 (?) 
Venus . 
11 - (?) 
8-1 (?) 
Bar th . 
1 - 
l-o 
Mars 
•89 
•026 
Jupiter . 
•00005 
2-3 
f -000020 
•n ] 
Saturn . 
■< to 
to > 
•000066 
' 
•54 J 
This table only refers to solar tidal friction, and the numbers are computed on the 
hypothesis of the identity of the coefficient of tidal friction for all the planets. 
The figures attached to Mercury and Venus are open to much doubt. Perhaps the 
most interesting point in this table is that the rate of solar tidal retardation of Mars 
is nearly equal to that of the earth, notwithstanding the comparative closeness of the 
latter to the sun. The significance of these figures will be commented on below. 
I shall now consider— 
(/3) The manner in which solar tidal friction and the contraction of the 'planetary 
nebula work together. 
It will be supposed that the contraction is the more important feature, so that the 
acceleration of rotation due to contraction is greater than the retardation due to tidal 
friction. 
Let h be the rotational momentum of the planet at any time ; then 
_ 5__f 
Cn — h or n 
ma~ 
(29) 
