524 
MR G. H. DARWIN ON THE 
subsystems is very small compared with the orbital momentum of the planet in its 
motion round the sun. This ratio is largest in the case of Jupiter, and here the 
nternal momentum is '00026 whilst the orbital momentum is 13 ; hence in the case 
of Jupiter the orbital momentum is 5000 times the sum of the rotational momentum 
of the planet and the orbital momentum of its satellites. From this it follows that if 
the whole of the momentum of Jupiter and his satellites were destroyed by solar tidal 
friction, the mean distance of Jupiter from the sun would only be increased by 3 Woth 
part. The effect of the destruction of the internal momentum of any of the other 
planets would be very much less. 
If therefore the orbits of the planets round the sun have been considerably enlarged, 
during the evolution of the system, by the friction of the tides raised in the planets 
by the sun, the primitive rotational momentum of the planetary bodies must have 
been thousands of times greater than at present. If this were the case then the 
enlargement of the orbits must simultaneously have been somewhat increased by the 
reaction of the tides raised in the sun by the planets. 
But it does not seem probable that the planetary masses ever possessed such an 
enormous amount of rotational momentum, and therefore it is not probable that tidal 
friction has considerably affected the dimensions of the planetary orbits. 
It is difficult to estimate the degree of attention which should be paid to Bode’s 
empirical law concerning the mean distances of the planets, but it may perhaps be 
supposed that that law (although violated in the case of Neptune, and only partially 
satisfied by the asteroids) is the outcome of the laws governing the successive epochs 
of instability in the history of a rotating and contracting nebula. Now if, after the 
genesis of the planets, tidal friction had considerably affected the planetary distances, 
then all appearance of such primitive law in the distances'would be thereby obliterated. 
If therefore there be now observable a sort of law of mean distances, it to some 
extent falls in with the conclusion arrived at by the preceding numerical comparisons. 
The extreme relative smallness of the masses of the Martian and Jovian satellites 
tends to show the improbability of very large changes in the dimensions of the orbits 
of those satellites; although the argument has not nearly equal force in these cases, 
because the distances of the satellites from these planets is small. 
The numbers given in column iii. of Table II. show in a striking manner the great 
difference between the present physical conditions of the terrestrial system and those 
of Mars, Jupiter, and Saturn. These numbers may perhaps be taken as representing 
the amount of effect which the tidal friction due to the satellites has had in their 
evolution, and confirms the conclusion that, whilst tidal friction may have been (and 
according to previous investigations certainly appears to have been) the great factor 
in the evolution of the earth and moon, yet with the satellites of the other planets it 
has not had such important effects. 
In previous papers the expansion of the lunar orbit under the influence of terrestrial 
tidal friction was examined, and the moon was traced back to an origin close to the 
