280 On the Principles of Energetics. 
the first step towards a rational is the discovery of an empirical 
law of the rotations, in which such an element as the inclination 
of the rotation axis to the plane of revolution (easily calculable 
except for the two innermost and two outermost planets) would 
evidently be involved. 
Such a law seems pointed to by the regularity of the decrease 
of the rotations, when the angular, ins stead of the linear velocities 
or times are considered, The respeetive angular velocities of 
rotation of the inner family are "29811, 26902, 26181, and 
25879; and of Jupiter and Saturn, 63313 and ‘59907 re- 
spectively. 
15, The attempts I have made to discover the law of the pla- 
netary rotations have had as yet no complete result*, But the 
following incidental observation with regard to the angular velo- 
cities of revolution and the distances may perhaps be worth noting 
towards such a theory of the formation of the system as above 
alluded to. 
By Kepler’s third law, 
r 
y 
P=cD*; whence = or w=cl —: 
D Dp: 
But under this law there might, in comparing successive velo- 
cities and distances, be found relations of inequality ad infinitum. 
The actual relations may, however, be thus expressed :—The 
angular velocities of revolution and the distances are in inverse 
gcometrical progressions with inverse differenees, except the in- 
nermost planet of each family. 
To say that the distances are in geometrical progression, each 
nearer planet being half the distance of the next more remote, 
or that the angular velocities of revolution are in geometrical 
progression, cach nearer planet revolving with twice the velocity 
of the next more remote, would be very far from accurate ; but 
it seems interesting to ‘observe, as by this law, that when the 
distance of a planet is more than twice that of the next inner, 
its angular velocity of rotation is /ess than half that of the next 
inner, and vice versd, And that the only exceptions to this rule 
should be the innermost planet of each family, viz. Mereury and 
Jupiter, appears significant, 
* The results of an approximative formula were given in a paper “On a 
general Law of Rotation applied to the Planets,” read by me at the Oxford 
Meeting of the British Association, June 1860, 
t See Tumboldt’s remarks on the Law of Bode, or rather of Titius. 
Cosmos, vol, 1. pp. 319, 820, 
