THE ASTRONOMICAL DEDUCTIONS. 11 



The retrograde revolution of the ninth satellite of Saturn still further 

 and seriously complicates the case from the centrifugal point of view. 



The rotations of Uranus and Neptune are unknown, but, whether they 

 are concordant with the revolutions of their satellites or not, they present 

 difficulties under the centrifugal hypotheses because of the great obliquity 

 of the planes of revolution of their satellites to the common plane of the 

 s)'^stem, and because of their retrograde motions. This has long been 

 recognized, but these difficulties gain not a little in force when they are 

 associated with other rotational difficulties which have been insufficiently 

 considered in connection with them. 



There are still other rotational features of the existing planets which 

 seem to be inconsistent with all forms of a contractional-centrifugal hypoth- 

 esis of planetary origin, and, what is especially to the point in the matter 

 in hand, which seem inconsistent with the very high rotational velocities 

 which such a hypothesis necessarily postulates. Among these are the great 

 differences in the rotational features of the members of the system. If 

 the system started from a common spheroid and if its derivatives were 

 shed by systematic centrifugal action, it is very difficult to see how so great 

 variety of rotational velocities, so varied inclinations of the rotational 

 axes, and so diverse directions of rotation as the system actually presents, 

 could have arisen. 



Under the planetesimal hypothesis, the rotation of each planet is held 

 to have arisen independently of every other planet. Its rate of rotation 

 depended on the special conditions that attended the expulsion of its 

 nucleus from the sun, and on the mode of accession of the rest of its material 

 from the planetesimal state — conditions that were quite certain to vary 

 with each planet. Rotations, rapid or slow, direct or retrograde, with 

 inclinations of any degree, are consistent with the hypothesis. There is, 

 however, a decided balance of presumption in favor of forward rotations, 

 of moderate inclinations of axis, and of moderate velocities of rotation. 

 As none of the planets rotate at speeds that even remotely approach that 

 requisite for equatorial discharge, as their rates of rotation differ widely 

 from one another, as the inclinations of their axes vary greatly, and as the 

 majority of their rotations are direct and the minority retrograde, this 

 hypothesis seems to be concordant with the facts of the case. 



If we are thus permitted to start with a genesis which leaves us free 

 to suppose that the rate of the earth's rotation at the outset may have 

 been essentially what it is to-day, or may have been faster or slower in any 

 degree, the preconceptions that have led to former rotational views do not 

 trammel us. The determination of the past history of the earth's rotation 

 rests unhampered upon the evidences presented by its own phenomena 

 and upon those deducible from the necessary influence of its neighbors. 



The most important of the rotatory influences of neighboring bodies on 

 the earth is the friction of the tides, particularly of the lunar tides. The 

 assigned mode of this action is familiar and may be stated briefly as fol- 

 lows: If the tidal protuberance has a position in advance of the position 

 of the moon, as at A in fig. 1, a component of the moon's attraction tends 

 to antagonize the earth's rotation and to accelerate the moon's motion. 



