10 THE TIDAL PROBLEM. 



under any hypothesis that rests on centrifugal separation, that the present 

 speed of the sun's equator would certainly be much greater than 38 miles 

 per second, and should approach the higher figures given. As a matter of 

 fact, the sun's equatorial velocity of rotation is only about 1.3 miles per 

 second. Such a rate seems, therefore, to be altogether inconsistent with 

 the doctrine of centrifugal separation. If, for a moment, the thought be 

 entertained that tidal retardation may have reduced the sun's rotation 

 from a high primitive rate consistent with the centrifugal hypothesis, to 

 the present rate, it will become obvious, on a study of the nature and value 

 of the tidal influence of the planets on the sun, that this is wholly unten- 

 able. The quantitative estimates of Sir George Darwin are decisive on this 

 point.^ So also is the remarkable fact that the equatorial portion of the 

 sun has a higher rotational velocity than the portions in higher latitudes 

 instead of lagging, as it should if it were affected by tidal retardation. 



The obliquity of the sun's axis is a further grave objection to all forms 

 of the doctrine of centrifugal separation. On the other hand, some such 

 obhquity is extremely probable under the hypothesis that the system was 

 developed by the influence of a passing star, for the axis of the ancestral 

 sun might obviously sustain any relationship to the orbital plane of the 

 disturbing body. The position of the present axis, under this hypothesis, is 

 the result of a composition of moments of momentum derived in part from 

 the ancestral rotation and in part from the passing star, and it could not 

 therefore be expected, except by a remote chance, to be exactly normal 

 to the common plane of the planetary system. Under this hypothesis the 

 obliquity of the sun's axis, together with its slow rotation, suggest, if they 

 do not distinctly imply, that the direction of rotation of the ancestral sun 

 was opposite to that of the present sun, and that its axis was more inclined 

 than now to the plane of the present system. 



Of similar rotational import is the relationship between the time of 

 rotation of Mars and that of the revolution of its inner satellite, Phobos. 

 It is obvious that, under any hypothesis of centrifugal separation, if a 

 revolving spheroid acquires by contraction an equatorial velocity sufficient 

 to leave behind the material of a satelHte, and afterwards continues to 

 contract until its radius is but a small fraction of its value at the time of 

 separation, the rate of rotation of the spheroid must be greatly increased 

 and its period must be much shorter than the revolutionary period of the 

 derived satelHte, unless some very potent agency intervenes to reverse 

 the systematic process of the evolution. Now, the satelHte Phobos revolves 

 around Mars about three times while the planet rotates once. In an anal- 

 ogous way the little bodies that make up the inner edge of the inner ring 

 of Saturn revolve about that planet twice while the planet rotates once. 

 These are, on their face at least, seriously out of accord with the doctrine 

 of centrifugal separation by planetary contraction. Darwin has suggested 

 that tidal retardation may be a possible solution in the special case of 

 Phobos, but Moulton has called attention to the insuperable difficulties 

 of applying this explanation consistently to the Saturnian case and the 

 Martian case at the same time.^ 



' Trans. Phil. Soc. Lond., 1881. ^ Astrophys. Jour., vol. 11, Mar., 1900, p. 109. 



