236 



NATURE 



[Jan. 8, 1880 



We know that no solids are either perfectly rigid or 

 perfectly elastic, and that no fluids are devoid of internal 

 friction, and therefore the tides raised in any planet, 

 whether consisting of oceanic tides or of a bodily distor- 

 tion of the planet, must be subject to friction. From 

 this it follows that the dynamical investigation must be 

 applicable to some extent to actual planets and satellites. 

 For myself, I believe that it gives the clue to the history 

 of the system, but of course an ample field for criticism is 

 here opened. 



The investigation is intended to be more especially 

 applicable to the case of the earth and rhoon, and there- 

 fore, instead of planet and satellite, the expressions earth 

 and moon are used. 



The effect of tidal friction upon the eccentricity and 

 inclination of the lunar orbit here affords the principal 

 topic. The obliquity of the ecliptic, the diurnal rotation 

 of the earth, and the moon's periodic time were considered 

 in a paper read before the Royal Society on December 19, 

 1878, and which will appear in the Philosophical Trans- 

 actions for 1879. 



The present paper completes (as far as I now see) the 

 main investigation for the case of the earth and moon, and 

 therefore it is now possible to bring the various results to 

 a focus. 



It appears then that, when we trace backwards in time 

 the changes induced in the system of the earth and moon 

 by tidal friction, we are led to an initial state which is 

 defined as follows : — 



The earth and moon are found to be initially nearly in 

 contact ; the moon always opposite the same face of the 

 earth, or moving very slowly relatively to the earth's sur- 

 face ; the whole system rotating in from two to four hours, 

 about an axis inclined to the normal to the ecliptic at an 

 angle of 1 1° 45', or somewhat less ; and the moon moving 

 in a circular orbit, the plane of which is nearly coincident 

 with the earth's equator. 



This initial configuration suggests that the moon was 

 produced by the rupture, in consequence of rapid rotation 

 or other causes, of a primeval planet, whose mass was 

 made up of the present earth and moon. The coincidence 

 is noted in the paper, that the shortest period of revolution 

 of a fluid mass of the same mean density as the earth, 

 which is consistent with an ellipsoidal form of equilibrium, 

 is two hours twenty-four minutes; and that if the moon 

 were to revolve about the earth with this periodic time, the 

 surfaces of the two bodies would be almost in contact with 

 one another. 



The rupture of the primeval planet into two patts is a 

 matter of speculation, but if a planet and satellite ba given 

 in the initial configuration above described, then a system 

 bearing a close resemblance to our own, would necessarily 

 be evolved under the influence of tidal friction. 



The theory postulates that there is not sufficient diffused 

 matter to materially resist the motions of the moon and 

 earth through space. Sufficient lapse of time is also re- 

 quired. In a previous paper I showed that the minimum 

 time in which the system could have degraded from the 

 initial state, just after the rupture into two bodies, down 

 to the present state, is fifty-four million years. The time 

 actually occupied by the changes would certainly be much 

 longer. 



It appears to me that a theory, reposing on a vera 

 causa, which brings into quantitative correlation the 

 lengths of the present day and month, the obliquity of the 

 ecliptic and the inclination and eccentricity of the lunar 

 orbit, must have considerable claims to acceptance. 



It was stated that the periodic times of revolution and 

 rotation of the moon and earth might be traced back to a 

 common period of from two to four hours. In a pn 

 paper the common period was found to be a little oxer five 

 hours in length ; but that result was avowedly based on a 

 partial neglect of the sun's attraction. In this papi 

 certain further considerations are adduced, which show 



that, while the general principle remains intact, yet the 

 common period of revolution of the earth and moon must 

 initially have been shorter than five hours to an amount 

 which is uncertain, but is probably large. The period of 

 from two to four hours is here assigned, because it is 

 mechanically impossible for the moon to revolve about the 

 earth in less than two hours, and it is uncertain how the 

 rupture of the primeval planet took place. 



But if tidal friction has been the agent by which the 

 earth and moon have been brought into their present 

 configuration, then similar changes must have been going 

 on in the other bodies which make up the solar system. I 

 will therefore make a few remarks on the other satellites 

 and planets. 



In the first place it is in strict accordance with the 

 theory, that the moon should always present the same 

 face towards the earth. Helmholtz, was, I believe, the 

 first who suggested tidal friction as the cause of the reduc- 

 tion of the moon's axial rotation to identity with her 

 orbital motion. It is interesting to note in this connection 

 that the telescope seems to show that the satellites of 

 Jupiter, and one at least of the satellites of Saturn, also 

 have the same peculiarity. 



The process by which tidal friction brings about the 

 changes in the configuration of a planet and satellite is 

 a destruction of energy (or rather its partial conversion 

 into heat within the planet, and partial redistribution), and 

 a transference of angular momentum from that of planet- 

 ary rotation to that of orbital revolution of the two bodies 

 about their common centre of inertia. 



Now a large planet has both more energy of rotation 

 and more angular momentum ; hence it is to be expected 

 that large planets should proceed in their changes more 

 slowly than small ones. 



Mars is the smallest of the planets, which are attended 

 by satellites, and it is here alone that we find a satellite 

 revolving faster than the planet rotates. This will also be 

 the ultimate fate of our moon, because after the joint 

 lunar and solar tidal friction has reduced the earth's rota- 

 tion to an identity with the moon's orbital motion, the 

 solar tidal friction will continue to reduce it still further, 

 so that the earth will rotate faster than the moon 

 revolves. 



Before, however, this can take place with us, the moon 

 must recede to an enormous distance from the earth, and 

 the earth must rotate in forty or fifty days instead of in 

 twenty-four hours. But the satellites of Mars are so 

 small, that they would only recede a very short way from 

 the planet, before the solar tidal friction reduced the 

 planet's rotation below the satellite's revolution. The rapid 

 revolution of the inner satellite of Mars may then, in a 

 sense, be considered as a memorial of the primitive rota- 

 tion of the planet round its axis. 



The planets Jupiter and Saturn are very much larger 

 than the earth, and here we find the planets rotating with 

 great speed, and the satellites revolving with short periodic 

 times. The inclinations of the orbits of Jupiter's satellites 

 to their " proper planes " arc very interesting from the 

 point of view of the present theory. 



The Saturnian system is much more complex than that 

 of Jupiter, and it seems partially in an early stage of 

 development and partially far advanced. 



The details of the motions of the satellites are scarcely 

 well enough known to afford strong arguments either for 

 or against the theory. 



I have not as vet 'investigated the case of a planet or 

 star attended by several satellites, but perhaps future in- 

 vestigations may throw further light both on the case of 

 Saturn, and on the whole solar system itself. 



The celebrated nebular hypothesis of Laplace and Kant 

 supposes that a revolving nebula detached a ring, which 

 ultimately became consolidated into a planet or satellite, 

 and that the central portion of the nebula continued to 

 contract, and formed the nucleus of the sun or planet. 



