484 kepobt — 1878. 



tidal standard, this is neither a very great nor a very small viscosity, for the crest 

 of the semi-diurnal tide precedes the moon hy 17° 30'. 



I found, then, that if the changes in the system are tracked hack for 56 million 

 years, we find the day reduced to 6 hours 50 minutes, the obliquity to the ecliptic 

 9° less than at present, and the moon's period round the earth reduced to 1 day 

 14 hours. 



This very short period for the moon indicates of course that her distance from 

 the earth is small. As the moon goes on approaching the earth, the problem 

 becomes much more complex ; and for periods more remote than 56 million years 

 ago, I abandoned the attempt to obtain a scale of times. The solution up to this 

 point shows that the times requisite for these causes to produce such startling 

 effects are well within the time which physicists have admitted to have elapsed 

 since the earth existed. 



From this point in the solution the parallel changes of the obliquity, day and 

 month, were traced without reference to time. 



It appears, then (still looking backwards in time), that the obliquity will only 

 continue to diminish a little more beyond the point already reached ; for when the 

 month has become equal to twice the day there is no longer any tendency for the 

 obliquity to diminish, and for yet smaller values of the month the tendency is to 

 increase again. 



From this we learn that when the day is equal or less than half the month, 

 the position of the earth's axis at right angles to the plane of the moon's orbit is 

 one of dynamical stability. The whole decrease of obliquity from the present value 

 back to the critical point, where the month is equal to twice the day, is 10°. 



From this point in the solution back to the initial state to which the earth and 

 moon are tending, the obliquity to the plane of the lunar orbit was neglected. I 

 then found that the limiting condition, beyond which it was impossible to go, was 

 one in which the earth and moon are rotating, fixed together as a rigid body in 5 

 hours and 40 minutes. This condition was also found to be one of dynamical in- 

 stability, so that if the month had been a little shorter than the day, the moon 

 .aiust have fallen into the earth ; but if the month had been a little longer than the 

 day, the moon must have receded from the earth, and have gone through the series 

 of changes which were traced backwards up to this initial condition. 



This periodic time of the moon of 5 hours 40 minutes corresponds to an interval 

 of only 6,000 miles between the moon's centre and the earth's surface. Moreover, 

 if the earth had been treated as heterogeneous instead of homogeneous, this interval 

 between the primeval earth and moon would have been yet further diminished, as 

 also would be the common periodic time. The conclusion, therefore, appears to me 

 almost irresistible, that if the moon and earth were ever molten viscous bodies, then 

 they once formed parts of a common mass. 



With respect to the obliquity of the ecliptic, the question is one of considerable 

 difficulty ; but on the whole I incline to the view that while a large part of the 

 obliquity may be referred to these causes, yet that there remains an outstanding 

 part which is not so explicable. 



Besides the results of which the outlines have been given, I have obtained some 

 others which, as I believe, will aid in the formation of a modified edition of the 

 nebular hypothesis — such as some of the changes to which an annular satellite 

 would be subjected. 



One of the collateral results which appeared in considering the secular changes 

 of such a system fas the earth, moon, and sun, was that a large amount of heat 

 would have been generated in the interior of the earth by means of friction. If, 

 then, it is permissible to suppose that any considerable part of these changes have 

 taken place during geological history, Sir William Thomson's problem of the secular 

 cooling of the earth would require some modification. 



The magnitude of the undertaking has not allowed me time as yet to apply 

 these ideas to the questions of the eccentricity and inclination of the orbit of the 

 satellite, nor to the cases of other planets besides the earth. 



I think, however, that I see in Asaph Hall's wonderful discovery of the Mar- 

 tian Satellites a confirmation of this theory. Their extreme minuteness has, I 



