AND ON THE REMOTE HISTORY OF THE EARTH. 
529 
is such, that an observer taking the earth as his clock would conceive a moon, which 
was undisturbed by tidal reaction, to be 7"'l in advance of her place at the end of a 
century. But the actual moon is 3"T behind her true place, and thus our observer 
would suppose the moon to be in advance 7'1 — 3'1 or 4" at the end of the century. 
Lastly, the obliquity of the ecliptic is diminishing at the rate of 1° in 500 million 
years. 
The other hypothesis considered is that the earth is very nearly perfectly elastic. In 
this case the semi-diurnal and diurnal tides do not lag perceptibly/and the whole of the 
reaction is thrown on to the fortnightly tide, and moreover there is no perceptible tidal 
frictional couple about the earth’s axis of rotation. From this follows the remarkable 
conclusion that the moon may be undergoing a true secular acceleration of motion of 
something less than 3 //- 5 per century, whilst the length of day may remain almost un¬ 
affected. Under these circumstances the obliquity of the ecliptic must be diminishing 
at the rate of 1° in something like 130 million years. 
This supposition leads to such curious results, that I investigated what state of 
things we should arrive at if we look back for a very long period, and I found that 
700 million years ago the obliquity might have been 5° greater than at present, whilst 
the month would only be a little less than a day longer. The suppositions on which 
these results are based are such that they necessarily give results more striking than 
would be physically possible. 
The enormous lapse of time which has to be postulated renders it in the highest 
degree improbable that more than a very small change in this direction has been taking 
place, and moreover the action of the ocean tides has been entirely omitted from 
consideration. 
The results of these two hypotheses show what fundamentally different interpreta¬ 
tions may be put to the phenomenon of the secular acceleration of the moon. 
Sir William Thomson also has drawn attention to another disturbing cause in the 
fall of meteoric dust on to the earth.* 
Under these circumstances, I cannot think that any estimate having any pretension 
to accuracy can be made as to the present rate of tidal friction. 
Since the obliquity of the ecliptic, the diurnal rotation of the earth, and the moon’s 
distance change, the whole system is in a state of flux ; and the next question to be 
considered is to determine the state of things which existed a very long time ago 
(Part II.). This involved the integration of three simultaneous differential equations; 
the mathematical difficulties were, however, so great, that it was found impracticable 
to obtain a general analytical solution. I therefore had to confine myself to a 
numerical solution adapted to the case of the earth, sun, and moon, for one particular 
degree of viscosity of the earth. The particular viscosity was such that, with the 
present values of the day and month, the time of the lunar semi-diurnal tide was 
retarded by 1 hour and 10 minutes; the greatest possible lagging of this tide is 
* ‘ Glasgow Geological Society,’ Vol. III. Address “ On Geological Time.” 
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