THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
879 
In Part VI. the equations giving the rate of change of eccentricity are integrated, 
on the hypothesis that the earth has small viscosity. 
The first step is to convert the time-rates of change into distance-rates, and thus 
to eliminate the time, as in the previous integrations. 
The computations made for the paper on “Precession” were here made use of, as 
far as possible. 
The results of the retrospective integration are given in Table XVI., § 28. This 
table exhibits the eccentricity falling from its present value of yg-th down to about 
ToA'oo'th, so that at the end the orbit is very nearly circular. 
The integration in the case of large viscosity is not carried out, because the actual 
degree of viscosity will exercise so vei’y large an influence on the result. 
If the viscosity were infinitely large, we should find the eccentricity getting larger 
and larger retrospectively, and ultimately becoming infinite, when 2 months were equal 
to 3 days. This result is of course absurd, and merely represents that the larger the 
viscosity, the larger would be the eccentricity. On the other hand, if the viscosity 
were merely large, we might find the eccentricity decreasing at first, then stationary, 
then increasing until 2 months were equal to 3 days, and then decreasing again. 
It follows therefore that various interpretations may be put to the present eccen¬ 
tricity of the lunar orbit. 
If, as is not improbable, the more recent changes in the configuration of our system 
have been chiefly brought about by oceanic tidal friction, whilst the earlier changes 
were due to bodily tidal friction, with considerable viscosity of the planet, then, sup¬ 
posing the orbit to have been primevally circular, the history of the eccentricity must 
have been as follows : first an increase to a maximum, then a decrease to a minimum, 
and finally an increase to the present value. There seems nothing to tell us how large 
the early maximum, or how small the subsequent minimum of eccentricity may have 
been. 
VIII. 
REVIEW OF THE TIDAL THEORY OF EVOLUTION AS APPLIED TO THE EARTH 
AND THE OTHER MEMBERS OF THE SOLAR SYSTEM. 
I will now collect the various results so as to form a sketch of what the previous 
investigations show as the most probable history of the earth and moon, and in order 
to indicate how far this history is the result of calculation, references will be given to 
the parts of my several papers in which each point is especially considered. 
We begin with a planet, not very much more than 8,000 miles in diameter,and 
probably partly solid, partly fluid, and partly gaseous. This planet is rotating about 
* “ Precession,” § 24. 
5 u 2 
