882 
MR. a. H. DARWIN - ON" THE SECULAR CHARGES IX 
increase. The inclination of the lunar orbit to its proper plane increases to a maximum 
of 6° or 7°,* * * § ** and ever after diminishes ; the inclination of the equator to its proper 
plane increases to a maximum of about 2° 45',+ and ever after diminishes. The 
maximum inclination of the lunar orbit to its proper plane takes place when the day is 
a little less than 9 of our present hours, and the month a little less than 6 of our 
present days. The maximum inclination of the equator to its proper plane takes 
place earlier than this. 
Whilst these changes have been going on, the proper planes have been themselves 
changing in their positions relatively to one another and to the ecliptic. At first they 
were nearly coincident with one another and with the earth’s equator, but they then 
open out, and the inclination of the lunar proper plane to the ecliptic continually 
diminishes, whilst that of the terrestrial proper plane continually increases. 
At some stage the earth has become more rigid, and oceans have been formed, so 
that it is probable that oceanic tidal friction has come to play a more important part 
than bodily tidal friction.J If this be the case the eccentricity of the orbit, after 
passing through a stationary phase, begins to increase again. 
We have now traced the system to a state in which the day and month are increas¬ 
ing, but at unequal rates; the inclination of the lunar proper plane to the ecliptic and 
of the orbit to its proper plane are diminishing; the inclination of the terrestrial 
proper plane to the ecliptic is increasing, and of the equator to its proper plane is 
diminishing ; and the eccentricity of the orbit is increasing. 
No new phase now supervenes,§ and at length we have the system in its present 
configuration. The minimum time in which the changes from first to last can have 
taken place is 54,000,000 years.|| 
In a previous paper it was shown that there are other collateral results of the vis¬ 
cosity of the earth; for during this course of evolution the earth’s mass must have 
suffered a screwing motion, so that the polar regions have travelled a little from west 
to east relatively to the equator. This affords a possible explanation of the north and 
south trend of our great continents.^ Also a large amount of heat has been generated 
by friction deep down in the earth, and some very small part of the observed increase 
of temperature in underground borings may be attributable to this cause."""" 
* Table XY„ Part IV. 
t Found from the values in Table XV., and by a graphical construction. 
j Compare with “ Precession,” § 14, where the present secular acceleration of the moon’s mean motion 
is considered. 
§ Unless the earth's proper plane (or mean equator) be now slowly diminishing in obliquity, as would 
be the case if the bodily tides are more potent than the oceanic ones. In any case this diminution must 
ultimately take place in the far future. 
|| “ Precession,” end of § 18. 
■" “ Problems,” Part I. 
** “ Problems,” Part II. 
