1879.] On Secular Changes in the Orbit of a Satellite. 3 



maximum value, and again earlier it was very small, or zero ; or else 

 the maximum value never occurred, and the eccentricity has always 

 been increasing. The history of the eccentricity depends on the 

 nature of the tides in the earth, but the former of these alternatives 

 seems the more probable. 



We will now consider the earth. 



At the present time the earth rotates in 24 hours, its equator is in- 

 clined at an angle of about 9" to a plane, which is called in this paper 

 "the proper plane of the earth." This proper plane is inclined at an 

 angle of 23° 28' to the ecliptic, and its intersection with the ecliptic is 

 the equinoctial line. 



(In the ordinary mode of statement the proper plane is called the 

 mean equator, and the true equator is described as nutating about the 

 mean equator with a period of 19 years, and an amplitude of 9".) 



It is here proved that the frictional tides in the earth have caused 

 changes, which may be summarised as follows : — 



5. The earth's period of rotation, or the day, must have been 

 shorter in the past, and it may be traced back from the present value 

 of 24 hours, until initially it was from 2 to 4 hours in length. It was 

 then identical with the moon's period of revolution as described in (1). 



6. The inclination of the equator to " the earth's proper plane," must 

 have been larger in the past, and may be traced back from the present 

 value of 9", until it was about 2° 45'. This 2° 45' was a maximum 

 inclination, and in the more remote past the inclination was less, and 

 initially it was very small, or zero. 



7. The inclination of "the earth's proper plane " to the ecliptic 

 must have been smaller in the past, and may be traced back from its 

 present value of 23° 28', until initially it was 11° 45', or perhaps 

 somewhat less. It was then identical with the proper plane of the 

 lunar orbit ; and this is true whether or not 11° 45' was a maximum 

 inclination of the lunar proper plane to the ecliptic, as described 

 m (1). 



The preceding statements may be subject to varieties of detail, 

 according to the nature of the tides raised in the earth, but the above 

 is a summary of what appears to be the most probable course of 

 evolution. 



The hypothesis which is suggested as most probable is, that the 

 more recent changes in the system have been principally due to 

 oceanic tidal friction, and that the more ancient changes were pro- 

 duced by bodily tidal friction. 



These seven statements, when taken together, exhibit the earth and 

 moon 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 2 to 4 hours, about an axis 

 inclined to the normal to the ecliptic at an angle of 11° 45', or some- 



b 2 



