"2 



Mr. G. H. Darwin. 



[Dec. 18, 



strictly appropriate to an abstract, since they do not occur in the 

 paper, and merely serve as a rough substitute for analysis. 



In this and the previous papers it is supposed that tides are raised 

 in a planet by its satellites, and the problem is to determine the 

 various effects which result from the friction of those tides. 



The hypothesis generally adopted in these papers is that the planet 

 is a viscous body, and that the tides are a bodily distortion of the 

 whole mass of the planet, but nearly all the results would also follow 

 from the friction of oceanic tides upon a rigid nucleus. 



The investigation is principally directed towards the case of the 

 earth, sun, and moon, and the phraseology of the paper is taken from 

 our own planet and satellite ; but the methods may be extended to the 

 other planets. 



The subject will be most easily explained by inverting the order of 

 the paper, and by beginning with the sketch of the results. 



Sketch of Results. 



At the present time the moon revolves round the earth in 27"3 days. 

 The orbit has an eccentricity of y^-, and is inclined at an angle of 

 5° 9' to a certain plane, which is said to be " proper to the orbit." 

 This proper plane is inclined to the ecliptic at an angle of about 8", 

 and intersects the ecliptic in the equinoctial line ; it lies on the same 

 side of the ecliptic as the earth's equator. 



In this statement the " periodic inequalities " of the moon's motion 

 are neglected. 



In this and the previous papers it is proved that frictional tides in 

 the earth are causing, and must have caused, changes in the configu- 

 ration of the system. The changes in the past may be summarised as 

 follows : — 



1. The lunar period must have been shorter in the past, and may 

 loe traced back from the present 27"3 days, until initially the moon 

 xevolved round the earth in from 2 to 4 hours. 



2. The inclination of the orbit to the proper plane must have 

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

 5° 9' until it was 6° or 7°. This 6° or 7° was a maximum inclination, 

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

 Tery small, or zero. 



3. The inclination of the proper plane to the ecliptic must have 

 been greater in the past, and may be traced back from the present 8", 

 until it was in very early times about 11° 45'. It is possible that 

 initially this inclination was less, and that the 11° 45' of inclination 

 was a maximum value. 



4. The eccentricity of the orbit must have been smaller in the past. 

 Either at one time it had a minimum value, before which it had a 



