LUNAR DECLINATION. IT 



the ecliptic at a mean rate of 19 19' 42-31G" a year; 

 they will therefore recur to similar points of the 

 ecliptic in cycles of about 18*6 years. But, as the 

 plane of the ecliptic is inclined to the earth's equator, 

 the cycle in which a similar series of amounts of 

 lunar declination from the equator recurs will be 

 that in which similar nodes recur at similar points of 

 the ecliptic at similar periods of the year. And, as 

 the nodes make eight complete revolutions in 149 

 years with approximate accuracy; therefore the tidal 

 influence resulting from variations of lunar declina- 

 tion, will recur approximately in cycles of 149 years. 

 That is to say; since the nodes regress at the average 

 rate of 19 19' 42-316" a year, they therefore in 149 

 years regress 2879 56' 5.084"; which differs less 

 than 4' from 2880, or 8 complete revolutions. And 

 we may therefore, as far as our present purposes are 

 concerned, regard this as a recurring cycle. 



And, since the angle at which the plane of the 

 moon's motion in its orbit round the earth is inclined 

 to the plane of the earth's motion in its orbit round 

 the sun is about 5; and the angle at which the 

 plane of the earth's motion in its orbit round the sun 

 is inclined to the plane of the earth's axial rotation 

 is about 23^; therefore in consequence of the 

 changing of the points of intersection of these planes, 

 before mentioned the oscillations of the moon in lati- 

 tude extend, during some parts of the cycle of 149 

 years, to more than 28 from the equator on each side ; 



VOL. II. C 



