VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 437 



has a tendency to make the equator approach towards the sun's place, or to di- 

 minish the angle of the sun's declination, by making the earth's axis to turn 

 round its centre in the plane of the circle of the sun's declination. 



The earth has then, at every instant, 1 motions of rotation ; one about the 

 axe of the equator, calletl also the earth's axe; and this is the diurnal motion, 

 whicii is unifomi ; the other motion of rotation is performed about the axe of 

 the circle of the sun's declination, which is a diameter of the equator ; and this 

 motion is produced by the action of the sun on the redundant matter about the 

 equator, and is continually accelerated from the continual application of the 

 solar action producing it. 



The point e, fig. 9, pi. 9, which is the intersection of the circumference of 

 the equator and the circumference of the circle of declination, has '2 motions, 

 whose directions are perpendicular to each other. Let ec be the space which it 

 runs through in an instant, in the circumference of the equator, by the uniform 

 diurnal motion, and let Et be the space it runs through in the same instant, in 

 the circumference of the circle of declination, by an accelerated motion, as has 

 been explained. The point e, in virtue of these 1 motions ec and es, will not 

 circulate either in the circumference ec ge' q'e of the equator, or in the circum- 

 ference E:-pe'p'e of the circle of declination ; but, forming the rectangular paral- 

 lelogram Eee'f, the diagonal ec' will be the elementary arc of the circumference 

 Ee'qE', in which the point e will circulate, and the angle cec' will be equal to 

 the angle acq, and equal to the angle p'c'p', which the pole p' runs through in 

 an instant in the circumference p'p'oqpQ'p', whose plane is perpendicular to the 

 plane of the circle of declination ; and when the lines Ee, ee are known at every 

 instant, p'p' will also be known, since the angle cec' is = to the angle acq = to 

 the angle p'cp'. 



The instantaneous motion of the pole, which is p'p', or pp, may be resolved 

 into two, PR and pm, perpendicular to each other, and both to the earth's axe. 

 The former causes the pole p to move parallel to the ecliptic T 25 ^ Vy, and 

 alters the place of the solstice 25, and consequently also that of the equinoc- 

 tial points y and £i: ; the latter, which is according to pm, alters the inclination 

 of the earth's axe to the ecliptic. 



To have the motion of the pole parallel to the ecliptic, or, which is the sarne^ 

 the motion of the node f, or the precession, in the same time that the sun 

 passes from the equinox "f to the solstice 25, take the integral of the lines pr,, 

 supposing PR generally to express the instantaneous precession for any declinatioa 

 of the sun s. 



And to have the alteration of the inclination in the same time that the sun is 

 passing from "|f to 25, take the sum, or the integral of the lines pm, supposing 



