l64 PHILOSOPHICAL TRANSACTIONS. [aNNO I764. 



and longitude into time of the primum mobile, instead of converting them into 

 mean solar time, which, says he, may produce an error of 1 seconds and a half; 

 3dly, because the equation of the sun's centre was not known exactly before, 

 every minute of which answers to 4 seconds in the equation of time." 



I readily agree with M. Delalande, that the equation of time could not be 

 had so exactly formerly, as it may now, when we have a much more exact 

 theory of the sun, and are lately made acquainted with new equations of his 

 motion. I cannot, however, assent to his position, that the equation of the 

 equinoctial points is to be taken into this account, together with the other 

 equations, since this is not an inequality in the sun's motion, but arises from a 

 motion of the equator itself; yet of such a kind as cannot accelerate or retard 

 the coming of the sun, or any star lying within the tropics, to the meridian, by 

 above a quarter of a second of time. This will, perhaps, appear in a good 

 measure plain, if it be considered that the diurnal motion of the earth round its 

 axis is neither accelerated nor retarded by the action of the sun and moon in 

 producing the precession of the equinoxes, and variations of the inclination of 

 the earth's axis to the ecliptic. The effect of these actions is, that the terrestrial 

 pole, each day, describes a small arc of a circle about the center of the earth, 

 in the plane of a celestial meridian passing through the sun or moon, or rather 

 one between botli ; and consequently the equator of the earth has its motion in 

 its own plane neither accelerated nor retarded, but obtains a new motion, whose 

 axis is one of its own diameters. This is the true origin, as well of the minuter 

 and periodical nutations, as of the regular and perpetual motion of the earth's 

 axis about the pole of the ecliptic, observed in all ages, on which the continual 

 precession of the equinoxes depends. 



But, to illustrate more fully the point in question, let p, see fig. ] , pi. 5^ 

 represent the north pole of the celestial equator, which suppose to be translated, 

 in any certain time from p to q, through the small space pq, on the meridian 

 PD, by the actions of the sun and moon ; let a be the equinoctial point of Aries, 

 and s the sun or star. It is evident that as the rotation of the earth round its 

 axis is no way affected, the translation of the celestial pole from p to q along the 

 arch pa, of the celestial meridian pd, will occasion no alteration in the time of 

 any given meridian of the earth coming to the fixed celestial meridian pd, nor 

 consequently in the time of the sun or stars, when lying in this meridian, ap- 

 pearing to pass the meridian of the given place, contrary to what should follow 

 from the method of computing the equation of time, used in the Connoissance 

 des Mouvements Celestes ; according to which, as long as the equation of the 

 equinoxes is any thing, the equation of time must be affected by it, and con- 

 sequently the absolute time of the sun's passing the meridian. 



But if the sun or star lie not in the celestial meridian pd, but in some other 



