34 



'* The Moon," says Sir Isaac Newton, " is revolved about its 

 axis by a motion most equable in respect of the fixed stars, viz., 

 in 27 days, 7 hours, 43 minutes, that is in the space of a sidereal 

 month ; so that this diurnal motion is equal to the mean motion 

 of the moon in its orbit : upon which account the same face of 

 the moon always respects the centre about which this mean mo- 

 tion is performed, that is, the exterior focus of the moon's orbit 

 nearly ; and hence arises a deflection of the moon's face from the 

 earth, sometimes towards the east, and other times towards the 

 west, according to the position of the focus which it respects: and 

 this deflection is equal to the equation of the moon's orbit, or to 

 the difierence betwixt its mean and true motions, and this is the 

 moon's libration in longitude." The moon, at apogee, directly 

 faces the earth ; but, when she leaves that point to move along 

 the west side of her orbit, if she were to move under the influ- 

 ence of the centrifugal force alone, that force would make her 

 inner points of circumference turn gradually outwards, in the di- 

 rection from east to west preserving their parallelism ; but, as she 

 proceeds, the elliptic orbit becomes gradually flatter, and that 

 increasing flatness proportionally diminishes her tendency to re- 

 tro-rotate, or parallelize, in as much as the direction of the cen- 

 trifugal impetus gradually approaches the line of the orbit de- 

 scribed by her axis, and consequently carries forward all the par- 

 ticles of her mass in lines always becoming more nearly concen- 

 tric to or parallel with that orbit. At the same time she is get- 

 ting continually nearer the earth, and that approach directly 

 increases the earth's power of attraction on the nearest parts of 

 her circumference, enabling it to hold them faster. She is also 

 continually increasing her orbital velocity, and the immediate ef- 

 fect of that increase is to leave the attracted portions of her body 

 more rapidly behind, while the less attracted axis and outward 

 parts roll forward. None of the parts ever move backward ; for, 

 if they did, that would imply two motions in the same body, in 

 contrary directions, at the same time, which is impossible. They 

 are simply left behind in the forward positions which they had 

 previously gained. By the combined operation of these causes 

 the result mentioned by Sir Isaac, that the moon's nose or 

 point «, in one with the radius-vector at apogee, instead of 

 being turned 90° away from it, at the end of the first quadrant 

 of the orbit, is just where it was, not, indeed, in one with the 

 radius-vector, but directly in one with the centre of mean mo- 

 tion, several degrees to the eastward or right hand of the ra- 

 dius, which of course is directed to the eccentric earth. Af- 

 ter passing this point, the flexure of the orbit begins again to 

 increase, which increases the tendency to retro-rotate ; the velo- 

 city is still continually increasing also, which increases the oppo- 



