3a 



of self-rotation is required to bring the same point of the cir- 

 cumference continually hack to the radius-vector. But if the 

 doctrine of gravitation be true, then the earth's attraction acts, 

 not merely upon the moon's axis to the effect of keeping her in 

 her orbit, but also upon every point of her circumference, and 

 every molecule of her mass, with a force proportional to the ra- 

 dial distance of those particles from the earth. The earth's at- 

 traction is consequently strongest upon the nearest parts of the 

 moon's circumference, and its effect is to neutralize the forward 

 moving impulse of the centrifugal power on those particles, 

 and hold them fast, while the axis and the outward parts move 

 forward in obedience to the centrifugal impetus. The gene- 

 ral result is that the parts of the moon's mass revolve in their 

 respective concentric orbits with different degrees of velocity 



f)roportional to the dimensions of those orbits, without rotating on 

 ler axis, which actually describes a larger orbit, or moves faster 

 forward than the inner point that is said to rotate round it. 

 Astronomers are indeed perfectly aware of this real influence of 

 the earth's attraction, though they have all agreed to overlook it ; 

 for they say, to use the words of Mrs Sommerville, varied a little 

 from Laplace, '' the lunar spheroid has three principal axes of dif- 

 ferent lengths at right angles to each other. The one directed 

 towards the earth is the greatest. The attraction of the earthy 

 as if it had drawn out that part of the moon's equator, constantly 

 BRINGS the greatest axis, and consequently the same hemisphere, 

 towards us.^^ If, instead of brings, they were to say keeps, this 



? [notation would, in my opinion, express the true state of the case; 

 or, certainly the point remaining in one with the radius-vector 

 never falls back a hair's breadth ; it moves constantly and con- 

 tinually forward with the radius-vector, in line with the axis it- 

 self, and never changes its relation either to the axis of the moon, 

 or to any thing else within the orbit of that axis, except to a small 

 extent occasioned by the eccentricity of the orbit, the earth's posi- 

 tion in one of the foci, and the varying velocity of her progressive 

 movement. To that extent the moon vibrates or oscillates on 

 her axis, but she certainly never completes a rotation. 



This oscillation or vibration, very properly called the moon's 

 lihration in longitude, is said Ijy astronomers to be the effect or 

 result of the uniformity of her rotation^ and the irregularity of 

 her orbital movements ; for '* the motion of revolution is some- 

 times slower, sometimes more rapid. The apparent vibration, 

 therefore, which it occasions cannot always exactly counterba- 

 lance the actual rotation, which remains constantly the same; and 

 these two effects will surpass each other by turns." But, the 

 moon's so-called "uniform rotation" being no rotation at all, 

 some other cause must be sought for the libration than the one 

 assigned ; and it seems to be this. 



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