35 



site tendency of the axis to leave the attracted jKJints of circum- 

 ference behind ; and the result of the antagonism is to bring the 

 point a again to the radius-vector at perigee. From perigee 

 backwards to apogee, the same process is gone through in the 

 reverse order, along the other side of the orbit, so that, when 

 the revolution is completed, a is again in one with the radius. 

 But the variations which the moon exhibits are the effects of real 

 rotation^ or turning round on her axis, to the extent of the librae 

 tion ; and the whole process is a real libration or balancing on 

 the axis, and not merely an optical deception, as some astro- 

 nomers call it, though it may be true enough that the earth's ec- 

 centricity with respect to the orbit makes the libration appear 

 larger than it would be, under the effect of the antagonist forces 

 only. If the moon were not to rotate at all, the same point a 

 would remain continually in one with the radius-vector. The 

 radius-vector, however, being nothing in itself but an imaginary 

 straight line drawn between the earth's axis and the moon's, the 

 divergence of n from that line indicates a real movement of the 

 moon's circumference past it, in the direction of the libration for 

 the time ; and the return of the point a to the radius equally in- 

 dicates an oscillation of the moon on her axis in that direction, 

 for the radius-vector itself never turns backwards on the moon's 

 axis. Its motion is always forward only, along with the axis. 

 These movements, however, are subject to the perturbing influence 

 which act upon the moon, to the effect of changing continually 

 the form and extent of her orbit ; and so far the libration will 

 vary considerably from what it would be in a regular and steady 

 elliptical orbit In a perfect orbit or circle there would be no 

 libration. 



Paradoxical as it may seem, 1 believe the same causes that 

 prevent die moon's rotation actually produce the rotation of the 

 earth on her axis, and such different effects of the same cause are 

 to be accounted for by the earth's very great degree of velocity 

 compared with that of the moon. She flies along her orbit 

 thirty times faster than the moon in hers ; and this amazingly 

 greater velocity makes her axis and outer mass leave the intra- 

 orbital parts of the mass for the time being so much more rapid- 

 ly behind than the moon's comparatively slow movement makes 

 her axis leave her inner circumference l>ehind, that the difference 

 of effect, so far from contradicting the hypothesis, seems to afford 

 a strong confirmation of it Various h}'pothese8 have been sug- 

 gested to acount for the rotation of the earth, and the moon, and 

 the other planets ; but the one that seems to have been received 

 with most favour, and to have been considered as the most pro- 

 bable, is that of John Bernouilli, who " has shown on mechani- 

 cal principles that one impulse would produce both simultaneous 



