Oy THE LAWS OF GRAVITATIOX. 521 



a certain point, which is called the lovver apsis, it becomes per])endicular to 

 it: but if the central force increase in a greater proportion than is necessary 

 for the description of the ellipsis, the point where the velocity prevails over 

 it will be more remote than in the ellipsis; and this is expressed by saying 

 that the apsis moves forwards. When, on the contrary, tlie force varies 

 more slowly, the apsis has a retrograde motion. Since, therefore, the force 

 attracting the moon towards the earth, increases, on the whole, a little more 

 rapidly than the square of the distance decreases, the apsides must have, on 

 the whole, a direct motion. And a similar theory is applicable to the mutual 

 perturbations of the primary planets. (Plate XXXlV. Fig. 488.) 



The secular acceleration of the moon's mean motion, which had long pre- 

 sented a difficulty amounting almost to an exception, against the sufficiency 

 of the theory of gravitation, has at last been satisfactorily deduced by Mr. 

 Laplace from the effect of the gradual change of the eccentricity of the earth's 

 orbit, which is subject to a very slow periodical variation, and which causes 

 a difference in the magnitude of the sun's action on the lunar revolution. 



The perfect coincidence of the period of the moon's rotation, with that of 

 a mean revolution, has been supposed to be in some degree an effect of the 

 attraction exerted by the earth on a prominent part of her surface; there are 

 however, many reasons to doubt of the sufficiency of the explanation. If 

 the periods had originally been very nearly equal, we might imagine that 

 the motion of the earth would have produced a librAtion or oscillation in the 

 position of the moon, retaining it always within certain limits with respect 

 to the earth: no libration is, however, observed, that can be derived from 

 any inequality. in the moon^s rotation; and it has very properly been sug- 

 gested that the same attraction towards the earth ought to have made the 

 moon's axis precisely perpendicular to the plane of her orbit, instead of 

 being a little inclined to it. At the same time the appearance of a similar 

 coincidence, in the periods of the rotation and revolution of many other 

 satellites, makes it probable that some general cause must have existed, which 

 has produced the same effect in so many different cases. 



The orbits of the comets afford no very remarkable singularity in the applica- 

 tion of the laws of gravity, excepting the modifications whicli depend on 

 VOL. I. 5 X 



