Royal Astronomical Society. 585 



disturbing force of Venus is to pull the moon from the earth. To 

 arrive at this conclusion, we have considered only four points of the 

 moon's orbit : in other points the effects of the perturbation are 

 more complicated ; but they do not alter this general conclusion. 



The same remark applies to the disturbing effect of Venus upon 

 the moon when at a given point of its orbit, provided the nature of 

 that point be such that at different times it is in all possible posi- 

 tions relative to Venus. For instance, the moon's apogee is (in 

 consequence of the motion of the line of apses, and of the relative 

 motions of the earth and Venus) sometimes between the earth and 

 Venus, sometimes more distant from Venus than the earth is, some- 

 times 90° to the right, sometimes 90° to the left. We may assert 

 therefore that, upon the whole, the disturbing force of Venus upon 

 the moon, when she is in apogee, tends to draw her away from the 

 earth. The same may be predicated when the moon is in perigee. 



Next, it is important to ascertain how the disturbing force de- 

 pends upon the moon's distance from the earth. For this purpose, 

 instead of supposing, as before, that the moon's distance is y^-g- part 

 of the distance of the earth from Venus, let us suppose it y^ part of 

 that distance. Then when the moon is between the earth and Venus, 

 the force upon the moon is VWx" °^ ^^^^ upon the earth, and there- 

 fore the excess, or the disturbing force, is ^qj, or nearly -^ of the 

 whole force upon the earth. In the former assumed instance it was 

 ■gL. Thus, upon doubling the moon's distance from the earth, the 

 disturbing force is doubled. And similarly for other distances of 

 the moon from the earth, the disturbing force (in similar positions 

 with regard to Venus) is proportional to the moon's distance. Thus, 

 when the moon is at apogee, in a given position with regard to Venus, 

 the disturbing force is greater than when the moon is in perigee in 

 the same position. And, upon the whole, in all possible relative 

 positions of the moon and Venus, the action of Venus pulls away 

 the moon from the earth, more when she is in apogee than when she 

 is in perigee. 



Now we may consider the general effect of these forces upon the 

 dimensions of the moon's orbit. So long as the force which draws 

 the moon towards the earth is always the same at the same distance, 

 the moon will continue to describe an orbit of the same dimensions 

 over and over again. But if at any time the force directed towards 

 the earth suddenly grows smaller, the moon will immediately rush off 

 in an orbit which, on the opposite side, is larger. If the force 

 towards the earth gradually grows smaller, the dimensions of the 

 orbit will gradually increase. And the periodic time in the orbit 

 described at every successive revolution will undergo the change 

 corresponding to the change of dimensions (that is, to the change of 

 major axis) of the orbit, and will therefore become continually 

 greater and greater. 



These are the changes which produce the most serious disturbance 



in the apparent place of the moon. If a force, after acting for a long 



time, produce a small change in the eccentricity of the moon's orbit, 



the effect on the moon's place is simply the amount of the corre- 



Phil. Mag. S. 3. Vol. 31. No. 209. Nov. 1 847. 2 C 



