88 Sir Oliver Lodge on 



compound additively, and towards the sun during the other 

 half where they compound subtractively. If the sun's motion 

 concurs generally with that of the planet at aphelion, the 

 virtual decrease in solar attraction near aphelion will cause 

 that point to progress; while the virtual increase of solar 

 attraction at and near perihelion will cause that point also to 

 progress. On the other hand, a concurrence of the motions 

 at perihelion would cause both apses to regress. So the 

 line of apses steadily revolves either forwards or backwards 

 according to the sense of the sun's proper motion in the direc- 

 tion of the latus rectum. 



But if the sun's way is directed along the major axis, the 

 varying inertia of the planet is equivalent to a radial force 

 acting oppositely on the approaching and receding halves of 

 the orbit; so one apse progresses while the other recedes, 

 and there is no cumulative effect on the line of apses. 



Nevertheless there should in this case be a change in the 

 excentricity. If the sun's proper motion concurs generally 

 with the motion of the planet from aphelion to perihelion, 

 this half of the orbit will be subject to a virtually diminished 

 solar attraction, and so the excentricity will diminish. The 

 other or receding half of the orbit will be subject to a 

 virtually increased solar atraction, and that also will 

 diminish the excentricity. The causes combine. 



A reversal of the sun's motion, so that the component 

 velocities are added from perihelion to aphelion and sub- 

 tracted on the reverse journey, will hnve an opposite effect; 

 and in that case, in both halves of the orbit, the excentricity 

 will increase. 



Concerning any possible effect on the Moon: — astronomers 

 appear satisfied that Dr. G. W. Hill and Professor E. W. Brown 

 have settled the small residual discrepancy in the acceleration 

 of the moon's mean motion, but inasmuch as the frequency 

 of revolution in the case of the moon is considerable, and its 

 speed through the sether is compounded of many causes, it 

 may seem worth while to examine whether its fluctuations 

 of inertia do not call for residual attention. True its monthly 

 speed is almost insignificant, being only about a thirtieth of 

 the earth's orbital speed, but it shares in the motions of earth 

 and sun, and so the iv±v to be compounded with it is con- 

 siderable. Any cumulative effect, however, can only be a 

 slight residual one, since its monthly orbit presents every 

 aspect to the sun's way in the course of a year or a decade. 



As to the constant term in equation (3), it would seem 

 that a modified fju might affect the period of revolution, because 

 T = 27r v / (a 3 / /bb); unless there were a compensating effect on a. 



