532 Brown — Effects of Magnetic and Gravitational 



the number of months contained in the period ; but if the 

 force has the same period as the effect, then the factor is only 

 the first power of this number. With a period of 270 years, 

 the factor is 3600, so it makes an essential difference whether 

 the force is of long period or approximates to a month. If it 

 approximates to the period of the perigee, or to that of the 

 node, we still get the square of the factor, but there are small 

 factors which enter and which may diminish the square of the 

 large factor to some number between 10 6 and 10 6 . 



6. Certain forces may be rejected with but little calculation. 

 Those which arise from a supposed resisting medium will give 

 secular and periodic changes, the latter with periods the same 

 as those of known terms in the moon's motion. Again, Jupiter 

 has an ellipticity of about 1/17, and therefore might affect the 

 motion of the moon. I have examined this and find that its 

 effect on the moon is at most about 1/1300 of the principal 

 effect produced by the planet. A small factor in the disturb- 

 ing function reduces this very considerably. It is certain that 

 theeffect of Jupiter's ellipticity must be insensible. Further, 

 there is a group of small planets lying between Jupiter and 

 Mars which will undoubtedly have some influence on the 

 moon's motion ; but this influence, when calculated, is seen to 

 affect chiefly the motions of the perigee and node. The result- 

 ing addition to these motions cannot be more than a few hun- 

 dredths of a second per annum ; otherwise the group would 

 more seriously alter the motions of the inner planets than is 

 possible, owing to the close agreement between theory and 

 observation. 



It may therefore be assumed that no gravitational action of 

 the sun, earth, and planets, considered as particles, has been 

 left out of account. Further, the figures of the earth and 

 Jupiter, considered as spheroids, have been treated ; the other 

 planets are too small or too far away for their figures to have 

 sensible influence. A possible non-spherical form of the sun 

 will be treated in § 7. The constant term due to the figure of 

 the moon has been taken into account, but an effect which 

 would be caused by a certain kind of minute libration of the 

 moon, if it existed, will be considered in § 9. Light pressure 

 is also ineffective in producing a long-period term, and, indeed, 

 any effect from it is too small to be detected within historic 

 times. 



7. Hypothesis of an equatorial ellipticity of the surf s figure. 

 — Owing to its rotation, the figure of the sun is not a perfect 

 sphere. There w T ill be a slight difference between the equa- 

 torial and polar axes. This difference cannot, however, do 

 more than alter the mean motions of the perigee and node by 

 a minute amount. 



