Sir J. W. Lubbock on Hhootiiig Slavs. S5 



depending on the mass of the earth, which may be eliminated 

 by means of the moon's period, a the semi-axis major, 



{U-¥cf 



We cannot however determine the quantity 8a. from the 

 angular motion, as seen by the spectator. 



If fortunately the disappearance be observed by two spec- 

 tators on the same night at diflferent times, we should then 

 obtain all the elements of its orbit. For as the satellite moves 

 in a plane passing through the earth's centre, the equation to 

 the plane ofits orbit referred to the same coordinates as before is 



^p cos « sin ^ + i?p sin a sin ?+C{p cos ^ +/?} =0, 



where A, B, C are constants, which express the cosines of 

 the inclination of the plane of the orbit to the planes y.t, xz^ 

 and xy. 



If we possessed another complete observation, 



^p' cos a' sin 5' + -Bp' sin a' sin ^' + C{p' cos ^' + J?} =0, 



such equations would determine completely the position of the 

 orbit in space, and two points in the orbit. Hence Ix would 

 be known, and a[l—e-). The two places would also furnish 

 e and tt, the longitude of the perihelion. After the interval of 

 days or weeks, the orbit of a satellite might have become 

 materially altered by disturbances, but not in a few minutes, 

 separating independent observations by spectators at different 

 points of the earth's surface. 



The perturbations of satellites may be very considerable, 

 and hence their motions, as seen from any place on the earth's 

 surface, may be very irregular; for while the mass of Jupiter, 

 the planet which produces ihe greatest perturbations in the 

 solar system, is only about yo\j(j of that of the sun, the pri- 

 mary, the moon, which produces the perturbations of satellites, 

 is probably at least J-^ that of the earth or fourteen times 

 greater. It will be recollected also that the magnitude of the 

 perturbations depends upon the mass of the disturbing body, 

 and scarcely at all upon that of the disturbed body, when mi- 

 nute. The deviation of the figure of the earth from that of a 

 sphere may also have a considerable eifect, and even perhaps 

 the irregularities ofits surface and the unequal density of its 

 substance. These circumstances, taken together, may account 

 for the great irregularity of their appearance, even if their 

 orbits are nearly circular. If their orbits are eccentric, we 

 have another cause of irregularity, to which may also contri- 

 bute that their period is not nearly the aliquot part of a day. 

 Their numbers may be considerable, even allowing for the 



