TRANSACTIONS OF THE SECTIONS. 25 



In the absence of any arrangement for this purpose, the action of the primaiy on 

 the protuberant solid or liquid matter which swells by its enormous tidal force on 

 the satellite, must constantly accelerate or retard the rotation of the latter, until it 

 is caused to keep exact trace with the orbital movement. Whilst the synchronism 

 confines the great tide-wave to a limited range, the tendency of the shortest dia- 

 meter to become the axis of rotation will gradually bring the equator into a coin- 

 cidence with the plane of the orbit ; and both causes woidd have the ultimate effect 

 of giving the body a permanent elongation at the same localities. If the eccentri- 

 city of the orbit were then sufficiently great to occasion high tides on its seas or 

 oscillation in its solid matter, the resulting deviation from a sphere will not reach 

 its highest limit until some time after the central distm-bance became most ener- 

 getic, while a coiTesponding interval must elapse between the periods when the 

 ellipticity and the distiurbing power sink to the lowest degree. It will readily 

 appear that such changes in the form of the satellite must cause it to feel a greater 

 amount of attractive force while retiring from the primary than while approaching 

 it ; and a constant diminution of the eccentricity of the orbit is an inevitable con- 

 sequence. Notwithstanding the small size of the four nearest moons of Saturn, it 

 is not impossible that commotions on their siu^ace may serve, in this way, to check 

 the increase of eccentricity which might be expected to arise fi'om the relation in 

 their periods of revolution. 



As a veiy large satellite, revolving within the range of a great central disturb- 

 ance, must idtimately have its diiunal motion, the position of its axis, and the form 

 of its orbit arranged in the peculiar manner necessary for keeping the same point of 

 its surface always directed to the centre of the primary, the statical condition which 

 the equilibrium of its parts assumes, presents a more easy subject for accm-ate scien- 

 tific inquiry. In the April Number of the ' Philosophical Magazine,' I have shown 

 that a homogeneous fluid satellite, whose size is very small compared with that of 

 its orbit, would find repose in a form varying little from an ellipsoid, and that the 

 intensity of gravity on its surface would be almost exactly proportional to the nor- 

 mal con-esponding to each locality. It was also proved by the investigation, that 

 the equilibrium is not possible when more than f of the attraction along the major 

 axis is neutralized by the centrifugal force and the distm'bance emanating from the 

 primaiy. In a former article, the radius of the smallest circular orbit in which the 



3 /D 

 planetary form could be preserved was estimated as nearly equal to 2-48 R * / — , 



R being the radius of the primary, D its density, and d the density of the satellite. 

 To cases of instability which may occur at any remote period m the systems of 

 Jupiter and Satm-n, these results would apply, with tolerable accuracy, even veithout 

 coiTCctions for the variable density of the Dodies in their different parts. But were 

 the central and the subordinate world iu the same ratio as the earth and moon 

 with respect to mass and volume, whUe their linear dimensions were ten times as 

 great, the range of dangerous proximity would be a little wider than my estimate 

 indicates, and the consequences near the confines of this dangerous domain would 

 be much modified. The form of the lesser body would de\'iate considerably from 

 a true ellipsoid ; the disturbing forces miist be very imequal at both extremities of 

 the longest diameter ; and the equilibrium cannot "be equally secm-e at both locali- 

 ties. If, therefore, so large a satellite were introduced into the region of instability 

 by the resistance of a space-pervading medium, the dismemberment would be con- 

 fined to the side tiuned to the primary, and it would commence before weight en- 

 tirely disappeared at any part of the surface. If it were composed of a fiuid of 

 uniform density, a reduction of even less than sixty per cent, in the attraction at the 

 point neai-est to the central orb would give rise to a movement towards this point, 

 and cause it to assume such a character that it must be accelerated instead of oeing 

 checked by the resulting change of form. A body of small size, in such circum- 

 stances, must soon have its whole contents scattered into space, from its two pro- 

 minent extremities. In the present case, where the matter is pressed out only at 

 the place next the primaiy, the enlargement which necessaiily occm-s in the orbit 

 of the remaining mass lessens the distm'bance, and biings the dismembering action 

 to a close. The advantages for stability would also increase, as the large portion 

 of the satellite lavmched into space retii-ed far enough to make its attraction inap- 

 preciable. Accordingly a very large member of a dark system must close its mun- 



