THE 



LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



SUPPLEMENT to VOL. XXII. FOURTH SERIES. 



LXIII. Static and Dynamic Stability injhe Secondary Systems, 

 By Daniel Navgka^ Esq.* 



SO small are the primary planets compared with their distances 

 from the sun, that they are regarded as material points in 

 the investigations of physical astronomy, and that no effects 

 arising from the unequal intensity] of solar attraction on their 

 parts can vitiate in any sensible degree the results which analysis 

 gives for their movements. But in the systems of Jupiter and 

 Saturn many satellites are exposed to an enormous tidal force in 

 consequence of their proximity to their primaries ; and the planet- 

 ary theory requires some modification when applied to the revolu- 

 tions of these minor worlds. My chief object at present is to 

 show that the unequal attraction of a primary occasions slow 

 secular changes in the orbits of its attendants, especially when 

 the presence of fluids on their surfaces brings tidal commotions 

 into play. But I deem it first necessary to prove what I have 

 assumed in my former communications, in regard to the physical 

 necessity for a synchronism of the orbital and rotatory motions 

 of these bodies, and for the small inclination of their equators 

 to the planes of their orbits. 



On previous occasions I endeavoured to show that such an 

 arrangement would be the ultimate consequence of excessive 

 tides, when a satellite contained large bodies of fluid, or when, 

 from its close proximity to the primary, the solid matter of which 

 it may be composed were not possessed of sufficient cohesive 

 force to withstand the effects of the great disturbance. But the 

 same result would ultimately arise from slow secular changes 

 which must occur in every possible case. Let us suppose, for 

 instance, that the first satellite of Jupiter were composed entirely 

 of solid materials sufficiently strong to resist all crushing strains 

 to which they may be exposed, and that its form, in the absence 

 of all disturbing forces, were an exact sphere. Such a body, 

 turning on an axis perpendicular to the plane of its orbit and in 

 * Communicated by the Author. 



Phil. Mag. S. 4. No. 150. Suppl. Vol. 2.2. 2 K 



