1879.] 



Researches in Chemical Equivalence. 



181 



we have most probably found the state where the satellite first had 

 a separate existence. 



The conditions of stability of a rotating mass of fluid are very 

 obscure, but it seems probable that, if the stability broke down and 

 the mass gradually separated into two parts, then the condition im- 

 mediately after separation might be something like the unstable 

 configuration described above. 



In conclusion, I will add a few words to show that the guiding point 

 on an energy surface need not necessarily move down the steepest path, 

 but may even depart from the bottom of a furrow or move along 

 a ridge. Of this two cases will be given. 



The satellite will now be again supposed to be merely an attractive 

 particle. 



First, with given moment of momentum, the energy is greater when 

 the axis of the planet is oblique to the orbit. Hence, if we draw 

 an energy surface in which one of the co-ordinate axes corresponds to 

 obliquity, then there must be a furrow in the surface corresponding to 

 zero obliquity. To conclude that the obliquity of the ecliptic must 

 diminish in consequence of tidal friction would be erroneous. In fact, 

 it will appear, in my paper on the " Precession of a Viscous Spheroid," 

 that for a planet of small viscosity the position of zero obliquity is 

 dynamically unstable, if the period of the satellite is greater than 

 twice that of the planet's rotation. Thus the guiding point, though 

 always descending on the energy surface, will depart from the bottom 

 of the furrow. 



Secondly. For given moment of momentum the energy is less if 

 the orbit be eccentric, and an energy surface may be constructed in 

 which zero eccentricity corresponds to a ridge. Now, I believe that I 

 shall be able to show, in a future paper, that for small viscosity of 

 the planet the circular orbit is dynamically stable if eighteen periods 

 of the satellite be less than eleven periods of the planet's rotation. 

 This will afford a case of the guiding point sliding down a ridge ; 

 when, however, the critical point is passed, the guiding point will 

 depart from the ridge and the orbit become eccentric. 



IX. " Researches in Chemical Equivalence. Part III.* Nickelous 

 and Cobaltons Sulphates." By Edmund J. Mills, D.Sc. 

 F.R.S., and J. J. Smith. Received June 2, 1879. 



Although the chemistry of nickel and cobalt is interesting from 

 many points of view, it is more especially attractive from the probable 

 isomerism of these metals. Their combining proportions, in fact, 



* For Part II, see "Proceedings," vol. xxviii, p. 270. 

 VOL. XXIX. 



