Manchester Memoirs, Vol. Iv. (1910), No. 1. 19 



its revolution may be determined independently of the 

 times of B and C. 



As the ring A is postulated to be the first annular 

 ejection from the planet, its outer edge would be the 

 extreme limit of the ejective force, and it would conse- 

 quently revolve in the same time as a satellite at the 

 same distance, in accordance with Kepler's third law. 

 Now the period of Mimas, the first satellite of Saturn, is 

 22 hours 37 minutes, hence we have for the outer edge of 

 the ring a periodic time of 12 hours 48 minutes ; and ii 

 hours 45 minutes as the time of rotation at the middle of 

 its breadth. 



Dealing with the second ring B in the same manner, 

 we have for the outer edge a period of 10 hours 9 minutes, 

 and for the middle breadth, 8 hours 24 minutes as the 

 period of revolution. 



The determination of the time of revolution of the 

 dusky crape ring C presents some difficulty on account 

 of the wide separation of the discrete particles of which it 

 is composed, and its apparently close contact with the 

 interior of the ring B, but as by Kepler's law the time of 

 revolution of the interior of B would be 6 hours 44 

 minutes, the exterior parts of C may be assumed to 

 revolve at the same rate, and the inner edge of C in 

 5 hours 15 minutes. 



From the principle of the transformation of energy it 

 may be rightly inferred that some of the molar motion of 

 the vast assemblage of discrete particles constituting the 

 rings would be converted into heat, with a consequent slow 

 •contraction of their orbits. The observations collected by 

 O. Struve in favour of such contraction have been 

 discussed by astronomers, but without so far arriving at 

 any definite conclusion. 



