358 SCIENCE PROGRESS 



Considering first the case in which the particles in the rings 

 are all equal, it is confirmed that, in certain places, the perturba- 

 tions would increase until the particles in a particular ring 

 would leave the ring and mingle with those of other rings, so 

 leaving; — theoretically — a " division." The effect of unequal 

 particles is then taken into consideration, and it is found that 

 the effect of the inequality in mass would be to make the divi- 

 sions become more extended and therefore more readily visible. 



If some of the particles are assumed to be very small, 

 Cassini's division is at once obtained, produced by the satellite 

 Mimas Theory, indicates that the ring should commence at a 

 mean instance of i6"'g, which is in exact accordance with ob- 

 servation. Particles of larger mass cause an extension of the 

 division outwards from Saturn. By making use of the observed 

 width of this ring (from i6''-87 to iy''-6^), an upper limit for the 

 mass of the particles can be obtained. This upper limit is 

 supposed to hold also for the remaining rings. 



In general, it is found that any satelhte may be expected to 

 produce at least two zones of clearance. The first zone extends 

 from the origin (the centre of Saturn) to a distance dependent 

 upon the mass of the satellite in question. The second zone 

 extends from a second and greater distance, which is also 

 dependent upon the mass of the satelhte, up to the satellite itself. 



For the various satellites, the dimensions deduced for the 



The first three of these limits fall within Saturn itself, and 

 therefore need not be considered. The value 9''-34 corresponds 

 approximately with the distance of the inner edge of the Crepe 

 Ring, the observed value being io''-83, whilst the value 13 "-07 

 agrees almost exactly with the observed value (i3"-oo) of the 

 distance of the inner edge of ring B. 



Here the theory meets with a difficulty. Although this 

 numerical agreement is good, the existence of the Crepe Ring 

 within the dissipative area of Rhea, and of all the rings (the 

 distance of whose outermost edge is only 20") within the dissipa- 

 tive area of Titan require to be explained. A somewhat closer 

 examination of the theory indicates that the rate of dissipation 

 of the rings by the satellites must be a very slow process ; the 

 rate is not uniform, however, but is greatest near the outer 

 limits of the areas under consideration and decreases uniformly 



