SATELLITES UPON THE FORM OF SATURN’S RING. 
129 
We have found the maximum value of F appearing as 0*0173. It was previously 
shown that the limiting value of F was 0'0096n s wl/M. Hence 
0'0096u. 3 m/M = 0*0173, 
which gives 
0*0173 
0'0096?i 3 
= 1*8 /n z . 
That is, the size of the largest particles is just below that given by Maxwell’s 
criterion. 
§ 7. Summary and Conclusion. 
(1) Assuming that a planet is surrounded by concentric rings of particles performing 
approximately circular orbits when unperturbed, and that the influence of one ring 
upon another may be neglected to a first approximation, the effect upon these rings 
of a satellite performing also an unperturbed circular orbit is discussed. 
If the particles in the rings are all equal, it is shown that we should expect, 
in certain places, large perturbations to take place, such that the particles in a 
particular ring would leave that ring and mingle with those of other rings, and so 
leave a “ division.” 
(2) As there is no reason to believe that the particles in any ring are all equal, the 
analysis is extended to cover the case of unequal particles. 
We assume that in any ring the number of particles is large, and that therefore we 
shall probably have one specimen at least of all particles from the smallest to 
the largest. 
It is then shown that the divisions would become more extended, and therefore 
more readily visible. 
(3) On the supposition that some of the particles at any rate are indefinitely small, 
we obtain Cassini’s Division at once. On making use of the dimensions of this 
division to estimate the greatest magnitude of the particles in any ring, we find the 
following results :— 
Satellite Mimas should produce a clearance of particles from radius 20*2 // up to 
itself. The ring should therefore terminate at 20*2". Observation shows that it 
terminates at 20*01". 
Satellite Mimas should produce a division from radius 16'9 // to 17*64 // . (This last 
measurement was used as a datum for estimating the magnitude of the greatest 
particles.) Observation gives the limits of Cassini’s Division as 16*87" and 17*64". 
Satellite Dione should produce a clearance of particles from the region of the 
surface of the planet up to radius 9*34". The Crepe Bing is observed to begin with 
a diffused edge at 10*83". 
