2:3 of Mimas and 1:2; 2:3 of Enceladus falling outside the ring system. 1:2 of Mimas and 1:3 of Enceladus fall in Cassini’s division, which separates ring A from ring B.... 1:3 of Mimas’ period falls at the boundary of ring B and ring C at 1:50 radii of Saturn from the centre.”
In the following years this supposition was reinforced by the discovery of six new divisions in the rings. Three of them were in ring A and three in ring B, two of them in each case seen by Percival for the first time. This led to very careful measurements of Saturn’s ball and rings in 1913-14 and again in 1915; recorded in Bulletins 66 and 68 of the Observatory. Careful allowance was made for irradiation, and the results checked by having two sets of measurements, one made by Percival, the other by Mr. E. C. Slipher. The observations were, of course, made when the rings were so tilted to the Earth as to show very widely, the tilt on March 21, 1915, showing them at their widest for fifteen years.
But unfortunately, as it seemed, the divisions in the rings did not come quite where the commensurate ratios with the two nearest satellites should place them. They came in the right order and nearly where they ought to be, but always a little farther from Saturn. It occurred to Percival that this might be due to an error in the calculation of the motion of the rings, that if the attraction of Saturn were slightly more than had been supposed the revolutions of all parts of the rings would be slightly faster, and the places in them where the periods would be commensurate with the satellites would be slightly farther out, that is where the divisions actually occur. Everyone knows that the earth is not a perfect sphere but slightly elliptical, or oblate, contracted from pole to pole and enlarged at the equator; and the same is even more true of Saturn on account of its greater velocity of rotation. Now its attraction on bodies as near it as the rings, and to a less extent on its satellites, is a little greater than it would be if it were a perfect uniform sphere; and it would be greater still if it were not uniform throughout, but composed of layers increasing in density, in rapidity of rotation, and hence in oblateness, toward the centre. Percival made, therefore, a highly intricate calculation on what the attraction of such a body would be (“Observatory Memoir on Saturn’s Rings,” Sept. 7, 1915), and found that it accounted almost exactly for the discrepancy between the points of computed commensurateness and the observed divisions in the rings. Such a constitution of Saturn is by no means improbable in view of its still fluid condition and the process of contraction that it is undergoing. He found it noteworthy that a study of the perturbations of the rings by the satellites should bring to light the invisible constitution of the planet itself:
“Small discrepancies are often big with meaning. Just as the more accurate determination of the nitrogen content of the air led Sir William Ramsay to the discovery of argon; so these residuals between the computed and the observed features of Saturn’s rings seem to lead to a new conception of Saturn’s internal constitution. That the mere position of his rings should reveal something within him which we cannot see may well appear as singular as it is significant.” (p. 5); and he concludes: (pp. 20-22).
“All this indicates that Saturn has not yet settled down to a uniform rotation. Not only in the spots we see is the rate different for different spots but from this investigation it would appear that the speed of its spin increases as one sinks from surface to centre.[37]
“The subject of this memoir is of course two-fold: first, the observed discrepancy, and second, the theory to account for it. The former demands explanation and the latter seems the only way to satisfy it. From the positions of the divisions in its rings we are thus led to believe that Saturn is actually rotating in layers with different velocities, the inside ones turning the faster. If these layers were two only, or substantially two, this would result in Saturn’s being composed of a very oblate kernel surrounded by a less oblate husk of cloud.”
ASTEROIDS and SATURN’S RINGS
The divisions so made in Saturn’s rings by its satellites may be seen in the lower of the two diagrams opposite; the three fractions followed by an E indicating the divisions caused by Enceladus, the rest those caused by Mimas. The upper diagram represents, as already remarked, the similar effects by Jupiter on the asteroids. A slight inspection shows their coincidence.