292 ON THE STABILITY OP THE MOTION OF SATURN'S RINGS. 



gives little light compared with the other rings, and is seen where it crosses 

 the planet as an obscure belt, but it is so transparent that the limb of the 

 planet is visible through it, and this without distortion, shewing that the rays 

 of light have not passed through a transparent substance, but between the 

 scattered particles of a discontinuous stream. 



It is difficult to estimate the thickness of the system ; according to the 

 best estimates it is not more than 100 miles, the diameter of A being 176,418 

 miles ; so that on the scale of our figure the thickness would be one thousandth 

 of an inch. 



Such is the scale on which this magnificent system of concentric rings is 

 constructed ; we have next to account for their continued existence, and to 

 reconcile it with the known laws of motion and gravitation, so that by rejecting 

 every hypothesis which leads to conclusions at variance with the facts, we may 

 learn more of the nature of these distant bodies than the telescope can yet 

 ascertain. We must account for the rings remaining suspended above the planet, 

 concentric with Saturn and in his equatoreal plane ; for the flattened figure of the 

 section of each ring, for the transparency of the inner ring, and for the gradual 

 approach of the inner edge of the ring to the body of Saturn as deduced 

 from all the recorded observations by M. Otto Struvd (Sur les dimensions des 

 Anneaux de Saturne Recueil de Me*moires Astronomiques, Poulkowa, 15 Nov. 

 1851). For an account of the general appearance of the rings as seen from the 

 planet, see Lardner on the Uranography of Saturn, Mem. of the Astronomical 

 Society, 1853. See also the article "Saturn" in Nichol's Cyclopaedia. of the 

 Physical Sciences. 



Our curiosity with respect to these questions is rather stimulated than 

 appeased by the investigations of Laplace. That great mathematician, though 

 occupied with many questions which more imperiously demanded his attention, 

 has devoted several chapters in various parts of his great work, to points con- 

 nected with the Saturnian System. 



He has investigated the law of attraction of a ring of small section on a 

 point very near it (Mec. Cel. Liv. in. Chap, vi.), and from this he deduces the 

 equation from which the ratio of the breadth to the thickness of each ring is 

 to be found, 



^?_ X(X-l) 



~~ 



where R is the radius of Saturn, and p his density; a the radius of the ring, 



