504 JAMES CLERK MAXWELL. 



would tend to fly off into space, while if they rotated with 

 the velocity proper to the exterior of the outer ring, the inner 

 portions would tend to fall towards the planet ; and even if 

 they rotated with the velocity proper to any intermediate 

 portion of the system, the parts beyond would tend to fly 

 outwards, and the parts within would tend to fall towards 

 the planet, unless this tendency were compensated by the 

 attraction of the ring itself. But there is another objection 

 to the hypothesis of the rings being uniform solids, viz. the 

 instability of the motion. If the motion of the ring were 

 slightly disturbed, as is always the case, it would not return 

 to its original orbit, but its deviation would increase until 

 it came in contact with the planet itself. 



Laplace was the first to investigate the conditions of 

 stability of Saturn's ring system. He concluded that if the 

 rings are solid, they must consist of a great number of very 

 small concentric rings, each rotating independently with its 

 proper velocity about the planet. The velocity calculated 

 by Laplace for the circumference of the outer ring agreed 

 with that determined, as above mentioned, by Herschel. 

 Laplace avoided the difficulty of the instability of the rings 

 above alluded to by supposing that they were not homogene- 

 ous, but that their centres of gravity were at some distance 

 from their geometrical centres. Laplace also showed that, 

 for the attraction of the ring to neutralise its tendency to 

 split up, it is necessary that its density should be -J- that of 

 the planet. In 1851 Professor Pierce showed that the 

 number of rings in the system must be very much greater 

 than Laplace had supposed. This was the position of the 

 question when it was taken up by Maxwell. 



On March 23d, 1855, the Examiners announced the 

 subject for the Adams Prize in the following terms : 



The University having accepted a fund raised by several 

 members of St. John's College, for the purpose of founding a 

 prize to be called the Adams Prize, for the best essay on some 

 subject of pure mathematics, astronomy, or other branch of 

 natural philosophy, the prize to be given once in two years, and 

 to be open to the competition of all persons who have at any time been 

 admitted to a degree in this University : 



