OF ARTS AND SCIENCES. 379 



banks from overflow, — highly complimentary to the scientific 

 character of their investigations. Professor Peirce proposed 

 to offer a future and more detailed report, in conjunction 

 with Mr. Runkle, who, upon his suggestion, was added to the 

 Committee. 



Professor Peirce made a second communication 



Upon the System of Saturn. 



The especial subject of this communication was, " The considera- 

 tion of the subdivision of the ring into numerous small solid rings, and 

 of the invalidity of the argument derived from statical conditions 

 which has been urged against this subdivision." The investigation 

 was conducted by the aid of completely integrated formulas, which 

 were obtained after much laboi\ The formulae were embarrassed 

 by terms which were subject to a reversal of sign when in a finite 

 state, which can never happen in physical phenomena of this kind ; 

 but the embarrassment disappeared when it was observed that there 

 were two different terms subject to the same paradoxical change 

 of sign, and which were mutually antagonistic. From an exact numer- 

 ical computation, it appears that, without violating the condition of 

 statical equilibrium proposed in Mr. Bond's originail memoir, Saturn's 

 ring can be subdivided into about thirty -six rings of 600 miles of aver- 

 age breadth, with intervals of 150 miles between them. The inner and 

 outer rings must be the broadest of all, and have a breadth of 800 or 

 1,000 miles, while the smallest of the intermediate rings will only have 

 a breadth of 350 miles. It is curious that, with regard to the inner 

 and outer rings, the attraction of each of these rings upon the surface 

 which is towards the main body of the ring — that is, of the inner ring 

 upon its outer edge, and of the outer ring upon its inner edge — is over- 

 balanced by the attraction of the rest of the ring. Each of these por- 

 tions of these rings, therefore, depends upon the combined action of 

 Saturn and of its own centrifugal force to resist the destructive tendency 

 of this external attraction. They have, therefore, each of them a time 

 of revolution about Saturn, which properly belongs to no point of their 

 mass, but to points of the general ring, intermediate between them. 



The possibility of thus subdividing the ring into smaller ones with- 

 out violating the statical condition proposed by Mr. Bond, proves that 

 his argument was insufficient to demonstrate that the ring was not 

 solid 



