Kirkwood.] 1U4: [Nov. 21, 



Library^ 



Henry Phillips, Jr., Edwin J. Houston, William Y. McKean, 

 Thomas H. Dudley, John R. Baker. 



The Treasurer presented the annual report of the Trustees 

 of the Building Fund. 



And the meeting was adjourned. 



2he limits of stability of nebulous Planets, and the consequences resulting 

 from their mutual relations.* By Prof. Daniel Kirkwood. 



{Bead before the American Philosophical Society, November 21, IS84.) 



To determine the height of the atmosphere is a problem of no common 

 difficulty. This is evident from the fact that estimates derived from the 

 phenomena of twilight, luminous meteors, and the aurora boreal is have 

 been widely various. It cannot extend, however, beyond the limit at 

 ■which its elasticity is counterbalanced by the foi'ce of gravity — a limit 

 probably not less than two hundred miles from the earth's surface. Even 

 the volume and weight of this atmospheric envelope are not absolutely 

 constant, as small quantities of gaseous matter are doubtless brought into 

 it from time to time by meteors and meteoric streams. Nor has this acces- 

 sion of matter from without been the only source of variation ; it has been 

 shown by several writers that the extent and density during the cycles of 

 geologic time were in all probability much greater than at present. 



But whatever the mass or density of the earth's gaseous envelope, an 

 absolute limit — corresponding to the earth's present time of rotation — may 

 be assigned it. "The atmosphere," says Laplace, "can only extend itself 

 at the equator to the point where the centrifugal force exactly balances the 

 force of gravity ; for it is evident that beyond this limit the fluid would 

 dissipate itself." This limit for the earth is 26,240 miles from the centre ; 

 for Saturn it is within the system of rings ; and for the sun it is at the dis- 

 tance of sixteen millions of miles. These distances, however, were ob- 

 viously greater before the members of the system had contracted to their 



* A preiiminary discussion of equation (1) in the following paper was given in 

 the Analyst for January, 1881. Those solutions are here revised, and the results 

 for each planet carefully determined. 



