]881.] bUO [ChasiB. 



which the masses of the clifFerent bodies are fe'o adjusted to their mean dis- 

 tances as to insure to tlie system a greater degree of permanence than 

 would be possible hj any other distribution of masses. The mathematical 

 expression of a criterion for such distribution of masses has not yet been 

 fully developed ; and the pending illustrations have been introduced here, 

 more for the purpose of calling the attention of mathematicians and as- 

 tronomers to this interesting problem than for any certain light we have 

 yet been able to obtain in regard to its solution." 



"When I began my investigation of the harmonies which illustrate the 

 laws of sethereal elasticity, the only published evidence of any connection 

 between planetarj' mass and distance was Alexander's approximate equal- 

 ity between the products of the masses of Jupiter and Saturn by the 

 squares of their respective major axes : 



Jupiter to4t:8T9 X 5.2027982= .025833. 

 Saturn 35^1:^ X 9.5388522 = .025985. 



Laplace, however, had indicated elements of stability in the sums of 

 various products, and had demonstrated the tendency of approximate syn- 

 chronisms to become exact ; Herschel had shown that "subsidence, and 

 the central aggregation consequent on subsidence, may go on quite as well 

 among a multitude of discrete bodies under the influence of mutual attrac- 

 tion and feeble or partialh^ opposing projectile motions, as among the par- 

 ticles of a gaseous fluid" ; * various physical investigations, based upon 

 propositions in Newton's Principia, had indicated the fact that all persist- 

 ent oscillations or cyclical motions in elastic media, must be subject to har- 

 monic laws. 



In studying Herschel's statements of the nebular hypothesis, it soon be- 

 came evident that Sun, at the principal centre of nucleation, Earth, at 

 the centre of the belt of greatest condensation, and Jupiter, at the centre 

 of the primitive nebula, had some important common relations which had 

 exerted a controlling influence over the other cosmical masses. The four 

 following are specially noteworthy. 



qt\ 



1. The "nascentvelocity " of Sun, g- , is equivalent to the velocity of ligM. 



2. The nascent velocities of Earth and Jupiter are nearly equal. 



3. Earth's nascent velocity is about 3 per cent, less, while Jupiter's ap- 

 pears to be slightly greater, than the limit of possible circular- orbital 

 velocity, V gr at Sun's surface. 



4. The aggregate orbital vis viva of Earth, vv-^, and Jupiter, vv-^, is a 



3 

 simple function of mean distance from Sun, d, and orbital time, d'^. 



{^\ ' = A?_0?I5^\ ' =rz 61.T436 = 1 + 60.7436 = vi\ + vn-^ (1) 



*Outlines &f Astronomy, Sect. 871. 



t< being time of solar rotatiou, and g being the acceleration of superficial 

 gravitation. 



