1881.] 57 J . [Chase. 



arranged in tlie following order ; Neptune (iV), Jupiter (J"), Mars (M), Sun 

 (S), Mercury (Me), Venus (V), Earth (E), Saturn (Sa) Uranus {U). 

 Let subscript 1, 2, 3, 4, 5 designate, respectively, secular perihelion, mean 

 perihelion, mean, mean aphelion, secular aphelion. Then 



1. Subsidence from JV^ would produce a rupturing node at C4.* Stock- 

 well's values are, JV^ = 30.034, f/"^^: 30.044, the rupturing locus being f of 

 30.034 = 20.033. Newcomb's estimate of iVs is 80.070, which would give 

 20.047 for the rupturing locus. 



3. Midway between these primitive nodes comes the primitive nebular 

 centre, tZj- Thi'ee of Jupiter's cardinal loci are thus approximately indi- 

 cated, viz. : 



(iVs —U^) -^2 = 4.995 ; J^ = 4.978 

 (iV^5 — ?7j) -- 3 r^ 5.313 ; J, = 5.203 

 (iV: — C/3) --- 3 = 5.435 ; J^ — 5.437. 



3. The rupturing locus of the early nebular centre, J^, and the locus of 

 incipient subsidence at the centre of the belt of greatest condensation, ^5, 

 present the most significant evidence of parametral influence. 



j; 4. ^5 = 5.954 ; 2p Bs = 5.950 



4. Other important loci in the dense belt show a like influence. 



J,+ r^ = 5.953 

 ^5 + M?, = 5.975 



5. The inflvience of the parameter on other fundamental abscissas is 

 equally evident. 



2p Me^ = 1.770 ; if, = 1.736 

 2p M^ — 9.066; Sa.,— 9.078 

 2p M^ =10.333; 8a^= lO.MS 

 2p J^ = 39.633 ; JST^ = 39.598 

 2p Stti = 59.504 ; 2W^= 59.465 



6. Simple ordinal influence is shown in the relations of Laplace's limit (L) 

 to the centre of condensation, and of the three inner to the three outer 

 planets, if we take Sun's semi-diameter (r^) as the unit of measurement. 



V2p E^ -r- ?■„ = 36.333 ;i: = 36.366?-„ 

 V2^1\~^^^= 83.338; ife,= 83.048r„ 

 l/^'TV^T^ = 156.491 ; F3 =155.184?'„ 

 V2pN^^r^ = 197.333 ; E^ = 300.008?-„ 



7. A similar influence is shown with E^ as the fundamental abscissa. 



l/Sp E; = 3.439 ; ^^ + ifa = 3.437 

 2V2p E, = 4.879 ; J^ = 4.886 



8. Some of the relative nodes show simple multiples of the parameter. 



ip = 11.901 ; iVi — Ui = 11.910 ; U^ — Sa^ = 11.945 

 6^ = 17.851; f7i =17.688 



lOp = 39.750 ; JV, = 39.733 



* Ibid, xvii, 100. 



PKOC. AMER. PHILOS. SOC. XIX. 109. 3u. FEINTED DEC. 31, 1881. 



