Chase.] 1*^ [April 16, 



Astronomical Approximations. V., VL By Pliny Earle Chase, LL.D., 

 Professor of Philosophy in Haverford College. 



{Bead before the American Philosophical Society, April 16, 1880.) 



V. Cometary Paraboloids. 



Some recent communications to the French. Academy, by MM. G-aus- 

 sin* and Faye,f have led me to re-examine some of my earlier discussions 

 of the influence of projectile forces and perifocal collisions, upon nebular 

 rupture and cosmical nucleatiou. :t I have embodied some of the results of 

 this examination in a comparison of my applicatiou§ of the general equa- 

 tion 



\=^A"^ CD 



with Gaussin's analogous equation || 



a =^a k'\ (2) 



If we let ro = 1 =: Sun's radius ; ^ = 16.164 ; tj = 1.6-353 ; ^ = 1.013, 

 equation (1) gives a series of paraboloidal abscissas which represent im- 

 portant cosmical relations. 



Bodies falling towards the centre of a cosmical system, from a distance 



%(?, acquire the (Z-velocity of revolution, (i/^(?j, at the distance — . 



n -\- 1 



Therefore, _^, -?^, -Ml, . . . represent points at which nebular 

 3 3 4 



subsidence would tend to produce rupture, with consequent orbital revo- 

 lution at df^, (Zj, d^ . . . 



In Table I, P represents Stockwell's values for the secular perihelion 

 points of rupture, in units of r^ ; A, the values for secular aphelion ; T, 

 the theoretical rupturing distances as determined by equation (1). 



TABLE I. 



* Comptes Rend us t. xc, pp. 518, 593. 



tib., p. 586. 



JProc. Am. Phil. Soc. Vols, ix— xii. 



§ lb. xil, 520. 



II Loc cit, p. 520. Equation (2) is a special case of equation (1), with ^ = 1. 



