1881.] »*^^5 [Chase. 



The explosive force proceeds radially in all directions from the centre, 

 so that the particles are subjected to cones offeree, introducing oscillations 

 which may be represented by a conical pendulum of j the height, or 

 503.54 miles. In seeking equilibrium, the particles tend towards their 

 own centre of gravity, at |- of 503.54 =:= 251.77 m., and also, on account 

 of resistance at the Earth's surface, towards the linear centre of oscilla- 

 tion, at f of 503.54 = 385.69 miles. 



The action of Earth on the centre of gravity of the mass produces a 

 secondary centre of oscillation, in which the primary centre of oscillation 

 acts as a point of suspension, and the centre of gravity as a pendulum- 

 extremity of wave propagation. This secondary centre of oscillation is at 

 f of 503.54 = 279.745 m., which represents the mean ms viva of oscilla- 

 tory projection relatively to Earth ; the vis viva relatively to Sun being 

 represented by Earth's semi-axis major. 



Let r=: 3963.8 miles; 7ir = Earth's semi-axis major; t^ ^1 year = 



31558149 seconds ; t^^ = 2■^^J — = 5073.6 sec. ; itIq = Sun's mass ; m^ = 

 Earth's mass ; h = 279.745 miles. Then we have 



(T> ' m 



nr : 7i, 



.-. Too = 331,631 m, 



nr = 92,772,200 miles. 



17. Centres of Density and of Nudeation. 



The rotating photodynamic action which is represented by the equations, 



o" = velocity of light, r- = modulus, is shown in its greatest simplicity at the 



nucleal centres of cosmical systems. In all other places it is complicated 

 with orbital motions, which increase the difficulty of determining the sum 

 of the photodynamic actions which are balanced by an equal sum of gravi- 

 tating reactions. Doubtless methods will be found hereafter for making 

 the proper allowances in all the most important cases ; but at present we 

 can take only a few steps towards the goal. The first step, naturally, is 

 from Sun. the centre of nucleation, to Earth, the centre of density. Here 

 we are helped, as in the first instance, by the study of maxima. The 

 limit between association and dissociation at the nucleal centre is the 

 velocity of light, or the greatest known velocity of wave propagation ; the 

 centre of density is revolving about the nucleal centre, and its "nascent" 

 limit shows the greatest possible tendency to circular-orbital velocity in the 

 system. 



Earth's nascent velocity, if its orbit were strictly circular, would be 

 gt 86164 32.088 

 -g- = 2 ^ 5^8i7 ^^ 261.82 miles. This needs to be multiplied by 



(1 -(- e)^ = (1.01677)^ in order to allow for orbital "subsidence" from 

 aphelion to mean position. We thus get 270.68 miles, for the value of Vgr 

 at Sun's equatorial surface. If we knew the precise quotient of Earth's 



PROC. AMER. PHILOS. SOC. XIX. 108. 2s, PRINTED MAT 3, 1881. 



