Chase.] -"'^ [Jan. 21. 



cosmical influence of harmonic nodes in an elastic medium. Let v , be the 

 velocity of light ; g^, the acceleration of gravity at r^., the radius of Sun's 

 photodynamic sphere ; Vx = \/ QxVx ^= orbital velocity at r^ ; ®o = orbital 



/ gt\ 

 velocity at r^ (Sun's surface), and modulus velocity, ( "o" )< ^^^ centres of 



nebulosity and of condensation (.Tupiter and Earth), the modulus velocity 



having been slightly changed, as we have seen, by forces which produce 



gJx 

 orbital eccentricity ; Mi = '-^ ; r^ radius of orbital revolution synchro- 



(«,\^ Mx g^x'' ,. o ^ 



_^ 1 = — = -T~ ; M oc ?v oc 1\- ; T-j OC 

 Vx' '''' ' 



0^^' ; r., = i/r^i oc rx^ OC r^ OC Mi^ ; r.p~ oc M ; r/ OC M^ OC — OC — X 



(rx\ h — 



— ) OC ]/ro. If we take r^ as the unit of distance, we have, for the 



present condition of the solar system, ri= \/M.}\; \ — ) =-\' — =— X 



("-V ; therefore (— V^ = — = 7^ . But / =the time in which light 

 would traverse Saturn's orbit, divided into the time of Saturn's orbital re- 

 volution ; therefore ( ^)'^ = 9.5389* years -4- (9.5389 X 2- X 497.825 



seconds) = 31160.4 ; — = (311 60 .4)^^ = 2046.8. This gives for Earth's 

 ■'0 



2046. 8ro 

 semi axis major 95309 = 214.575?*o. 



13. Earth's Rupturing or Projectile Locus. 



In Note 6, I have shown the relation of Earth's accelerated rotation to 

 Neptune's subsidence and Sun's mass. In Note 5, I deduced a value for 

 Earth's mass from simple considerations of linear oscillation, between the 

 nebular centre of the solar system and the centre of greatest condensa- 

 tion. Since the stability of the system requires that all its oscillations 

 should be harmonic, we may also account for Earth's rotary accel- 

 eration by simple solar and terrestrial inter-actions. The propagation 

 of rays of equal length, in an elastic medium, produces a terrestrial re- 

 action to its orbital motion, through a radius equal to Sun's radius. 

 The centre of linear oscillation, in terrestrial revolution, which limits 

 the tendencies of photodynamic vis viva towards the earth, is at only 



0-03 from Earth, or near Venus's secular perihelion ; the pendulum of solar 



action upon Earth (o.,) is three times as great. The sum of the masses of 

 Earth and Sun being involved in these actions and reactions, there is a con- 

 sequent acceleration which would give the Earth nine rotations per annum 

 from this source alone. This acceleration is further increased by the rela- 



