1882.] ■^"♦^ [Chase. 



161. Orbital Momentum. 



The division of m V r by r gives tlie product of mass by orbital velocity, 

 or orbital momentum, together with the following suggestions of phot^dy- 

 namic or nebular activity : 



TO -i- i/l^ Cardinal Kadii. 



r. 



5.203 



l3s 10.000 



a, 20.679 



«8 30.470 



r, 1.000 



Jupiter's exponent represents the ratio of its photodynamic orbital vol- 

 ume to that of Earth ; Saturn's, the ratio of orbital times ; Uranus' s the 

 influence of mean rotary vis viva in an elastic medium ; Neptune's the 

 influence of a centre of linear oscillation in an elastic medium. 



162. Coefficient of Solar Torsion. 



In applying the oscillatory equation, ^ r= - '\ — , at the centre of gravity 



of a stellar system, let t represent the duration of an oscillation or half- 

 rotation, g the acceleration of gravity at the stellar equatorial surface, 

 Tz^ I the stellar modulus of light or the height of a homogeneous oethereal 

 atmosphere which would propagate undulations with the velocity of light. 

 Then, if the stellar rotary oscillation is due to the reaction of cosmical 

 inertia against sethereal influence, gt is equivalent to the velocity of 

 light, Vy 



n'^a^ W ^ 

 In Coulomb's formula of torsional elasticity, /= » „^2 > TT represents 



a weight suspended by a wire, a the coefticieut of the radius of torsion, 



/the coeflicient of torsion for the extended wire, g gravitating acceleration, 



t time of oscillation -when the force of torsion is removed. Applying this 



formula to solar rotation, we have 



m W T? a^ r. „ „ , 



But gt is the velocity which would be communicated by gravity, at 

 Sun's surface, in one oscillation of half- rotation, or the velocity of light ; 

 gt^ is the modulus of light at Sun's surface ; d^ r^ is the theoretical length 

 of a pendulum, at Sun's surface, which would oscillate once in each half- 

 rotation ; a r„ is tlie length of an equatorial radius rotating with Sun and 

 liaving the superficial orbital velocity, V gr, at its remote extremity. 

 These are the same results as have been already derived from simple gravi- 

 tating and radiodynamic considerations. Notes 17, 48, 100, etc. Their 

 statement in this form may be satisfactory to some readers who have not 

 followed the foregoing investigations through all their details. 



