1880.] ^^ rChase. 



relatively to Sun's centre, nearly, and perhaps exactly, equivalent to Sun's 

 diameter.* 



The two controlling bodies of the system, Sun and Jupiter, are of nearly 

 equal density, and their centre of gravity, which is also the centre of 

 greatest relative stability, has a locus of relative secular range about equiva- 

 lent to ^ of Sun's diameter, its secular perihelion, or locus of primitive 

 rupture, being at Sun's surface. The gravitating motions beyond the 

 limits of the system, and the iBthereal motions at all points, should be re- 

 ferred to the centre of greatest stability ; but as we approach that centre 

 the gravitating tendencies towards Sua's centre become more and more 

 preponderating. The gravitating motions are greatest at Sun's surface, 

 where solar gravity {g^), is 27.83 times as great as terrestrial superficial 

 equatorial gravity (g^). In solar rotation, the particles are subject to con- 

 tinual sethereal and gravitating forces, referable to the centre of stability 

 and to Sun's centre, respectively. 



Projectile velocities at Earth's surface, maj'- be represented either hj gt 

 or by i/fi'A, t being f the time of flight and h being twice the virtual rise 

 or fall. Reasoning from analogy we may, therefore, presume that t, in 

 equations A, B and C, represents ^ solar rotation, I represents the height 

 of a homogeneous sethereal atmosphere, at Sun's surface, which would have 

 a wave-velocity equivalent to that of light, and m represents a minimum 

 moMle, or constituent molecule. These conditions are all satisfied by the 

 values, solar rotation = 25.486 dys ; t — 12.743 dys. = 1100985 sec; 

 «A — 688.815 i/gr ; I = modulus of light = (688.815)2 r — 2206.5 Earth's 

 semi-axis major = 73.64 Neptune's semi-axis major. 



An sethqreai sphere, rotating with velocity i/gr at Sun's surfac?, would 

 have V , at 688.815 r. If mu ^=v.m both cases, the densities would be in- 

 versely as the distances. In a condensing or expanding nebula, the nucleal 

 radius varies as the | power of the* atmospheric or Laplace limiting radius, 

 and in an elastic atmosphere the density varies geometrically, with an ex- 

 ponent inverse to the arithmetical variation of the distances or to the squai'e 

 of arithmetical variation or vis viva of rotation. Sun's mean distance is 

 23395.4 terrestrial radii, and 23395.4 r ^ (f j^ of 688.815 = 60.38 ?•, which 

 is the value of Moon's semi-axis major, as found by the limiting time-ratio 

 of terrestrial rotation to satellite revolution, f 



The tendency of all movements in elastic media, either to complete or to 



harmonic synchronism, should introduce some simple relations of chemical 



vis viva to vis viva of terrestrial motion. The law of Dulong and Petit, 



with Clausius's modifying substitution of the square of the molecular 



wv- 

 velocity for the specific heat, may be expressed by the equation -7- = C, 



in which w represents the atomic weight, v the molecular velocity, accord- 

 ing to the kinetic theory of gases, and t the absolute temperature. Since 



* From a priori considerations I am inclined to tliiiik that tlie accordance Is 

 exact, 

 t Proc. Am. Pliil. Soc, xix, 9. 



