1883.J ^89 [Chase. 



librium ; in parabolic orbits, the centripetal vis viva is twice as great as 

 the centrifugal on approaching the centre, and one-half as great on reced- 

 ing from the centre ; in elliptical orbits, the ratio of the living forces varies 

 inversely as the ratio of the radius-vector to the semi-axis major. In 

 actual orbital motions, tlie alternate oscillations between the apsides are 

 equal, but in opposite directions. Tliis must be true of the tether, as well 

 as of planets and satellites, if the ajther has any orbital motion, and reason- 

 ing from analogy we might fairly suppose that it is true of a^thereal waves. 

 Wliat becomes of the heat which is supposed to be absorbed by the aether? 

 Does it increase the mean distance of the fethereal particles, does it main- 

 tain an ever increasing amount of fethereal undulation, or is it resolved 

 into some form of gravitating or other centHpetal activity, which furnishes 

 conclusive evidence of the universality of the law that "action and re- 

 action are equal and in opposite directions ? " A single fact is worth more 

 than a million theories, however plausible they may be. The second law 

 of thermodynamics is purely theoretical, inasmuch as it tries to account for 

 activities which are beyond the reach of experimental investigation. The 

 fundamental equality of Note 321 is a significant and far-reaching fact, 

 which illustrates Laplace's principle of periodicity (Note 333), and bears 

 satisfactory witness to the continuance of activities Avliich have hitherto 

 been the reproach of thermodynamics. 



355. Primitive Blotodya^mis Locus of JS'eptune. 



The combined influence of the tendencies to rotation and revolution 

 (Notes 348, 353, etc.), is shown in the outer limits, as well as at the centre 

 of the planetary system. The outer extremity of the photic radius (Note 

 345), has an oscillatory trajectory which is {-v^^ -=- v^) times as great as 

 that of p^. Its rotatory vis viva, and consequent! 3^ its radius of relative 

 projection, is (irv^ -r- vj'^ times as great, and the orbital period of this pro- 

 jectile radius is (tzVj^ -=- i\y x 27: '^(.r^-^ </„). Jupiter's secular eccentri- 

 city, according to Stockwell, is .0608274. This gives, for the linear centre 

 of oscillation of its locus of incipient subsidence, .0405516, and for the 

 solar radius vector of that centre, 1.0405516. If we take a like projection 

 of Neptune's locus of incipient subsidence (1.0405516 X 30.46955 =: 

 81.70514) as an original nucleal radius (p^) for which Laplace's limit 



2 



fnA was (7:v^-^ v^y p„, we find ^3 = (-^ v^ p^ -^ % />^)^ /»« ; ^a -^ % = 

 31558149 sec. ^ (2 :r X 497.827 sec.) = 10089.116 ; p^ = 214.461 p„; p^ = 

 6799.52 p^; p!, = 4684434 p,. 



356. Primitive Photodynamic Locus of Saturn. 



The value of Sun's apparent serai-diameter as deduced from the fore- 

 going note is 206264."806247 h- 214.461 = 961. "78, the British Nautical 

 Almanac estimate being 961. "82. A mean proportional between Sun's 

 semi-diameter and ^;^^ (2164.36 ^„ = 10.09206 p^) is within less than one 

 per cent, of Saturn's mean subsidence locus (10.000059 p^). The photic 



