1873.] l"o [Chase. 



THE MUSIC OF THE SPHERES. 

 By Plisy Eaele Chase. 



(Read before the American Philosophical Society, April Ath, 1873.) 



The cumulative evidences of a commensurable unity of law, in atmos- 

 pheric tides, gaseous explosions, sonant and luminous vibration, molar 

 and molecular inertia, satellite distances, solar and planetary rotation, 

 gravitating and magnetic action, encourage a more minute investigation 

 into the character of the planetary and stellar harmonies. 



We are at present unable to introduce any considerations connected 

 with the velocity of gravity, except the probability that it is uniform at 

 all distances. It seems reasonable, however, to extend the oscillatory 

 hypothesis to all primary forms of force, and to suppose that there may 

 be some tendency to harmonic vibrations, of inconceivable velocity, 

 which may have contributed bofh to the original arrangement and to the 

 present stability of the solar system. 



I have already shown (ante, xii, 518-522) a disposition to aggregation 

 in accordance with the coordinates of logarithmic curves, not only within 

 our immediate system, but also in the interstellar spaces. The same 

 tendency is seen in the differences of atmospheric pressure at different 

 altitudes, being a necessary consequence of gaseous or other analogous 

 elasticity. I have also shown, in the foregoing communication on "Oscil- 

 latory Forces in the Solar System," that the alternate planets, commen- 

 cing at either end of the series, are arranged in a more obvious geomet- 

 rical progression than the intermediate planets, but that all appear to be 

 posited by simple oscillatory laws. 



A closer scrutiny has detected additional relations, involving not only 

 the typical ratio between uniform luminous and gravitating motions (z:), 

 and the ratio of linear oscillation (3), but also, at the centre of inertia of 

 the planetary belt, the ratio between the squares of the distances of com- 

 parable actual and virtual fall ( _ ). The compared velocities being 



uniform, the distances vary as the times ; but the distances fallen through 

 by gravity, vary as the squares of the times, and, consequently, as the 

 squares of the distances in uniform velocities. The difference between 

 tz and 3 is so slight, that there might, perhaps, be some room to question 

 which of the two ratios is the more influential ; but the following com- 

 parisons seem to show that the ratio of linear oscillation is, perhaps, 

 slightly predominant : 



* See foregoing communication on ' ' Estimation of Solar Mass and Distance from the Equilib- 

 rium of Elastic and Gravitating Forces. ' ' 



A. P. S. — VOL. XIII. Y 



