200 Prof. P. E. Chase on Harmonic 



§ 14. The whole of the facts stated above under §§ 8, 9, 10, 

 11, 12 may be expressed in terms of Lothar Meyer's Curve of 

 the Elements as follows : — 



Elements standing on falling portions of the curve are redu- 

 cible with difficulty, and never occur in the free state in nature, 

 or in combination as sulphides, but always in combination with 

 oxygen, forming oxides or double oxides {silicates, sulphates, 

 carbonates, 8fc); whereas elements standing on rising portions 

 of the curve are easily reducible, and almost always occur {more 

 or less) in the free state in nature, and also in combination with 

 sulphur, and but rarely with oxygen. 



By stating the relations in this way, almost all the excep- 

 tions mentioned in §§ 8-12 are got rid of and fall in with the 

 rule. 



This example, with numerous others which might be men- 

 tioned, shows how truly Meyer's Curve of the Elements is an 

 exact exponent of the facts of nature. 



XXYI. Harmonic Motion in Stellar Systems. By Professor 

 Pliny E. Chase, Haverford College, Philadelphia, U. S. 

 America*. 



THE principle of harmonic motion is of " immense use not 

 only in ordinary kinetics, but in the theories of sound, 

 light, heat, &c." (Thomson and Tait, < Nat. Phil.' i. sec. 52). 



In studying kinetic correlations, we find that the most 

 obvious and immediate control is exercised by inertia, attrac- 

 tion, and repulsion. In the solar and stellar systems, the 

 principles of universal gravitation and of sethereal oscillation 

 are simultaneously and mutually operative, in ways which are 

 indicated, as I think, by observable relations among cosmical 

 masses, distances, velocities, and orbital periods. 



Various forms of cyclical oscillation may be represented 

 and coordinated by the formula 



gt 2 = ir 2 l = 7r 2 L d = M. = 2h. 



In this formula, g represents gravitating acceleration on an 

 oscillating particle ; t = cyclical time of a single oscillation (or 

 half-time of rotation or revolution); I = length of linear pen- 

 dulum, or radius of circular orbital revolution ; L = radius of 

 free revolution -f- radius of constrained nucleal rotation, as 

 explained in the following paragraph ; M = modulus, or 

 height of homogeneous elastic atmosphere which would pro- 



* Communicated by C. Piazzi Smyth, Astronomer Royal for Scotland, 



