18S2.] 4-j7 [Chase. 



279. Cosmic((l and Molecular Constant. 



If there is a natural unit of force we may look for a natural unit of 

 velocity. The hypothesis that all the particles of bodies are in constant 

 motion, involves oscillation of various kinds, orbital, pendulous, or wave. 

 Different transformations of similar oscillations are harmonic. Rota- 

 tion may be regarded as a pendulous oscillation due to retarded and modi- 

 fied revolution. The resemblance of LeSage's theory to the kinetic 

 theory of gases points to a probability that the natural unit of velocity 

 is oscillatory. This probability is strengthened if we assume the ex- 

 istence of molecular aud intermolecular elasticity. In looking to the 

 activities of the principal mass in our system for indications of a natural 

 unit of velocity, we find that gravitating velocities may be represented by 

 gt. In order that gt may be constant, t must vary inversely as g and, 

 therefore, directly as r^. This variation is found in the rotation of a 

 nebulous sphere, where it holds good for all stages of expansion or con- 

 traction which are not affected by external influence. Gravitating accelera- 

 tion should do its whole work in stellar rotation, as well as in planetary 

 revolution. Particles exposed to solar superficial gravitating acceleration, 

 during a single oscillation of half-rotation, would acquire a constant 

 velocity {gt = vy) which is equivalent to the velocity of light. la other 

 words, the unit of velocity which is indicated by the combined constant of 

 solar gravitation and rotation is the same as is indicated by light and by 

 electricity. 



280. Harmonious Development. 



The velocity of light, like the velocity of sound, represents an elastic 

 atmosphere whose height, it homogeneous, would be twice the virtual fall 

 which would give the velocity in question. The analogy is enhanced by 

 the fact that the hypothetical elasticity of the luminiferous aether is in har- 

 monic accordance with solar rotation and planetary revolution. The 

 identity of velocity 



represents three simple relations of light, electricity and gravitation. In- 

 terpret this feet as we may, it is strongly suggestive of some interplay 

 between sun and matter outside of it, which lias determined solar con- 

 stants. The invariability of Vy by nebular contraction indicates the same 

 determination for the present and for all future time. If Sun's mass and 

 magnitude are determined by cosmic causes, so that the solar system can 

 always be considered as undergoing a process of harmonious development, 

 the mass, rotation and other solar elements seem likely to be connected by 

 numerical relations, eitber with other bodies of the system or with cosmi- 

 cal or physical data. 



281. A Fundamental Time-Integral. 

 Thomson and Tait {Nat. Phil., i, § 52) speak of the principle of har^ 

 monic motion as one of "immense use, not only in ordinary kinetics, but- 



PROC. AMER. PHILOS. SOC. XX. 112. 3b. PRINTED NOVEMBER 24, 1883, 



