W4.] 143 [Chase. 



23. If t" = time of rotation, the integral of the impulses communica- 

 ted durinnr each rise or fall of the rotation-wave, is ^— . 



2 

 34. If the rotating body were to expand or contract uniformly, 



1}" oc ^, and t" QC r^ o: -■■, 9i[' is .-. a constant quantity for each par- 

 ticle. 



25. At the trough of the rotation-wave, the accumulated retrograde 

 velocity is exactly equal to the originating velocity of tangential orbital 



impulsion. In other words, ^^ = ^•^• 



2 



26. The velocity of rotation would become equal to the velocity of 



gt" gV ,,x 

 revolution, when the sphere had contracted so that ^r- = — r= ^' . The 



2~ '>— ~ 



limiting velocity of inertial aggregation is, therefore, such as would 



carry a body through the equatorial diameter of a spheroid, while v^ 

 would describe its equatorial circumference. 



27. The elasticity of the aether should give rise to harmonic vibrations, 



and especially to vibrations which involve multiples of y2,*3,f i,/.4, | 

 and -§. 



28. In consequence of the harmonic vibrations, there should be a 

 tendency to the establishment of points of inertia, and the consequent 

 aggregation of planets and satellites, at harmonic nodes. Such a ten- 

 dency is illustrated by the Chladni plates, and the 14th Thesis shows 

 that the supposed cause of aggregation is more than adequate for the 

 production of the su]3posed effects. 



29. The blending of different harmonic vibrations should produce 

 secondary vibrations of a lower order, giving rise to varying orbital ec- 

 centricities. 



30. The influence of harmonic vibrations should be traceable, not only 

 in planetary positions, but also in their masses, momenta, and moments 

 of inertia. 



31. The sethereal action upon inert masses or particles, should be 

 followed by a reaction of the particles upon the fether. Subordinate 

 rotating impulsions should thus be established among the planets, and 

 satellites, and particles. 



32. The same harmonic laws which introduce order among the various 

 bodies of the macrocosmic system, should also be operative in various 

 forms of orderly arrangement, within each of those bodies. 



*The velocity of fall from infinite distance^ y'2 gr. 

 tCentre of linear oscillation = f Z. 



li Centre of spherical oscillation = y^^ r. 

 §See Thesis 26. 



