No. IX. 



On llu Motion of Solids on Surfaces, in the two Hypotheses 

 of perfect Sliding ami perfect Rolling, with <> particular 

 Examination of their small Oscillatory Motions. By 

 Henry James Anderson, M.D. Professor of Mathematics 

 and Astronomy, in Columbia College. New York. — Dated 

 VQth Nov. 1827. Laid before the Society 4th Jan. 1828 



I. 



r INHERE an- I* u branches of Mechanical Philosophy is 

 -*- interesting in every point of view as the theory of Oscil- 

 latory .Motion. From the minutest vibrations of a harp-string 

 to the magnificent oscillations of a planet's axis, there are an 

 infinite number of analogous phenomena remarkable for their 

 curious properties or important uses. The common pendu- 

 lum, that little instrument which has rendered such essentia] 

 service to science and the arts, and will soon, in the hands oi 

 tin skilful observer, unfold to us the internal constitution o| 

 our globe, and give a (due to the process by which it lias ac- 

 quired its present state, is itself indebted for i1> accuracy to 

 tbe incessanl superintendence of a watchful mathematical 

 analysis. The science of Acoustics in all its parts, (be varied 

 phenomena of the tides, tbe theory of Saturn's ring, (bat won- 

 der of the solar system, and the philosophical explanation ol 

 tbe stability and harmony of the celestial motions, are in facl 



VOL. til. 4 I. 



