SOLIDS <»N -i ft] \< BS 317 



friction, ami may readily be extended to the cases in which 

 there are several supporting surfaces, even when these sur- 

 faces are themselves in motion. 



It was my original intention to prefix to the following dis- 

 sertation a detailed history of the problem of tli* motion of a 

 rigid body, with an account of the successive advance- which 

 have been made from the time of Galileo to the presenl tlav 

 towards a complete determination of the phenomena of oscil- 

 lating systems. The scantiness of the New York libraries 

 with respect to scientific works, and the impossibility under 

 which my engagements lay me of personally consulting the 

 more copious collections of Boston and Philadelphia, to saj 

 nothing of the fad thai some of the materials of such a ta-'k 

 are Dot to be found in America, and only on rare occasions 

 to be procured from Europe, have compelled me to defer un- 

 til a better opportunity the execution of this part of mj first 



a. I shall therefore content myself at presenl with a very 

 brief preliminary retrospect of what has been already done in 

 connexion with the subject of the following communication. 



Galileo appears to have been the first who considered in a 

 mathematical poinl of view even the simplest cases of the 

 problem before us, the de-cent of a material point along a 

 straight line inclined to the horizon', and it- oscillations in 

 the arc of a vertical circumference-. In the" first of these 

 two cases he succeeded in defining the motion of the point ; 

 in tlie second, he wa- far from attaining the same result, anil 

 in both the resistances of friction and the air were carefully 

 excluded. 'J lie well known law of oscillation round a hori- 

 zontal axis of support, firsl conjectured rather than demon- 

 strated by Descartes in the cases of plane surfaces vibrating 

 ////v. and afterwards generalized h\ the celebrated Huyg- 



Operedi Galileo Galilei. Milano, 1811. 

 Vol. viu. p. :<< — ;'» . The lit -i edition of the Dialogues of Galileo is that of 

 Leyden, l'J38. 



* O G Vol. nii, p. J53 — 160. 



" Renati I) I Ami. Mann, 1683. Epistola LX.WII Ad 



Mersennum. Mini, .. [i 



