l86 HINTS RELATIVE TO 



the axis, and let c be the circumferenceof a circle whofe 

 radius is unity : then becaufe the friction of each of the 

 elementary tubes MRSQ is as its preffure, and the pref- 

 fure is as the number ot lines Mk, and the preffure of 

 each; therefore as this number is as PM.Mn.c, we 

 have the n part of this expreffion for the force which, 

 acting at M, would overcome the friction of the cylin- 

 drical tube if moved round upon a horizontal plane: 

 but as the preffure of each elementary partis increafed 

 in the ratio of Mn to Mm, when moved on the folid 

 M AQ, the real force will be (PM.c.Mm.PN) : n; alfo 

 Pf : PM • : (PM.c.Mm.PN) : n to the fmall elementary 

 force which will overcome the laft force when acting at 

 f ; confequently the whole force will be equal to the 

 fluent of (PM 1 .PN.Mm.c) : (n.Pf.) 



Corollary. By means of the curves AM, HN, Sec, 

 conclufions may be drawn fimilar to thofe in the Co- 

 rollaries to the Scholium of the fourth Proportion. 



OF FRICTION IN THE LEVER. 



It has been already obferved, that a force afting per- 

 pendicular to the direction of a body in motion, does 

 not alter the body's motion in that direction ; therefore 

 if* we fuppofe DB to be an upright cylinder, and AB 

 a body touching it in a line as in the figure, and retained 

 clofe to it by an imaginary force, drawing it perpendi* 

 cular towards the axis; then if a force CP be applied to 

 C, the center of gravity of AB, and be always luppofed 

 to act perpendicularly to the radius CN,dt awn from the 

 center of the axis to the point C, the fii6tion will bo 

 the fame in drawing the body round the cylinder, as in 

 drawing it along a horizontal plane with an equal pref- 

 fure ; and if it be moved round by a force acting at a 

 greater diflance, the force will be reciprocal y as the 



diitaiiCe : 



* Fig. 11. 



