FRICTION IN MECHANICS. l8j 



thing when t is the n part of 5 ; and when Wd (tn—s) : 

 (n-\4) D becomes negative, it expreffes the quantity of 

 force which muft atl in a contrary direction to reduce 

 the body juft to a ftate of fufpenfion. 



SCHOLIUM. 



It would be needlefs to make any allowance for the 

 curvilinear furfaces of the threads of fcrews, as the) 

 feldom differ much from the two foregoing forms; nei- 

 ther is it of much confequence to allow for their parts 

 being at different di fiances from the axis, as their 

 breadth feldom bears any confiderable ratio to the 

 length of the levers by which they atl ; but the cafe is 

 different when large bodies revolve on each other, 

 and therefore it will be neceffary to fhew the mode of 

 proceeding in fuch cafes. 



Let MmAO be a convex folid,* generated bv the 

 revolution of the curve MAQ about its axis perpendi- 

 cular to the horizon, and MRSQ a concave body 

 exactly fitting it : then if this lad body be revolved 

 about the axis AP by means of the lever Pf, the force 

 neceffary to overcome the friction of one body turning 

 upon the other may be found as follows. Suppofe the 

 revolving body divided into an infinite number of con- 

 centric tubes, that may defcend independent of each 

 other, and prefs freely a gain ft the body on which they 

 revolve, and yet be fo connected that the lever Pf may 

 give the fame angular velocity at the fame time to each ; 

 alfo let theordinates PN of the curve HN reprefent the 

 weight or preffure (in a direction perpendicular to the 

 horizon) of each of the indefinitely final 1 parts Mk, or 

 elementary lines of the body at the diitance PM from 



Vol. I P the 



* Fig. 10. 



