194 Sl'KEW. 



Let the e of C from the axis of the cylinder = a ; 



and the radius of the cylinder = 6. 



. the forces which hold the cylinder in equilibrium are 

 W, P t and the reactions of tin- pressures of the various por- 

 tions of the thread on the corresponding portions of the ', 

 DC of the groove in which the thread rests; the.-' 

 actions are indeterminate in their number but they all act in 



ions at right angles to the surface of the groove. 

 therefore their directions make a constant angle with tin 



of the cylinder. Let - a be the angle which the thread of 



the screw makes with tho axis of the cylinder, then a is the 

 angle which the direction of each reaction makes with the 

 axis of the cylinder. If, then, li be one of these reactions, 

 R cos a, R sin a are the resolved parts vertically and horizon- 

 tally; the horizontal portions of the reactions act each at 

 right angles to a radius of the cylinder. Hence, resolving 

 the forces vertically, and also taking the moments of the 

 forces in horizontal planes, we have 



..................... (1), 



..................... (2): 



we might writedown the other four ('filiations of equilibrium, 

 but they introduce unknown quantities with which we aic 

 unconcerned in our question. 



,, W a cos aS. R , 



Hence -p = j. - ^ ., , because u and a are constant, 



_ a cos a 2?ra 

 sin a 27r6 tan a 



_ circumference of circle of which tho radius is a 



~~ vertical dist. between two successive winds of the thread * 



ew is used to gain mechanical power in many ways. 

 In excavating the Thames Tunnel, the heavy in-n frame-wmk 

 which supported the workmen was gradually advanced by 



means of large screws. 



