M1BCKLLANBOUB EXAMPLES. I'O 



23. Three equal heavy cylinder*, each of which toaches 



ther two, are bound together by a string and laid on a. 



table no tti;r xi are lion/. tension 



of tlie string bang given, timl tin* pressures between the 



ir 



Him/It. The horizontal pressure T- 



H - - N * 



T+ -j-; where 7* in the tension of the string, ami IT the 



lit i.fra. 



f equal spherical beads in placed upon a 

 mnooth cone ) :il, the beada beii 



t with . r, so th;i mutual pressure 



nuionoff -Mluce the 



ug value when the number of beada IB indefinitely great* 



\ *mooth * is supported on an inclined plane 



with ; horizonta VMS <>f A -triii:: which, passing 



1 attached 



to a fixed point and r to a wci -lt IT wiiiih hangs 



freely; if a be t!. fed the horizon, 



. vertical of that part of the string 

 i is fastened to the fixed point, the weight o: 

 uder is 



M^coafc 

 .-in 2 



i inoxtonsihlc string bi t \i^tlnr two 



smooth cylinders whose radii are ;_ fthe 



pressure between idcrs to the tension by which it is 



produced. 



RtsulL ^ r V ; where r t and r, are the given rail 



- whose \\ "Ablc along a smooth 



.< horizon at an angle a; another ring of 



alone a rod in the same vertical plane 



; and inclined at an angle a' to the horizon ; a 



Connects these rings passes through a thin I ring 



; shew that the system cannot be in equilibrium 



unless 



P tan a - F tan a -f ir (tan a - tan a ) - 0. 



