MISi'KLLANEOUB THEOREMS. 



ippose that a string i- :m under 



the a ii varies as the distance. 



iistance of any point from the centre of force; 

 -ordinatcs of the p<> axes having the 



as orii force on an 



i iii-- In. -tii ia Be and maas mos aitnaled at the 

 n this force can be resolved into 

 * and /lywot parallel to the axes of x and y respectively. 

 ce the components, parallel to the axes of x and y, of 

 the n force on any of the tt 



ids and pfymds respectively 



ti'inlin:; OW i " : t iom MMnMA N--w it .r an-i y IN- \\\t> 



co-ordinates of tlic centre of gravity of the portion, we have 



- 



ice we obtain the following theorem : The itrmght lint 

 wkwi* <*ntr< f any portion of tie * 



central force en the portion. 



tec combining this theorem with that obi 

 we ot i; property ot xible string v 



is in equilibrium ic action of a central force v:r. 



stance : The centre of gravity of any portion lies on 

 tie *' '* the centre of force with the point 



of the tangent* at the extremities of the portion. 

 we see t property here enunciated will 



hold :i form string in the form of the curve 



t* are connected by a string which 



al cylinder in a plane perpendicular to 

 the a red to determine the resultant of the 



; and the cylinder in the 

 state bordering on motion. 



mcnt la of the string may be 

 \i. andtl. '-y/o*: 



f*an a constant ratio to the normal 

 action, and the directions of the two force* are at right angles. 



