EXAMPLES. 



'iain be fixed at t\v.. points. . 



.nuinl' liberty t.> m..\v along 



smooth horizontal the same vertical plane, prove that 



tin- loops AB, BC, Cl>. ... will form them itO curves 



which will all be arcs of the same c 



6. Three links of a chain . 1. //. and C are move-able 

 freely aloi \ horizontal straight linos in the same 



il plane. If when J and C are pulled a irt as 



possible, their horizontal distances from B are equal, shew 

 that this will always be the case when they arc held in 

 any other position. 



7. A chain hangs in equilibrium over two smooth j 

 which are in a horizontal straight line and at a ^iven distance 

 apart; find the least length of the chain that equilibrium inay 

 be possible. 



Result. The least length is lie, where h is the given dis- 

 tance. 



8. Prove that the exertion necessary to hold a kite 

 diminishes as the kite rises higher, the force of the wind 

 being independent of the height, and th ire of tin; 

 wind on the string being neglected. 



9. A uniform heavy string rests on an arc of a smooth 

 whose plane is vertical, shew that the ten-ion at any 



point is proportional to its vertical height above the lowest 

 point of the string. If the string rests on a parabola whose 

 axis is vertical, determine the vertical distance of its ends 

 below the highest point so that the pressure at this point 

 may be equal to twice the weight of a unit of length of the 

 string. 



Result. The vertical distance is equal to half the lutus 

 rectum of the parabola, 



10. One end of a uniform heavy chain han over 

 the edge of a smooth table, and the other end passing 



pully reaches to the same distance below the table as 

 the pully is above it. Supposing half the chain to l>e on the 

 table in the position of equilibrium, compare its whole length 

 with lit ot' the pully. 



Result. The length is to the height as 6 4- 2 V3 is to 1. 



