2')2 MI8CELLAM \MPIJM. 



hinges 80 as to form a snuarr, two oppose m oon- 



nected by a string: this trnme-\\<. a ti.\rd point, 



horizontal; find the tension of the- string. 



Result. Twice the weight of a rod. 



38. Four equal and uniform heavy rods are conno< !'<! l>y 

 hinges; the system is suspended by a string attached to one 

 hinge, and the lowest hinge is in contact with a horizontal 

 plane; find the tension of tin- string and the pressure on the 

 plai 



Result. Each is twice the weight of a rod. 



39. A regular hexagon, compos. -d of six equal heavy nds 

 moveable about their angular points, is suspended from one 

 angle which is connected by threads with each of the opposite 

 angles. Shew that the tensions of the threads are as \ 

 Find also the strain along each rod. 



40. A regular hexagon is composed of six equal L 

 rods moveable about their angular points ; one rod is fixed in 

 .1 horizontal position, and the ends of this rod are conn 



by vertical strings with the ends of the lowest rod; h'nd the 

 tension of each string. 



Result. { W; where W is the weight of a rod. 



41. Suppose that in the preceding Example each end of 

 the fixed rod is connected with the more remote end of the 

 lowest rod, so that the strings instead of being parallel an- in- 

 clined at an angle of 60; find the tension of each string. 



Result. JFV3. 



42. A regular hexagon is composed of six equal 1. 

 rods moveable about their angular points, and two opposite 

 angles are connected by a horizontal strinir; "i>e nd is placed 

 on a horizontal plane, and a weight is placed at the middle 

 point of the highest rod ; find the tension of the string. 



Result. Let IT be the w.-i.^ht of ,-aeh rod, and W the 

 weight placed, on the highest rod ; then the tension is 



