\ M 1'LES. 



KXAMPLEa 



1. Four parallel forces act at the angles of a plan.- 

 rilatcral ajul an- inversely proportional to the segments 

 diagonals nearest t shew that the point of appli- 



of their resultant lies at the intersection of tin diagonals. 



Parallel forces act at the angles A, B, C of a Irian-le 

 aiul are respect i\ :-ti..nal to a, 6, c; shew that their 



resultant acts at the centre of the inscribed riivle. 



A cone whose vertical angle is 30, and wli<> 



[| II*. is placed with its vertex on a Smooth horizontal ]lane; 

 shew that it may be kept with its slant side in a v 

 position by a couple whose arm is equal to the length of the 



3 W 



slant side of the cone, and each force - . 



16 



4. Six equal forces act along the edges of a cube which 

 do not meet a given diagonal, taken in order; find their re- 

 sultant. 



Result. A couple, the moment of which is 2PaV3, v 

 P denotes each force and a the edge of the cube. 



5. A cube is acted on by four forces; one force is in a 

 diagonal, and the others in edges no two of which are in the 

 same plane and which do not meet the diagonal ; find the 

 condition that the forces may have a single resultant. 



Result. (XY+ YZ+ZX) V3 + P(-Y+ Y+Z) = o : where 

 X, y, Z denote the forces along the edges, and /' the force 

 along the diagonal 



6. If a triangle is suspended from a fixed point Ly string- 

 attached to the angles, the tension of each string is propor- 

 tional to its length. 



7. A uniform lieav 10 is supported in .1 horizontal 

 position by ti ngs attacned to the three sides 

 respectively; shew that there is an inf.nite number of ways 



