84 EQUIUHKir.M <-r A BQDT, 



'rst detenu in. vssure on the fixed point, and the 



othc T two are conditions which must be satisfied by the : 

 forces. 



If all the forces act in one plane passing through tin : 

 point, and we take this plane for that of (#, y), all the 1- 

 included in ^LZ vanish; also the ordinate parallel to ih< 

 of s of the point of application of each force is zero. Tims 

 L and M vanish; also Z vanishes, and the equations of equi- 

 librium reduce to 



the first two determine the pressure on the fixed point, and the 

 third is the only condition which the forces must satisfy. 

 Thus the forces will be in equilibrium if the sum of f/,- 



- of the forces with respect to the straight lim JH-/-JH tulicular 

 to their plane, and passing through the fixed point pant 

 and conversely, if the forces are in equilibrium tin- sum of the 

 moments of the forces with respect to this straight line will 

 vanish. 



87. To fnd the condition of equilibrium of a lotl*/ irhi>-h 

 has two point* in it fixed. 



Let the axis of z pass through the two fixed points; and 

 let the distances of the points from the origin In- .-_' and z'. 

 Also let A', F', /' be the resolved parts of the pressures 

 on one point, and A", 1'", Z" those on the other point. 



Then, as in Art. 86, the equations of equilibrium will be 



SZ-JT-JT-o, sr- r- r- = o, 



The first, second, fourth, and fifth of these equation will 



mine A", A", F, 7"; the third cquat' -\-Z", 



shewing that the pressures on the fixed points in the dir- 



of the line joining them are indeterminate. In 1114 connected 



;ie equation only. The last is the only condition of 



equilibrium, namely X=0. Thus the forces will be in r<jiii- 



111 if the sum of the moments of the forces with respect to 



the *' 'ne passing through the fixed points vanishes; and 



conversely, if the forces are in equilibrium the Hum of the 



moments of the forces with respect to this straight line will 



