306 Mr MOSELEY, ON THE 



so as to satisfy the third condition ; and where, and in what direction 

 they must be applied. 



In the first place it will be observed, that by diminishing the force 

 P', its direction and point of application remaining the same, the line 

 of pressure is made continually to assume more nearly that direction 

 which it would have, if P' were entirely removed. 



Provided then, that if P were thus removed, the line of pressure 

 would cut the surface, that is, provided the force P' be necessary to 

 the equilibrium ; it follows that by diminishing it, we may vary the 

 direction and curvature of the line of pressure until we at length make 

 it touch some point or other in the surface of the mass. 



And this is the limit; for if the diminution be carried further, it 

 will cut the surface, and the equilibrium will be destroyed. It ap- 

 pears then that under the circumstances supposed, when P' acting at 

 a given point and in a given direction, is the least possible, the line 

 of pressure touches the surface of the mass. 



In the same manner it may be shewn, that when it is the greatest 

 possible, the line of pressure touches the surface of the mass. 



Now by varying the direction and point of application of P', as 

 well as its amount, this contact may be made to take place in infinite 

 variety of different points, and each such variety supplies a new value 

 of P', producing the required contact. Among these, therefore, it 

 remains to seek the absolute maximum and minimum values of that 

 force. 



To express these conditions analytically, let Xi, y^, z.^ represent the 

 co-ordinates of a point where the line of pressure touches the surface 

 of the body. 



Since the point x^, y^, & is common to the line of pressure and 

 to the surface of the body, 



.-. -^Xty^Xi = 0, Xi = F%o, y., = F^x^. 



