MECHANICS. 155 



Therefore, 

 hx x 



- x i + 



This determination of the thickness of the pier, 

 proceeds on a hypothesis usually employed for de- 

 termining the resistance of walls, &c. ; but which, 

 nevertheless, is not quite conformable to the fact. 

 The hypothesis is, that the pier AF, if the weight of 

 the arch were too great to be sustained, would fall, 

 by turning round the point F as a fulcrum. Now 

 this is not what would happen ; the part of the 

 abutment behind SM would be thrust out in the 

 horizontal direction, till the arch had room to fall ; 

 it is therefore against the masonry immediately be- 

 hind the part AM, and chiefly in a horizontal di- 

 rection, that the force is exerted. 



The resistance made by a wall, is, in this view of it, 

 analogous to the friction of a body resting on a 

 rugged surface, and has, no doubt, a given ratio to 

 the weight of the wall, and may perhaps be regard- 

 ed as equal to it. Thus the mass of building im- 

 mediately behind SM, should be of force sufficient 

 to resist the thrust KQ ; or, the section of that 



part of the pier should be greater than 



We give this, however, only as a limit, to which it 

 may be right to pay attention in the construction 

 of such works. 



The 



