MECHANICS. 147 



APPENDIX. 



CONSTRUCTION OF ARCHES. 



. IF ABCD, DCEF, EFGH, &c. (Fig. 16.) 

 be a series of truncated wedges, resting on two 

 immoveable supports, and having the planes of the 

 faces that press against one another perpendicular 

 to a vertical plane, represented here by the plane 

 of the paper, they will be in equilibria, if their 

 weights be proportional to the differences of the 

 tangents of the angles which these planes make 

 with a vertical plane given in position. 



Thus if the weights be as the differences of the tan- 

 gents which AB, DC, EF, &c. make with the ver- 

 tical MN, the whole will remain in equilibria. This 

 follows from the properties of the wedge already 

 enumerated. PHONY, Architecture Hydraul. torn. I. 

 356. 



Truncated wedges disposed in this manner, form what 

 are called Arches in architecture ; and the most ad- 

 vantageous construction of them requires, that the 

 parts should be so adjusted as to be in equilibria, or 

 to balance one another by their weight only. An 

 arch, of which the parts balance one another in 

 this manner, is called an Arch of Equilibration. 

 K 2 Some 



