390 On the different Theories of Arches y Vaults^ (^c. 



the circle is inapplicable ; and that some other curve should 

 be adopted ; but the simplicity in the construction and 

 ancient practice have decided otherwise, and the semicircu- 

 lar arch has been generally sustained on vertical piers, where 

 an arch of greater altitude niii^ht have been adc-pted. 



By the theory elicited from an examination ot the arch, 

 it would follow, that if the vaussoir at the springing, lying 

 on a horizontal bed, must he iuilnite, in like manner the 

 pier on which it is sustained must be intiniie also; because 

 it canbcconsidered only as another vaussoir, or an additional 

 succession of vaussoirs : we may conceive the second vaus- 

 soir o\ an arch to be an abutment to the first, as the third is 

 to the second ; the hauce [query haunch] is as much an 

 abutment to the crown as the pier is to it. The abutment 

 or arch cannot be said to begin anywhere; it apjjcars there- 

 fore necessary, that the same theory should have cognisance 

 over the whole, and that v\hatever theory may be applicable 

 to the one, must also apply to the other: this mode of 

 considering the suViject, again confirms the propriety of 

 adopting jiracticallv, what has appeared a natural conse- 

 quence from tlie consideration of the properties of curves 

 used in arcuaiion. It is manifest, that an arcli may assume 

 externally any appearance, and exhibit on its face a semi- 

 circular arch ami abutment piers, and yet have internally 

 the properties and proportions of another curve, which may 

 be enclosed in that form. Admitting this, the theory of 

 abutment piers does not in any wise differ from that of 

 arches; for if an arch of eqiulibration be enclosed in an 

 ?irch of the same thickness at the vertex, and its abutment- 

 pier, it necessarily follows that they must stand ; if the 

 additional filling up, to produce the desired effect, does not 

 alter that equilibration : indeed, the angle at which friction 

 retains stone on an inclined plane would determine that 

 in all common cases; and though the direction of the joints 

 of the vaussoirs nmst be assutTied, in the investigation, at 

 right angles to the intrados of the enclosed arch, yet they 

 need not be so in practice, but have that relation to the vi- 

 sible arch. 



This principle of interpreting an arch standing on a 

 pier, into an arch of greater altitude, whatever theory of 

 equilibration of arches may be adopted, seems to offer a 

 mean of ascrrtaining the correctness of any different theory 

 that may be adopted for the piers, when considered sepa- 

 rate bodies, the enclosed arch being of the same curvature 

 at the vertex, and nearest approaching to the given arch 

 and pier. On the cpntrary, the theory of abutment piers 



has 



