Some Properties of a Rampant Arch. 303 



in it of rather smaller size. This valve is acted upon by a cord C 

 D Q, fastened to the projection at C, passing through a hole in D and 

 fastened to the end of the limb Q which is at right angles to the 

 valve. By drawing down the lower disk to a certain distance it is 

 evident the action of the cord will open the valve and the length of 

 the cord may be so adjusted as to cause this to happen in various po- 

 sitions of the disk and to occur always before the liquid arrives at the 

 lower end of the syphon. 



In the rude sketch I send you, the exhausting apparatus is much 

 larger than necessary. It would answer for a syphon four times as 

 large as that in the figure. 



Art. XV. — Some properties of a Rampant Arch ; by Thomas 

 Gorton, Civil Engineer. 



TO PROFESSOR SILLIMAN. 



Sir — Having had occasion of late to make the necessary calcula- 

 tions for describing what is sometimes called a rampant arch, it being 

 formed by the intersection of a parapet wall with an oblique descen- 

 ding culvert, I reduced these calculations to a problem which will 

 admit of a general application to arches of this description : and 

 thinking it might be of some service to Architects and Engineers, it 

 is herewith submitted for publication in your Journal. 



Suppose a plane to cut a semi-circular vault in such a manner as 

 to make an acute angle \vith a plane passing through the axis and 

 crown of the vault, and also with the springing plane of the same. 

 It is required to find the length and positions of the transverse and 

 s^mi-conjugate diameters of the semi-ellipse thus formed by the in- 

 tersection of the vault and cutting plane. 



Let the acute angle formed by the axis of the vault and the inter- 

 secting line of the axal and cutting planes be put = A ; and the 

 acute angle formed by the axis and the intersecting line of the 

 springing and cutting planes be put =B ; also put the radius of the 

 vault =r. 



