300 Mr.C. Fox on the Construction of Skew Arches. 
individual stones composing the arch; hence the whole thrust 
of ordinary arches, which is brought in upon the abutments, 
is exerted in the direction of the bridge itself, z. e. of the road 
passing over it. 
To devise some simple mode of setting out and working the 
courses of stone in a skew arch, so as to bring in the thrust 
in the proper direction, was the great object to be obtained. 
All practical men are aware of the vast difference between 
having to deal with straight and with twisted Jines; and the 
necessity of introducing twisted lines in the construction of 
skew bridges will soon be seen. 
In skew bridges, in order to keep the thrust in the proper 
direction, it is necessary to place the courses of stones at an 
angle with the abutment, whereby each stone loses its paral- 
lelism with the surface of the road, and is therefore laid on 
an inclining bed. 
In a common semicircular arch each course of stones is 
parallel with the axis of the bridge, and all the beds are 
wrought so as to point to the axis: the inclination of the stones 
varies in every course; but although the inclination of the 
stones varies in every course, both ends of the course have 
the same inclination, both ends are equally high in the arch, 
and both ends point to the centre. This is the case in the 
ordinary bridge; but in a skew bridge, as the courses run 
obliquely across the arch, one end of the course is necessarily 
higher up the arch than the other, and therefore would no 
longer point to the centre; but only make this point to the 
centre, and we immediately get the twisted form, that is, we 
make each bed of the courses of stones a true spiral plane. 
The principle which I have adopted is, to work the stones 
in the form of a spiral quadrilateral solid, wrapped round a 
cylinder, or in plainer language the principle of a square 
threaded screw; hence it becomes quite evident that the trans- 
verse sections of all these spiral stones are the same throughout 
the whole arch. It will be obvious that the beds of the stones 
should be worked into true spiral planes; but I am not aware 
that any rule has yet been published that would enable the 
stones to be wrought at the quarry into the desired form, or of 
any rule by which the true angle at which the courses cross the 
axis of the bridge is determined. Tig. 3. is a representation of 
the courses of the stones, each alternate course being omitted 
in order to show their form more distinctly; and the course 
forming the key-stone is carried out so as to show that it 
really is the thread of a square threaded screw wound round 
a cylinder, the cylinder being indicated by the two dotted 
lines. If the threads are cut at right angles to the cylinder, 
