304 Mr. C. Fox on the Construction of Skew Arches. 
the stone being marked, we obtain all the lines of the soffit 
itself. 
It will now be quite evident that the beds may be obtained 
by making use of a square, one limb of which shall be made 
to the curvature of the soffit, and the other the radius of this 
curve; always taking care that this square is kept at right 
angles to the axis, as will be seen in figures 13, 14, and 15. 
The first few stones were wrought in this manner; but 
finding it very difficult to prevent the workman from getting 
his soffit a little on one side, by which means he wasted much 
of the stone on one bed and rendered the other deficient, 
I had recourse to a method which I will describe. Having 
provided two straight edges, the one parallel and the other 
containing the angle of the twist, (see fig. 16,) we proceeded 
to work one of the beds by chiselling two draughts along the 
stone, so that these straight edges being kept at a proper di- 
stance from each other were let into the stone until they were 
out of winding on their upper edges. 
Having finished one'bed by straight edges, we then ob- 
tained the soffits and other beds by means of the square be- 
fore mentioned. By working a bed first instead of the soffit, 
the best will always be made of a block of stone. 
As we have before seen that all the stones constituting a 
skew arch are portions of the same square threaded screw, 
the workman having finished one stone has only to repeat the 
same operations with every other. 
Any stone in the face of the arch, taken from one side, and 
applied to the corresponding one face to face, will continue 
the true spiral plane: this fact enabled us to work all the 
stones for one bridge in pairs; that is, one stone having been 
wrought with the proper twist, and of sufficient length to make 
. two stones, was accordingly sawn in two at the proper angle: 
but of course this cannot be done advantageously when the 
stone is of a very hard nature. 
It has been shown that by developing all the various sur- 
faces, instead of having to think of complicated spiral lines, 
they are at once reduced to straight ones; and I will now very 
briefly show how simply the data necessary for the construc- 
tion of a skew arch may be obtained (see fig. 17). 
Let A represent the curvature of the intrados, and C the 
extrados, B being a line midway between A and C. Let 
DD, EE, F F represent the boundaries of three cylinders of 
which A, B, C are the transverse sections; let these cylinders 
be cut by the straight line G, H, at the angle of askew, that 
is, the angle formed by the two roads crossing each other ; 
and from the points I, J, K, draw three straight lines at right 
