AnrHUR.—Ün Skew Arches. 967 
contained between the face line and its position, if drawn at right angles to 
the abutment. Most writers give the complement of this, or B A D, as 
the angle of skew, but this does not appear appropriate; and Professor 
Rankine, I find, gives an angle of equal value to the one I have adopted. 
The spiral surfaces are the beds formed by the continuous courses of arch 
stones, or '*voussoirs,' which run from one face of the arch to the other. 
One such surface is shewn in Drawing No. 2, where cine is half of a 
hollow cylinder, and dy (as shaded) represents a spiral course, or a 
* coursing spiral," as it is called. It may be regarded as described by the 
revolution of radius yo through angle (y o l—d r p), simultaneously with its 
progression from the position dr to yo along the axis of the cylinder ro. 
The peculiar direction of the coursing spirals is necessary to bring these 
courses as nearly as possible at right angles to line of pressures. Beds 
running at right angles to these are.heading spirals, and in the actual arch 
are the end surfaces of arch stones, where these abut on one another. The 
best guidé to show the curious lines, angles, and surfaces which result from 
a bridge being built on the skew principle, is a model ; this simplifies many 
difficulties. 
Stability. 
It is not properly within the scope of this paper to go into the 
equilibrium of arches. But besides what I have unavoidably stated, that 
the coursing spirals should be at right angles to the line of pressures, I may 
add that the general principles of stability are the same as in ordinary 
arches, the chief one of which Ishallonly mention. Taking half the arch— 
of the spandril wall above it, with its load, acting | 
vertically through the centre of gravity of the mass, Ei 
and be supported by two pressures, one upward and B 
inclined from the abutment (see Fig. 1) and the $i 
other horizontal, passing through the keystone; these b/s 
pressures should intersect each other in the line of | 
gravity of the mass. It is not usual, unless arches 
are of great span, to investigate by actual calcula- 
tion the line of pressures; the ordinary formule in use are sufficient for 
determining the thickness of abutments and arch ring. 
Design. 
Fig. 1. 
In designing a skew arch a ground plan 4 B C D, as shown in drawing 
No. 2, is prepared provisionally from measurements made at the site of the 
bridge. Afterwards, as will appear, it may have to be slightly altered 
before finally fixing its dimensions. 
