This section is from the book "A Treatise On Architecture And Building Construction Vol2: Masonry. Carpentry. Joinery", by The Colliery Engineer Co. Also available from Amazon: A Treatise On Architecture And Building Construction.
167. Dormer-windows, a term applied to windows projecting from the roof of a building, are framed out when the roof is constructed. The size and the shape of the openings left for them between the rafters, depend upon the size and the character of their roofs.
Where a dormer-window is covered with a small gable, the main roof is framed for it in the manner described in Art. 149, and where the covering is a flat pitch, somewhat like the lean-to roof in Fig. 44, the opening in the rafters is left rectangular, with a header and a pair of trimmers, as was described in Art. 110, except that the header and tail-beams are not usually mortised and tenoned into the timbers to which they are joined. The sides of dormers are studded and sheathed in the same manner as the outside walls of the house.
168. Sometimes these roof openings are very small, and introduced as much for ornament as for light or ventilation; this is particularly the case in the form known as the eyebrow window, shown in Fig. 71, in which (a) is its front elevation and (b) a sectional side elevation through the center of its roof. This elevation shows the curvature of each of the ribs b, c, d, etc. of the front elevation by the dotted lines b', d', e', etc.
The example shown in Fig. 71 is 9 feet in length from g to h; the line gh is the top line of the main rafters, as shown at g', while the line sr is the top line of the roof sheathing, shown at s'. The height jp is 2 feet and the curve of the front elevation of the roof sp r is formed with three arcs of circles, whose centers tt and k are located as follows: Prolong the center line pj, and with some point k as a center, describe the arc up v with such a radius that the points u and v, where this arc intersects the lines pr and p s, will fall below p less than half the distance pj. Then from k the center of the above arc, draw through the points u and v the lines k t, and the points t t where these lines intersect r t and s t, drawn perpendicular to s r, will be the centers for the arcs ur and v s, which complete the compound curve of the top of the window. All the curved parts of the elevation are described from these centers, the arcs above the lines k t being described from k as a center, and those falling below the lines k t being turned on t, t as centers. The ribs, or rafters a, b, c, d, and e, are now spaced off to stand about 9 inches on centers, and, as will be observed, the top and bottom edges will be beveled to conform more closely to the curved outline of the roof, except the middle rib a, which is, practically, rectangular in section.
In the section through the center of the window shown at (b), a', b', c', d', and e' are the ends of the ribs, shown at at a, b, c, d, and e in the front elevation (a), and the lines fa', f b' etc. are the tops of these ribs and the profiles of their curvatures. The rafter l' m' shows the pitch of the main roof, and the roof of the eyebrow window curves upwards towards it until it becomes tangent at f'. All the ribs a' f', b'f, c'f', etc. become tangent at /', and the bevel of their top and bottom sides, shown in the front elevation (a), gradually diminishes as they recede, until at f they are all rectangular in section. The curvature of the ribs, as shown by the dotted lines f'c', f d', etc., is determined by striking the curve of the uppermost rib with the arc of a circle, whose radius must be perpendicular to the rafter l' m' at f', and the distances g' e', g' d' g' c', etc. are laid off to correspond with o c, n d, in c, etc. in the front elevation. From each of the points e' d', c' etc. is then drawn the top line of the rib to f', varying the curvature in each successive rib to such a degree as will keep them the same relative distances below one another as at their starting points a' b' c', etc. The ribs are sawed out of 2-inch plank on lines developed as above described, and the shingle lath are bent over the curve and continued on the main roof without interruption, as the curved outline of the window removes all necessity of valleys, and, consequently, of flashing.
When the roof is shingled, the lines of the shingle butts are carried along over the eyebrow window, so that, in reality, it forms simply a protuberance of the main roof.
169. Windows of the same general character as the eyebrow window, are sometimes constructed with a flat, square roof, curving upwards slightly as it recedes towards the main roof, so that the side elevation and section are similar in shape to (b); but the ribs forming the roof construction are all alike and rest on a straight plate in front, while the sides are shingled, or sheathed, in the same manner as a dormer-window.