This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
In Fig. 168 is shown a very simple form of what is known as a valley roof. It is a combination of two simple pitch roofs which intersect each other at right angles. In the figure both ridges are shown at the same height, but they are not always built in this way. Either ridge may rise above the other, and the two roofs may have the same pitch or different pitches. If the ridge of the secondary roof rises above the ridge of the main roof, the end which projects above the main ridge is usually finished with a small gable a, or a small hip b, as shown in Fig. 1G9. This arrangement does not make a pleasing appearance, however, and should be avoided if possible. Almost all roofs are hip and valley roofs, as it is very seldom that a building of any considerable size can be covered with a simple roof of any of the forms described above. There Inner Court are usually wings or projecting portions of some kind which must be covered with a separate roof which must be joined to the main body of the roof with valleys, and it is these valleys which are the cause of most of the leaky roofs, as a large quantity of water collects in them and it is no easy matter to make them waterproof.
Fig. 16S. Valley Roof.
Fig. 1C9. Hip and Valley Roof Showing Different Roof Levels Around.